Quasi-Mechanistic Analyses of Impact of Vibrational Dynamic Loading on Characteristics of Clayey and Gravelly Geomaterials

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Quasi-Mechanistic Analyses of Impact of Vibrational Dynamic Loading on Characteristics of Clayey and Gravelly Geomaterials

John Ngaya Mukabi

R&D/Design Dept.

Kensetsu Kaihatsu Consulting Engineers Ltd.

Nairobi, Kenya

Abstract A desirably realistic modelling and simulation approach for pavement and related geo-structures is to effectively replicate the effects of vibrational dynamic loading (VDL), which is the prevalent mode of loading on practically all live load- imposed structures. In this Study, an innovative comprehensive testing regime was designed to simulate the vibrational dynamic loading commonly experienced during in-service of highway and airport pavements. Based on experimental test results simulating a variety of testing and loading conditions adopted for varying geomaterials, sophisticated analytical models, introduced in this paper, were developed. The validity, lucidity and rationality of the proposed TACH-MD VDL analytical models is pragmatically demonstrated through comparison with experimental testing results. Effective application of these models in the design of highway and airport pavements is ascertained based on tabulated results, graphical plots and analytical discussions. It is rationally derived that the proposed TACH-MD VDL analytical models can be effectively applied for natural and hydraulically stabilized clayey and gravelly geomaterials as well as unbound and bound crushed stone aggregates.

Keywords Vibrational dynamic loading, VDL, analysis, analytical models, quasi-mechanistic, clayey, gravelly, geomaterial.

  1. INTRODUCTION

    The application of effective quasi-empirical and analytical models that can facilitate for the precise analysis and structural evaluation of the effects of vibrational dynamic loading is indeed one of the most fundamental prerequisites in pavement engineering. In this Study, TACH-MD VDL analytical models that can simulate and account for the effects of vibrational dynamic loading commonly experienced during in-service of highway and airport pavements, are introduced as part of essential design tools [1].

    Furthermore, consideration of the fact that some pavements will certainly not be subjected to high intensity dynamic loading, it is imperative that a more realistic approach based on a multi-stage loading regime that takes into account a rebound effect due to post-dynamic-static loading stress release, has been made accordingly. Consequently, a number of tests under sustained dynamic loading to simulate critical state conditions and consideration of future increase in load intensity were performed for this sake [1]. It is important to note that the Airports that can be appropriately characterized with due reference to the sustained dynamic loading model are the likes of Heathrow and JF Kennedy which have landings and take- offs every other minute [1]. Based on the foregoing considerations therefore, several modes of loading including sustained and multi-stage loadings were meticulously designed

    and carried out on specimens that represent typical pavement and subgrade materials as well as structural layer configurations in due consideration of the intensity and direction of the impacted stresses [1]. The reliability and effectiveness of applying the proposed models is explicitly manifested in this paper whereby explicable discussions are made in retrospect to the pragmatic pavement structural design of aerodromes in Kenya and Somalia.

  2. CORE TACH-MD MODELS FOR DERIVING SHEAR AND MAXIMUM IMPACT STRESSES

    Rutting is one of the most important load-induced distresses frequently encountered in flexible asphalt pavements. The primary mechanism of rutting is associated with shear deformation rather than densification. Clearly therefore, shear stress is one of the critical factors affecting pavements performance, hence the serious need to fully comprehend its characteristics in asphalt pavements. Accordingly, therefore, it is imperative to comprehend the loading and stress induction characteristics. However, most conventional pavement design methodologies assume that tyre pavement contact stress is equivalent to tyre inflation pressure and is uniformly distributed over a circular contact area, a theory which fairly contradicts the actuality. In this Study, analyses of the mode of loading, load impact/intensity and loading characteristics are fastidiously carried out by employing the TACH-MD models presented in Equations 1 ~ 6. Equation 1 defines the correlations between shear stress, load intensity, and

    pavement thickness, ; whilst Equation 2 expresses the same

    for tyre pressure, instead of load intensity, . The relation between the maximum shear stress, . and maximum tyre pressure, , is delineated in Equation 3, while the location of the maximum shear stress, , is defined in Equation 4. On the other hand, Equations 5 and 6 are adopted in computing the maximum impact and contact stresses for simulating aircraft landing impact and vehicular contact stresses, respectively.

    = [15.78() + 24.964]2 [2.1299() 3.648] + 0.0786() 0.092 () (1)

    = [5.8792 7.7879 15.769 ]2 + [1.7817(0.7443)] + 0.094() +

    0.2111 () (2)

    . = 6 × 1082 , + 0.0001, +

    Vertical Stress Distribution within the Baraawe Airport Runway Pavement and Subsurface Depth of Influence for Varying Design Contact Stresses

    0.1454 (),

    (3)

    Required Design Vertical Stress Capacity, v (MPa)

    0 0.5 1 1.5 2 2.5 3

    0

    , = 16.19(.) + 89.674 () (4)

    = 0.01132 14.835 + 6065.2 () (5)

    200

    Depth of Influence (Thickness), DI (mm)

    Depth of Influence (Thickness), DI (mm)

    400

    600

    Near Subsurface Ground Depth Investigated

    Range for Near Future Design Consideration

    & Structural Performance Evaluation

    = 0.0075712 9.93945

    + 4063.684 () (6)

    800

    1000

    Boundary Limit For Structural Subgrade

    Examples of the analytical results generated employing

    Equations 2, 5 and 6 are provided graphically in Figures 1 ~ 3. Figure 1 depicts the shear stress profile within the upper pavement layers indicating the location and profile of the maximum shear stress.

    Shear Stress – Tyre Pressure – Pavement Layer Thickness Relations

    1200

    1400

    1600

    1800

    2000

    DCS: Design Contact Stress in MPa; DCS = 1.250 MPa (1250 kPa)

    DCS=1.25 DCS=1.5 DCS=2 DCS=2.6

    Resulting Shear Stress, (MPa)

    0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

    Itp:

    Infl (Hi

    ated ghe

    Tyr r Va

    e P lue

    ress s fo

    ure r Air

    in k cra

    Pa ft

    & Si

    mu

    lati

    on)

    td/>

    Pr

    ofil Sh

    e of ear

    Ma Str

    xim ess

    um

    AC

    La

    yers

    BC

    =

    .

    .

    .

    +

    .

    .

    +

    .

    +

    .

    Itp:

    Infl (Hi

    ated ghe

    Tyr r Va

    e P lue

    ress s fo

    ure r Air

    in k cra

    Pa ft

    & Si

    mu

    lati

    on)

    Pr

    ofil Sh

    e of ear

    Ma Str

    xim ess

    um

    AC

    La

    yers

    BC

    =

    .

    .

    .

    +

    .

    .

    +

    .

    +

    .

    0

    Pavement Layer Thickness, tP (mm)

    Pavement Layer Thickness, tP (mm)

    25

    50

    75

    Fig. 2. Vertical stress distribution for varying pavement and subgrade layers.

    Vertical Strain Distribution within the Baraawe Airport Runway Pavement and Subsurface Depth of Influence for Varying Design Contact Stress

    Required Design Vertical Elastic/Resilient Strain Limit, [v]ELS (%) 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007

    0

    200

    100

    125

    150

    175

    200

    225

    Itp=200 Itp=300 Itp=400 Itp=460 Itp=500 Itp=600 Itp=700 Itp=810 Itp=900 Itp=1000 Itp=1050 Itp=1100 Itp=1200 Itp=1500 Itp=2000 Itp=2500 Itp=3000

    Fig. 1. Shear stress profile within the upper pavement layers.

    400

    PDepth of Influence (Thickness), DI (mm)

    PDepth of Influence (Thickness), DI (mm)

    600

    800

    1000

    1200

    1400

    1600

    1800

    2000

    Range for Near Future Design Consideration

    & Structural Performance Evaluation

    DCS: Design Contact Stress in MPa; DCS = 1.250 MPa (1250 kPa)

    Line of Initial Convergence

    @ DI = 100mm

    On the other hand, the influence of the magnitude of the tyre pressure and the initial impact stress on the stress and strain distributions and the resulting profile at varying depths is demonstrated in Figures 2 and 3, respectively. The following derivations can be made from these figures: i) the magnitude and characteristic profiles of the shear stress, vertical stress and vertical strain are dependent upon the contact tyre pressure; ii) the maximum shear stress occurs at approximately 0.5, where

    represents the upper pavement thickness; the shear and vertical stress distribution profiles are distinctly different; iii) the magnitude of the impact elastic strain decreases with increased contact stress; and iv) on the contrary, the secant elastic strain limit increases with increased design/impact stress, which is in agreement with the concepts of dynamic loading effects on limiting elastic strain and KHSSS (kinematic hardening soil small strain) models ([2],[3], [4], [5] [6], [7]).

    DCS=1.25 DCS=1.5 DCS=2 DCS=2.6

    Fig. 3. Vertical strain distribution for varying pavement and subgrade layers.

  3. VALIDATION OF THE QUASI-MECHANISTIC TACH-MD VDL ANALYTICAL MODELS PROPOSED/ADOPTED

    1. TACH-MD VDL models for determining progressive deformation

      The importance of developing reliable models for characterizing the progressive deformation of foundation ground, pavements and other geo-structures, cannot be overemphasized. The quasi-mechanistic TACH-MD VDL (vibrational dynamic loading) analytical models proposed/adopted in this Study are introduced hereafter. Characterization of progressive vertical (axial) and lateral (horizontal) deformation under sustained vibrational dynamic loading ([1], [6], [8],[9]) is achieved through the application of the models defined in Equations 7 ~ 14.

      = [0.0279(0.0937)] × () 0.5045(0.057) (7)

      . = {[0.0279(0.0937)] × () 0.5045(0.057)} × [0.864 0.063(0)] (8)

      0

      0

      . = 0.000177782 0.16540 + 37.726 35% 0 400 (9)

      . = (0.0735) (10)

      1. Cumulative Dynamic Stress Strain PI Universal Model for Clayey Geomaterials

        = 1 × 10149.0922 + 1.63 × 1095.003 +

        0 0

        0.33082 22.35 + 318.05 () (22)

        0

        0

        .

        0

        0

        . = 13.60544

        (11)

        Consequently;

      2. Cumulative Dynamic Stress Cumulative Loading Cycles PI Universal Model for Clayey Geomaterials

        = [0.0279(0.09370.000177782 0.16540 +

        = (0.33082 22.35 + 318.05)( )

        0

        ,

        37.726 )] × ()

        6.17882 + 231.55 2315.3 () (23)

        0.5045(0.0570.000177782 0.1654 + 37.726 )

        0 0

        (12)

      3. Cumulative Dynamic Stress Cumulative Loading Cycles PI Universal Model for Gravelly Geomaterials

        0

        0

        = {0.0279(1.6658 × 1052 0.01550 +

        3.53493 )} × () 0.5045{4.43346 × 1052

        = 1 {

        = 1097.81.612} ×

        0

        3 }

        =1

        and,

        9.4278 × 10

        0 + 2.50382

        .

        (13)

        [0.0279(0.0937)] × ()

        { 0.5045(0.057) }

        100 (24)

        = {0.0279 [1.27483 (

        0

        0

        0

        )]} × ()

        .

        = 1 {

        = 1097.81.612} ×

        0

        0

        0.5045 [0.77551 (

        )] (14)

        p>=1

    2. Other TACH-MD VDL models adopted

      0

      0

      [0.0279(0.0937)] × ()

      { 0.5045(0.057) }

      100 (25)

      Other quasi-mechanistic TACH-MD VDL analytical models proposed/adopted in this paper are defined in Equations 15 ~ 25.

      1. Secant Dynamic Stress – Cumulative Load Cycles – PI Model for Clayey Geomaterials

        = [0.06042 + 1.2562 + 43.922] ×

        (2×1052+0.0008+0.1208)

    3. Validation of the TACH-MD models

      The data that partially validates the TACH-MD models adopted in the characterization, modelling and simulation of vibrational dynamic loading is summarized in Table I.

      Loading Time

      Measured Values

      Predicted Values

      S/N

      (Hrs.)

      (mins.)

      Loading Cycles (No.)

      Neat BCS

      BCS +

      2% Lime

      BCS +

      Con Aid

      + 2%

      Lime

      BCS +

      5% Lime

      Neat BCS

      BCS +

      2% Lime

      BCS +

      Con Aid

      + 2%

      Lime

      BCS +

      5% Lime

      Loading Sequence

      Vertical Deformation, a (%)

      1

      0.017

      1

      2800

      1.15

      0.43

      0.12

      0.1

      1.315

      0.429

      0.564

      -0.086

      2

      0.033

      2

      5600

      1.703

      0.672

      0.831

      0.053

      3

      0.050

      3

      8400

      1.929

      0.814

      0.986

      0.134

      4

      0.067

      4

      11200

      2.22

      1.21

      0.87

      0.23

      2.090

      0.914

      1.097

      0.191

      5

      0.083

      5

      14000

      2.215

      0.992

      1.183

      0.236

      6

      0.167

      10

      28000

      2.603

      1.235

      1.450

      0.374

      7

      0.250

      15

      42000

      3.16

      1.28

      1.26

      0.27

      2.830

      1.377

      1.605

      0.455

      8

      0.333

      20

      56000

      2.991

      1.478

      1.716

      0.512

      9

      0.417

      25

      70000

      3.116

      1.556

      1.802

      0.557

      10

      0.500

      30

      84000

      3.28

      1.22

      1.59

      0.506

      3.218

      1.620

      1.872

      0.593

      11

      0.667

      40

      112000

      3.505

      1.25

      1.78

      0.67

      3.379

      1.721

      1.983

      0.651

      12

      0.833

      50

      140000

      3.503

      1.799

      2.069

      0.695

      13

      1.000

      60

      168000

      3.605

      1.863

      2.139

      0.732

      14

      1.167

      70

      196000

      3.692

      1.917

      2.198

      0.762

      15

      1.333

      80

      224000

      3.766

      1.963

      2.249

      0.789

      16

      1.5

      90

      252000

      3.832

      2.005

      2.295

      0.813

      17

      2.0

      120

      336000

      3.83

      1.66

      2.29

      0.69

      3.993

      2.105

      2.405

      0.870

      18

      2.3

      137

      384000

      5.33

      2.152

      2.457

      0.897

      19

      3.0

      180

      504000

      Neat BCS Failed After 0.364 Cycles

      2.01

      2.58

      0.82

      2.247

      2.561

      0.951

      20

      4.0

      240

      672000

      2.16

      2.57

      0.86

      2.348

      2.672

      1.008

      21

      5.0

      300

      840000

      2.28

      2.76

      1.37

      2.426

      2.758

      1.053

      22

      6.0

      360

      1008000

      2.39

      2.78

      1.41

      2.490

      2.828

      1.089

      23

      7.0

      420

      1176000

      Testing Terminated after 1Million Cycles

      2.544

      2.887

      1.120

      23

      19.0

      1,140

      3192000

      2.894

      3.271

      1.319

      24

      59.5

      3571

      9998800

      3.294

      3.710

      1.547

      Loading Time

      Measured Values

      Predicted Values

      S/N

      (Hrs.)

      (mins.)

      Loading Cycles (No.)

      Neat BCS

      BCS +

      2% Lime

      BCS +

      Con Aid

      + 2%

      Lime

      BCS +

      5% Lime

      Neat BCS

      BCS +

      2% Lime

      BCS +

      Con Aid

      + 2%

      Lime

      BCS +

      5% Lime

      Loading Sequence

      Vertical Deformation, a (%)

      1

      0.017

      1

      2800

      1.15

      0.43

      0.12

      0.1

      1.315

      0.429

      0.564

      -0.086

      2

      0.033

      2

      5600

      1.703

      0.672

      0.831

      0.053

      3

      0.050

      3

      8400

      1.929

      0.814

      0.986

      0.134

      4

      0.067

      4

      11200

      2.22

      1.21

      0.87

      0.23

      2.090

      0.914

      1.097

      0.191

      5

      0.083

      5

      14000

      2.215

      0.992

      1.183

      0.236

      6

      0.167

      10

      28000

      2.603

      1.235

      1.450

      0.374

      7

      0.250

      15

      42000

      3.16

      1.28

      1.26

      0.27

      2.830

      1.377

      1.605

      0.455

      8

      0.333

      20

      56000

      2.991

      1.478

      1.716

      0.512

      9

      0.417

      25

      70000

      3.116

      1.556

      1.802

      0.557

      10

      0.500

      30

      84000

      3.28

      1.22

      1.59

      0.506

      3.218

      1.620

      1.872

      0.593

      11

      0.667

      40

      112000

      3.505

      1.25

      1.78

      0.67

      3.379

      1.721

      1.983

      0.651

      12

      0.833

      50

      140000

      3.503

      1.799

      2.069

      0.695

      13

      1.000

      60

      168000

      3.605

      1.863

      2.139

      0.732

      14

      1.167

      70

      196000

      3.692

      1.917

      2.198

      0.762

      15

      1.333

      80

      224000

      3.766

      1.963

      2.249

      0.789

      16

      1.5

      90

      252000

      3.832

      2.005

      2.295

      0.813

      17

      2.0

      120

      336000

      3.83

      1.66

      2.29

      0.69

      3.993

      2.105

      2.405

      0.870

      18

      2.3

      137

      384000

      5.33

      2.152

      2.457

      0.897

      19

      3.0

      180

      504000

      Neat BCS Failed After 0.364 Cycles

      2.01

      2.58

      0.82

      2.247

      2.561

      0.951

      20

      4.0

      240

      672000

      2.16

      2.57

      0.86

      2.348

      2.672

      1.008

      21

      5.0

      300

      840000

      2.28

      2.76

      1.37

      2.426

      2.758

      1.053

      22

      6.0

      360

      1008000

      2.39

      2.78

      1.41

      2.490

      2.828

      1.089

      23

      7.0

      420

      1176000

      Testing Terminated after 1Million Cycles

      2.544

      2.887

      1.120

      23

      19.0

      1,140

      3192000

      2.894

      3.271

      1.319

      24

      59.5

      3571

      9998800

      3.294

      3.710

      1.547

      TABLE I. SUMMARY OF DATA COMPARING MEASURED AND MODELLED DYNAMIC LOADING RESULTS.

      0.612

      (15)

      = 10.978 () (16)

      = 1097.81.612 () (17)

      1. Secant Dynamic Static Stress Correlations for Clayey Geomaterials

        [] = 8.1720.7838 () (18)

      2. Secant Dynamic Static Stress Model for Gravely Geomaterials

        [] = 12.060.6304 () (19)

      3. Secant Dynamic Stress PI Model for Clayey Geomaterials

        [ ] = 2321542.14 () (20)

      4. Secant Dynamic Stress PI Model for Gravely Geomaterials

        [] = 75.660.896 () (21)

        On the other hand, the graphical depictions of the results tabulated in Table I are plotted in Figures 4 and 5 in both

        Comparison of Impact of Vibrational Dynamic Loading on Resulting Modulus of Deformation of

        Clayey Geomaterials Including Measured vs. Predicted Characteristic Curves for BCS

        Comparison of Impact of Vibrational Dynamic Loading on Resulting Modulus of Deformation of

        Clayey Geomaterials Including Measured vs. Predicted Characteristic Curves for BCS

        3000

        3000

        = . .

        = . .

        2500

        250

        2000

        2000

        Modlus of Deformation, ED (kPa)

        Modlus of Deformation, ED (kPa)

        arithmetic and semi-log scales, respectively. The tabulated data and graphical figures also make a comparison between measured and modelled results. It can be can be noted that, in all cases, an appreciable fitting of the characteristic curves is achieved for the varying natural and stabilized black cotton soils from the Lake Victoria Region of Western Kenya.

        1500

        1500

        Comparison of Measured vs. Predicted Deformation of Neat & Stabilized Black Cotton Soil

        1000

        1000

        6

        = . . × . .

        500

        500

        5

        0

        1000

        0

        1000

        Neat BCS

        10000

        10000

        100000

        100000

        1000000

        1000000

        Axial Strain, a (%)

        Axial Strain, a (%)

        4 Failed @

        Nvd=384000

        Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

        Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

        Cycles

        3

        Neat BCS: Measured

        Neat BCS: Predicted

        Afmadow Silty Clay

        Neat BCS: Measured

        Neat BCS: Predicted

        Afmadow Silty Clay

        2

        1

        0

        0 200000 400000 600000 800000 1000000

        Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

        Neat BCS: Measured Neat BCS: Predicted BCS+2% Lime: Measured BCS+2% Lime: Predicted BCS+Con Aid+2% Lime: Measured BCS+Con Aid+2% Lime: Predicted BCS+5% Lime: Measured BCS+5% Lime: Predicted

        Fig. 4. Comparison of measured and modelled deformation results under dynamic loading (arithmetic scale).

        Comparison of Measured vs. Predicted Deformation of Neat & Stabilized Black Cotton Soil

        Fig. 7. Comparison of measured and modelled results for impact of dynamic loading on modulus of deformation [ = 1].

        All the depicted graphs also include a comparison of measured and predicted results. It can be observed that, in conformity with their magnitude of initial stiffness, the Baraawe silty clay has the highest resistance to deformation, whilst the BCS registers the lowest. Measured vs. predicted BCS results show quasi-perfect superimposition.

        Further validation of the TACH-MD VDL models is udertaken throughout this paper by comparing measured and

        6

        = . . × . .

        5

        Axial Strain, a (%)

        Axial Strain, a (%)

        4

        3

        2

        1

        0

        Neat BCS

        Failed @ Nvd=384000

        Cycles

        geo-mathematically modelled results.

  4. PRINCIPAL RESULTS ADOPTED FOR VDL ANALYSES

      1. Example of parametric principal design parameters adopted for VDL analyses

        Table II presents a summary of the principal design

        parameters adopted for dynamic loading analysis undertaken for Bardhere and Diinsoor gravels sampled from Somalia.

        1000 10000 100000 1000000

        Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

        Neat BCS: Measured Neat BCS: Predicted BCS+2% Lime: Measured BCS+2% Lime: Predicted BCS+Con Aid+2% Lime: Measured BCS+Con Aid+2% Lime: Predicted BCS+5% Lime: Measured BCS+5% Lime: Predicted

        Fig. 5. Comparison of measured and modelled deformation results under dynamic loading (semi-log scale).

        20000

        20000

        15000

        15000

        Modlus of Deformation, ED (kPa)

        Modlus of Deformation, ED (kPa)

        Characteristics of the modulus of deformation of natural black cotton soil, Afmadow and Baraawe silty clays (Somalia) are graphically depicted in Figures 6 and 7 for loadings up to 10 million and 1 million cycles, respectively.

        30000

        Comparison of Impact of Vibrational Dynamic Loading on Resulting Modulus of Deformation of

        Clayey Geomaterials Including Measured vs. Predicted Characteristic Curves for BCS

        30000

        Comparison of Impact of Vibrational Dynamic Loading on Resulting Modulus of Deformation of

        Clayey Geomaterials Including Measured vs. Predicted Characteristic Curves for BCS

        = . .

        = . .

        25000

        25000

        0

        1000

        10000

        100000

        1000000

        0

        1000

        10000

        100000

        1000000

        Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

        Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

        Neat BCS: Measured

        Neat BCS: Predicted

        Baraawe Silty Clay

        Afmadow Silty Clay

        Neat BCS: Measured

        Neat BCS: Predicted

        Baraawe Silty Clay

        Afmadow Silty Clay

        10000

        10000

        5000

        5000

        Fig. 6. Comparison of measured and modelled results for impact of dynamic

        Summary of Principal Parameters Adopted for Dynamic Loading Analysis

        Construction Stage

        Pre-Construction

        Post-Construction

        Parametric Description

        Afmadow

        Hudur

        Bardhere

        Diinsoor

        Gravel Wearing Course (GCW) Bearing Capacity, CBR ( %)

        45

        20

        32

        14

        Equivalent Base Course (EBC) Bearing Capacity, CBR ( %)

        To Be Deterined During Design Stage

        To Be Deterined During Design Stage

        32

        14

        Equivalent Sub-Base (ESB) Bearing Capacity, CBR ( %)

        32

        14

        Structural Subgrade Bearing Capacity, CBR ( %)

        11

        20

        29

        8

        Gravel Wearing Course (GCW) Bearing Capacity, UCS (MPa)

        1.087

        0.483

        0.771

        0.338

        Equivalent Base Course (EBC) Bearing Capacity, UCS (MPa)

        To Be Deterined During Design Stage

        To Be Deterined During Design Stage

        0.771

        0.338

        Equivalent Sub-Base (ESB) Bearing Capacity, UCS (MPa)

        0.771

        0.338

        Structural Subgrade Bearing Capacity,UCS (MPa)

        0.700

        0.193

        Gravel Wearing Course (GCW) Elastic Modulus, Eo (Mpa)

        232

        95

        147

        72

        Equivalent Base Course (EBC) Elastic Modulus, Eo (Mpa)

        To Be Deterined During Design Stage

        To Be Deterined During Design Stage

        147

        72

        Equivalent Sub-Base (ESB) Elastic Modulus, Eo (Mpa)

        147

        72

        Structural Subgrade Resilient Modulus, MR (MPa)

        58

        95

        133

        44

        Mean Pavement Thickness Determined from DCP Tests, tdcp (mm)

        To Be Deterined Durng Design Stage

        To Be Deterined During Design Stage

        263

        205

        Computational Models Adopted

        Values Computed Based on Conventional SN/CBR Models

        Values Computed Based on Quasi-Mechanistic Models

        Structural Layer Designation

        GWC

        EBC

        ESB

        GWC

        EBC

        ESB

        GWC

        EBC

        ESB

        GWC

        EBC

        ESB

        Computed Discrete Structural Layer Thickness, tstr. (mm)

        To Be Deterined During Design Stage

        To Be Deterined During Design Stage

        107

        62

        94

        100

        48

        57

        Existing Thickness-Modulus Ratio (mm/MPa)

        0.728

        0.422

        0.639

        1.389

        0.667

        0.792

        Required Discrete Structural Layer Stiffness, Eo (MPa) [To Achieve a PBBD (Performance Based Balanced Design)]

        4573

        4573

        491

        3953

        3953

        1188

        Required Full Depth Composite Pavement Stiffness, Eo (MPa) [To Achieve a PBBD (Performance Based Balanced Design)]

        1365

        1365

        Existing Full Depth (Composite) Structural Thickness, TFD (mm)

        263

        205

        Example of Computed Values for Enhanced Structural Capacity Required for Fokker50 as Design Aircraft for Bardhere & Diinsoor Airstrips

        Computational Models Adopted

        Values Computed Based on Conventional SN/CBR Models

        Values Computed Based on Quasi-Mechanistic Models

        Allowable Full Depth (Composite) Pavement Thickness, TFD (mm)

        To Be Deterined During Design Stage

        To Be Deterined During Design Stage

        300

        420

        Required Full Depth (Composite) Pavement Thickness, TFD (mm)

        300

        450

        Structural Layer Designation

        GWC

        EBC

        ESB

        GWC

        EBC

        ESB

        GWC

        EBC

        ESB

        GWC

        EBC

        ESB

        Computed Discrete Structural Layer Thickness, tstr. (mm)

        To Be Deterined During Design Stage

        To Be Deterined During Design Stage

        100

        100

        100

        150

        150

        150

        Existing Thickness-Modulus Ratio (mm/MPa)

        0.022

        0.035

        0.216

        0.057

        0.119

        0.325

        Required Discrete Structural Layer Stiffness, Eo (MPa) [To Achieve a PBBD (Performance Based Balanced Design)]

        4573

        2835

        462

        2635

        1265

        462

        Required Full Depth Composite Pavement Stiffness, Eo (MPa) [To Achieve a PBBD (Performance Based Balanced Design)]

        853

        853

        Legend: SE -Structural Evaluation; GWC -Gravel Wearing Course; EBC -Equivalent Base Course; ESF : Equivalent Structural Foundation

        Summary of Principal Parameters Adopted for Dynamic Loading Analysis

        Construction Stage

        Pre-Construction

        Post-Construction

        Parametric Description

        Afmadow

        Hudur

        Bardhere

        Diinsoor

        Gravel Wearing Course (GCW) Bearing Capacity, CBR ( %)

        45

        20

        32

        14

        Equivalent Base Course (EBC) Bearing Capacity, CBR ( %)

        To Be Deterined During Design Stage

        To Be Deterined During Design Stage

        32

        14

        Equivalent Sub-Base (ESB) Bearing Capacity, CBR ( %)

        32

        14

        Structural Subgrade Bearing Capacity, CBR ( %)

        11

        20

        29

        8

        Gravel Wearing Course (GCW) Bearing Capacity, UCS (MPa)

        1.087

        0.483

        0.771

        0.338

        Equivalent Base Course (EBC) Bearing Capacity, UCS (MPa)

        To Be Deterined During Design Stage

        To Be Deterined During Design Stage

        0.771

        0.338

        Equivalent Sub-Base (ESB) Bearing Capacity, UCS (MPa)

        0.771

        0.338

        Structural Subgrade Bearing Capacity,UCS (MPa)

        0.700

        0.193

        Gravel Wearing Course (GCW) Elastic Modulus, Eo (Mpa)

        232

        95

        147

        72

        Equivalent Base Course (EBC) Elastic Modulus, Eo (Mpa)

        To Be Deterined During Design Stage

        To Be Deterined During Design Stage

        147

        72

        Equivalent Sub-Base (ESB) Elastic Modulus, Eo (Mpa)

        147

        72

        Structural Subgrade Resilient Modulus, MR (MPa)

        58

        95

        133

        44

        Mean Pavement Thickness Determined from DCP Tests, tdcp (mm)

        To Be Deterined During Design Stage

        To Be Deterined During Design Stage

        263

        205

        Computational Models Adopted

        Values Computed Based on Conventional SN/CBR Modes

        Values Computed Based on Quasi-Mechanistic Models

        Structural Layer Designation

        GWC

        EBC

        ESB

        GWC

        EBC

        ESB

        GWC

        EBC

        ESB

        GWC

        EBC

        ESB

        Computed Discrete Structural Layer Thickness, tstr. (mm)

        To Be Deterined During Design Stage

        To Be Deterined During Design Stage

        107

        62

        94

        100

        48

        57

        Existing Thickness-Modulus Ratio (mm/MPa)

        0.728

        0.422

        0.639

        1.389

        0.667

        0.792

        Required Discrete Structural Layer Stiffness, Eo (MPa) [To Achieve a PBBD (Performance Based Balanced Design)]

        4573

        4573

        491

        3953

        3953

        1188

        Required Full Depth Composite Pavement Stiffness, Eo (MPa) [To Achieve a PBBD (Performance Based Balanced Design)]

        1365

        1365

        Existing Full Depth (Composite) Structural Thickness, TFD (mm)

        263

        205

        Example of Computed Values for Enhanced Structural Capacity Required for Fokker50 as Design Aircraft for Bardhere & Diinsoor Airstrips

        Computational Models Adopted

        Values Computed Based on Conventional SN/CBR Models

        Values Computed Based on Quasi-Mechanistic Models

        Allowable Full Depth (Composite) Pavement Thickness, TFD (mm)

        To Be Deterined During Design Stage

        To Be Deterined During Design Stage

        300

        420

        Required Full Depth (Composite) Pavement Thickness, TFD (mm)

        300

        450

        Structural Layer Designation

        GWC

        EBC

        ESB

        GWC

        EBC

        ESB

        GWC

        EBC

        ESB

        GWC

        EBC

        ESB

        Computed Discrete Structural Layer Thickness, tstr. (mm)

        To Be Deterined During Design Stage

        To Be Deterined During Design Stage

        100

        100

        100

        150

        150

        150

        Existing Thickness-Modulus Ratio (mm/MPa)

        0.022

        0.035

        0.216

        0.057

        0.119

        0.325

        Required Discrete Structural Layer Stiffness, Eo (MPa) [To Achieve a PBBD (Performance Based Balanced Design)]

        4573

        2835

        462

        2635

        1265

        462

        Required Full Depth Composite Pavement Stiffness, Eo (MPa) [To Achieve a PBBD (Performance Based Balanced Design)]

        853

        853

        Legend: SE -Structural Evaluation; GWC -Gravel Wearing Course; EBC -Equivalent Base Course; ESF : Equivalent Structural Foundation

        TABLE II. EXAMPLE OF PARAMETRIC PRINCIPAL DESIGN PARAMETERS ADOPTED FOR VIBRATIONAL DYNAMIC LOADING (VDL) ANALYSIS.

        loading on modulus of deformation [

        = 10].

      2. Summary of results adopted for analyses of VDL impact

    Summaries of the results adopted for analyses of vibrational dynamic loading impact are tabulated in Tables III ~ V for natural clayey geomaterials and Tables VI ~ VIII for natural gravelly geomaterials.

    TABLE III. SUMMARY OF DATA ADOPTED FOR ANALYSIS OF DYNAMIC LOADING EFFECTS ON DEFORMATION CHARACTERISTICS OF CLAYEY GEOMATERIALS.

    Dynamic Loading Effects on Deformation & Modulus of Deformation Characteristics of Clayey Geomaterials

    Loading Cycles (No.)

    Neat BCS: Measured

    Neat BCS: Predicted

    Neat Baraawe Silty Clay

    Neat Afmadow Expansive Clay

    Neat BCS: Predicted from Measured Values

    Neat BCS: Predicted

    Neat Baraawe Silty Clay

    Neat Afmadow Expansive Clay

    Vertical Deformation, a (%)

    Resulting Modulus of Deformation, ED (kPa)

    2800

    1.15

    1.315

    0.564

    876

    706

    2764

    5600

    1.703

    0.831

    466

    1481

    8400

    1.929

    0.986

    381

    1122

    11200

    2.22

    2.090

    1.097

    304

    334

    945

    14000

    2.215

    0.031

    1.183

    305

    295015

    837

    28000

    2.603

    0.136

    1.450

    235

    27510

    603

    42000

    3.16

    2.830

    0.197

    1.605

    172

    205

    15102

    512

    56000

    2.991

    0.240

    1.716

    188

    10954

    460

    70000

    3.116

    0.274

    1.802

    176

    8867

    425

    84000

    3.28

    3.218

    0.301

    1.872

    162

    167

    7600

    400

    112000

    3.505

    3.379

    0.344

    1.983

    145

    154

    6118

    364

    140000

    3.503

    0.378

    2.069

    145

    5265

    340

    168000

    3.605

    0.406

    2.139

    139

    4702

    32

    196000

    3.692

    0.429

    2.198

    134

    4299

    308

    224000

    3.766

    0.449

    2.249

    129

    3992

    297

    252000

    3.832

    0.467

    2.295

    126

    3750

    288

    336000

    3.83

    3.993

    0.510

    2.405

    126

    118

    3250

    267

    383600

    5.33

    4.068

    0.530

    2.457

    74

    114

    3054

    258

    504000

    4.220

    0.571

    2.561

    108

    2708

    241

    672000

    4.381

    0.614

    2.672

    101

    2407

    225

    840000

    4.506

    0.648

    2.758

    97

    2209

    214

    1008000

    4.608

    0.676

    2.828

    94

    2066

    205

    1176000

    4.694

    0.699

    2.887

    91

    1956

    199

    3192000

    5.253

    0.849

    3.271

    76

    1429

    162

    9998800

    5.892

    1.021

    3.710

    63

    1061

    133

    Dynamic Loading Effects on Stress-Strain Characteristics of Clayey Geomaterials

    Loading Cycles (No.)

    Neat BCS: Measured

    Neat BCS: Predicted

    Neat Baraawe Silty Clay

    Neat Afmadow Expansive Clay

    Neat BCS: Predicted from Measured Values

    Neat BCS: Predicted

    Neat Baraawe Silty Clay

    Neat Afmadow Expansive Clay

    Strain, a (%)

    Resulting Deviatoric Stress, (kPa)

    2800

    1.15

    1.315

    0.564

    10.08

    9.29

    15.59

    5600

    1.703

    0.831

    7.93

    12.30

    8400

    1.929

    0.986

    7.34

    11.07

    11200

    2.22

    2.090

    1.097

    6.74

    6.99

    10.37

    14000

    2.215

    0.031

    1.183

    6.75

    91.80

    9.91

    28000

    2.603

    0.136

    1.450

    6.11

    37.29

    8.75

    42000

    3.16

    2.830

    0.197

    1.605

    5.43

    5.81

    29.70

    8.22

    56000

    2.991

    0.240

    1.716

    5.61

    26.29

    7.89

    70000

    3.116

    0.274

    1.802

    5.48

    24.26

    7.66

    84000

    3.28

    3.218

    0.301

    1.872

    5.31

    5.37

    22.88

    7.48

    112000

    3.505

    3.379

    0.344

    1.983

    5.10

    5.21

    21.08

    7.22

    140000

    3.503

    0.378

    2.069

    5.10

    19.91

    7.04

    168000

    3.605

    0.406

    2.139

    5.01

    19.07

    6.89

    196000

    3.692

    0.429

    2.198

    4.94

    18.43

    6.78

    224000

    3.766

    0.449

    2.249

    4.88

    17.92

    6.68

    252000

    3.832

    0.467

    2.295

    4.82

    17.50

    6.60

    336000

    3.83

    3.993

    0.510

    2.405

    4.83

    4.70

    16.58

    6.42

    383600

    5.33

    4.068

    0.530

    2.457

    3.94

    4.65

    16.19

    6.33

    504000

    4.220

    0.571

    2.561

    4.55

    15.47

    6.17

    672000

    4.381

    0.614

    2.672

    4.45

    14.79

    6.02

    840000

    4.506

    0.648

    2.758

    4.37

    14.32

    5.90

    1008000

    4.608

    0.676

    2.828

    4.31

    13.96

    5.81

    1176000

    4.694

    0.699

    2.887

    4.26

    13.67

    5.74

    3192000

    5.253

    0.849

    3.271

    3.98

    12.13

    5.32

    9998800

    5.892

    1.021

    3.710

    3.71

    10.84

    4.92

    Equivalent Dynamic Strength (kPa)

    135.6

    474

    193

    Static Strength, UCS (kPa)

    36.2

    169

    48.3

    CBR (%)

    1.5

    7

    2

    Dynamic Loading Effects on Stress-Strain Characteristics of Clayey Geomaterials

    Loading Cycles (No.)

    Neat BCS: Measured

    Neat BCS: Predicted

    Neat Baraawe Silty Clay

    Neat Afmadow Expansive Clay

    Neat BCS: Predicted from Measured Values

    Neat BCS: Predicted

    Neat Baraawe Silty Clay

    Neat Afmadow Expansive Clay

    Strain, a (%)

    Resulting Deviatoric Stress, (kPa)

    2800

    1.15

    1.315

    0.564

    10.08

    9.29

    15.59

    5600

    1.703

    0.831

    7.93

    12.30

    8400

    1.929

    0.986

    7.34

    11.07

    11200

    2.22

    2.090

    1.097

    6.74

    6.99

    10.37

    14000

    2.215

    0.031

    1.183

    6.75

    91.80

    9.91

    28000

    2.603

    0.136

    1.450

    6.11

    37.29

    8.75

    42000

    3.16

    2.830

    0.197

    1.605

    5.43

    5.81

    29.70

    8.22

    56000

    2.991

    0.240

    1.716

    5.61

    26.29

    7.89

    70000

    3.116

    0.274

    1.802

    5.48

    24.26

    7.66

    84000

    3.28

    3.218

    0.301

    1.872

    5.31

    5.37

    22.88

    7.48

    112000

    3.505

    3.379

    0.344

    1.983

    5.10

    5.21

    21.08

    7.22

    140000

    3.503

    0.378

    2.069

    5.10

    19.91

    7.04

    168000

    3.605

    0.406

    2.139

    5.01

    19.07

    6.89

    196000

    3.692

    0.429

    2.198

    4.94

    18.43

    6.78

    224000

    3.766

    0.449

    2.249

    4.88

    17.92

    6.68

    252000

    3.832

    0.467

    2.295

    4.82

    17.50

    6.60

    336000

    3.83

    3.993

    0.510

    2.405

    4.83

    4.70

    16.58

    6.42

    383600

    5.33

    4.068

    0.530

    2.457

    3.94

    4.65

    16.19

    6.33

    504000

    4.220

    0.571

    2.561

    4.55

    15.47

    6.17

    672000

    4.381

    0.614

    2.672

    4.45

    14.79

    6.02

    840000

    4.506

    0.648

    2.758

    4.37

    14.32

    5.90

    1008000

    4.608

    0.676

    2.828

    4.31

    13.96

    5.81

    1176000

    4.694

    0.699

    2.887

    4.26

    13.67

    5.74

    3192000

    5.253

    0.849

    3.271

    3.98

    12.13

    5.32

    9998800

    5.892

    1.021

    3.710

    3.71

    10.84

    4.92

    Equivalent Dynamic Strength (kPa)

    135.6

    474

    193

    Static Strength, UCS (kPa)

    36.2

    169

    48.3

    CBR (%)

    1.5

    7

    2

    TABLE IV. SUMMARY OF DATA ADOPTED FOR ANALYSIS OF DECAY STRESS CHARACTERISTICS OF CLAYEY GEOMATERIALS SUBJECTED TO VIBRATIONAL DYNAMIC LOADING EFFECTS.

    TABLE V. SUMMARY OF DATA ADOPTED FOR ANALYSIS OF CUMULATIVE STRESS-STRAIN CHARACTERISTICS OF CLAYEY GEOMATERIALS SUBJECTED TO VIBRATIONAL DYNAMIC LOADING .

    Summary of Dynamic Loading Effects on Stress-Strain Characteristics of Clayey Geomaterials

    Loading Cycles (No.)

    Neat BCS: Measured

    Neat BCS: Predicted

    Neat Baraawe Silty Clay

    Neat Afmadow Expansive Clay

    Neat BCS: Predicted from Measured Values

    Neat BCS: Predicted

    Neat Baraawe Silty Clay

    Neat Afmadow Expansive Clay

    Strain, a (%)

    Resulting Deviatoric Stress, (kPa)

    2800

    1.15

    1.315

    0.564

    10.08

    9

    16

    5600

    1.703

    0.831

    17

    28

    8400

    1.929

    0.986

    25

    39

    11200

    2.22

    2.090

    1.097

    6.74

    32

    49

    14000

    2.215

    0.031

    1.183

    38

    92

    59

    28000

    2.603

    0.136

    1.450

    44

    129

    68

    42000

    3.16

    2.830

    0.197

    1.605

    5.43

    50

    159

    76

    56000

    2.991

    0.240

    1.716

    56

    185

    84

    70000

    3.116

    0.274

    1.802

    61

    209

    92

    84000

    3.28

    3.218

    0.301

    1.872

    5.31

    67

    232

    99

    112000

    3.505

    3.379

    0.344

    1.983

    5.10

    72

    253

    106

    140000

    3.503

    0.378

    2.069

    77

    273

    113

    168000

    3.605

    0.406

    2.139

    82

    292

    120

    196000

    3.692

    0.429

    2.198

    87

    311

    127

    224000

    3.766

    0.449

    2.249

    92

    329

    134

    252000

    3.832

    0.467

    2.295

    97

    346

    140

    336000

    3.83

    3.993

    0.510

    2.405

    4.83

    101

    363

    147

    383600

    5.33

    4.068

    0.530

    2.457

    3.94

    106

    379

    153

    504000

    4.220

    0.571

    2.561

    111

    394

    159

    672000

    4.381

    0.614

    2.672

    115

    409

    165

    840000

    4.506

    0.648

    2.758

    119

    423

    171

    1008000

    4.608

    0.676

    2.828

    124

    437

    177

    1176000

    4.694

    0.699

    2.887

    128

    451

    183

    3192000

    5.253

    0.849

    3.271

    132

    463

    188

    9998800

    5.892

    1.021

    3.710

    136

    474

    193

    Equivalent Dynamic Strength (kPa)

    135.6

    474.1

    193.1

    Static Strength, UCS (kPa)

    36.2

    169

    48.3

    CBR (%)

    1.5

    7

    2

    TABLE VI. SUMMARY OF DATA ADOPTED FOR ANALYSIS OF MODULUS OF DEFORMATION CHARACTERISTICS OF GRAVELLY GEOMATERIALS SUBJECTED TO VIBRATIONAL DYNAMIC LOADING.

    Dynamic Loading Effects on Axial Strain & Modulus of Deformation Characteristics of Somalia Gravel Geomaterials

    Loading Cycles (No.)

    Hudur Gravel

    Afmadow Gravel

    Bardhere Gravel

    Diinsoor Gravel

    Baraawe Silty Clay

    Hudur Gravel

    Afmadow Gravel

    Bardhere Gravel

    Diinsoor Gravel

    Baraawe Silty Clay

    Vertical Deformation, a (%)

    Resulting Modulus of Deformation, ED (MPa)

    Post-

    Construct

    Pre-

    Construct

    Pre-

    Construct

    Post-

    Construct

    Post-

    Construct

    Pre-

    Construct

    Pre-

    Construct

    Post-

    Construct

    2800

    5600

    8400

    11200

    14000

    0.031

    295

    28000

    0.136

    28

    42000

    0.197

    15

    56000

    0.240

    11

    70000

    0.274

    9

    84000

    0.011

    0.301

    1569

    8

    112000

    0.038

    0.344

    212

    6

    140000

    0.018

    -0.074

    0.059

    0.378

    720

    105

    5

    168000

    0.034

    -0.063

    0.076

    0.406

    261

    69

    4.7

    196000

    0.005

    0.047

    -0.053

    0.091

    0.429

    5527

    153

    52

    4.3

    224000

    0.015

    0.058

    -0.044

    0.104

    0.449

    917

    107

    42

    4.0

    252000

    0.025

    0.068

    -0.036

    0.115

    0.467

    433

    83

    36

    3.8

    336000

    0.014

    0.047

    0.093

    -0.018

    0.142

    0.510

    1064

    153

    50

    26

    3.3

    383600

    0.023

    0.057

    0.104

    -0.009

    0.154

    0.530

    465

    111

    42

    22

    3.1

    504000

    0.043

    0.078

    0.128

    0.009

    0.180

    0.571

    176

    67

    30

    2297

    17

    2.7

    672000

    0.063

    0.101

    0.153

    0.027

    0.207

    0.614

    94

    45

    23

    363

    14

    2.4

    840000

    0.079

    0.118

    0.172

    0.009

    0.042

    0.228

    0.648

    65

    35

    19

    2029

    183

    12

    2.2

    1008000

    0.092

    0.132

    0.187

    0.020

    0.054

    0.245

    0.676

    51

    29

    16

    593

    123

    11

    2.1

    1176000

    0.103

    0.144

    0.201

    0.029

    0.064

    0.260

    0.699

    43

    25

    15

    326

    93

    10

    2.0

    3192000

    0.174

    0.221

    0.286

    0.088

    0.128

    0.354

    0.849

    18

    12

    8

    55

    30

    6

    1.4

    9998800

    0.256

    0.310

    0.385

    0.156

    0.202

    0.462

    1.021

    10

    7

    5

    22

    14

    4

    1.1

    TABLE VII. SUMMARY OF DATA ADOPTED FOR ANALYSIS OF SECANT STRESS DECAY CHARACTERISTICS OF GRAVELLY GEOMATERIALS SUBJECTED TO VIBRATIONAL DYNAMIC LOADING.

    Dynamic Loading Effects on Deformation Characteristics of Somalia Gravel Geomaterials

    Loading Cycles (No.)

    Hudur Gravel

    Afmadow Gravel

    Bardhere Gravel

    Diinsoor Gravel

    Baraawe Silty Clay

    Hudur Gravel

    Afmadow Gravel

    Bardhere Gravel

    Diinsoor Gravel

    Baraawe Silty Clay

    Vertical Deformation, a (%)

    Resulting Secant Deviatoric Stress, (kPa)

    Post-

    Construct

    Pre-

    Construct

    Pre-

    Construct

    Post-

    Construct

    Post-

    Construct

    Pre-

    Construct

    Pre-

    Construct

    Post-

    Construct

    2800

    5600

    8400

    11200

    14000

    0.031

    91.80

    28000

    0.136

    37.29

    42000

    0.197

    29.70

    56000

    0.240

    26.29

    70000

    0.274

    24.26

    84000

    0.011

    0.301

    173.14

    22.88

    112000

    0.038

    0.344

    81.01

    21.08

    140000

    0.018

    0.059

    0.378

    128.80

    61.91

    19.91

    168000

    0.034

    0.076

    0.406

    87.66

    52.97

    19.07

    196000

    0.005

    0.047

    0.091

    0.429

    279.24

    71.51

    47.61

    18.43

    224000

    0.015

    0.058

    0.104

    0.449

    141.19

    62.54

    43.98

    17.92

    252000

    0.025

    0.068

    0.115

    0.467

    106.19

    56.70

    41.32

    17.50

    336000

    0.014

    0.047

    0.093

    0.142

    0.510

    149.39

    71.49

    46.94

    36.28

    16.58

    383600

    0.023

    0.057

    0.104

    0.009

    0.154

    0.530

    109.07

    63.32

    43.74

    196.26

    34.46

    16.19

    504000

    0.043

    0.078

    0.128

    0.009

    0.180

    0.571

    75.40

    52.22

    38.65

    200.09

    31.35

    15.47

    672000

    0.063

    0.101

    0.153

    0.004

    0.027

    0.207

    0.614

    59.38

    44.79

    34.69

    334.24

    99.30

    28.77

    14.79

    840000

    0.079

    0.118

    0.172

    0.009

    0.042

    0.228

    0.648

    51.78

    40.64

    32.26

    190.87

    76.59

    27.12

    14.32

    1008000

    0.092

    0.132

    0.187

    0.020

    0.054

    0.245

    0.676

    47.20

    37.92

    30.59

    119.68

    65.77

    25.94

    13.96

    1176000

    0.103

    0.144

    0.201

    0.029

    0.064

    0.260

    0.699

    44.06

    35.96

    29.34

    95.29

    59.24

    25.04

    13.67

    3192000

    0.174

    0.221

    0.286

    0.088

    0.128

    0.354

    0.849

    31.97

    27.64

    23.60

    48.51

    38.56

    20.72

    12.13

    9998800

    0.256

    0.310

    0.385

    0.156

    0.202

    0.462

    1.021

    25.29

    22.49

    19.70

    34.27

    29.18

    17.61

    10.84

    Equivalent Dynamic Strength (kPa)

    594

    923

    707

    823

    765

    749

    474

    Static Strength, UCS (kPa)

    483

    1086

    627

    1070

    852

    701

    169

    CBR (%)

    20

    45

    26

    44

    35

    29

    7

    Plasticity Index, PI (%)

    10

    11

    12

    8

    9

    13

    18

    TABLE VIII. SUMMARY OF DATA ADOPTED FOR ANALYSIS OF CUMULATIVE STRESS-STRAIN CHARACTERISTICS OF GRAVELLY GEOMATERIALS SUBJECTED TO VIBRATIONAL DYNAMIC LOADING.

    Cumulative Stress-Strain Characteristics Under Vibrational Dynamic Loading: Effects on Deformation Characteristics of Somalia Gravel Geomaterials

    Loading Cycles (No.)

    Hudur Gravel

    Afmadow Gravel

    Bardhere Gravel

    Diinsoor Gravel

    Baraawe Silty Clay

    Hudur Gravel

    Afmadow Gravel

    Bardhere Gravel

    Diinsoor Gravel

    Baraawe Silty Clay

    Vertical Deformation, a (%)

    Resulting Secant Deviatoric Stress, (kPa)

    Post- Construct

    Pre- Construct

    Pre- Construct

    Post- Construct

    Post- Construct

    Pre- Construct

    Pre- Construct

    Post- Construct

    2800

    5600

    8400

    11200

    14000

    0.031

    92

    28000

    0.136

    129

    42000

    0.197

    159

    56000

    0.240

    185

    70000

    0.274

    209

    84000

    0.011

    0.301

    173

    232

    112000

    0.038

    0.344

    254

    253

    140000

    0.018

    0.059

    0.378

    129

    316

    273

    168000

    0.034

    0.076

    0.406

    216

    369

    292

    196000

    0.005

    0.047

    0.091

    0.429

    279

    288

    417

    311

    224000

    0.015

    0.058

    0.104

    0.449

    420

    351

    461

    329

    252000

    0.025

    0.068

    0.115

    0.467

    527

    407

    502

    346

    336000

    0.014

    0.047

    0.093

    0.142

    0.510

    149

    598

    454

    538

    363

    383600

    0.023

    0.057

    0.104

    0.009

    0.154

    0.530

    258

    661

    498

    573

    379

    504000

    0.043

    0.078

    0.128

    0.009

    0.180

    0.571

    334

    714

    537

    604

    394

    672000

    0.063

    0.101

    0.153

    0.004

    0.027

    0.207

    0.614

    393

    758

    571

    633

    409

    840000

    0.079

    0.118

    0.172

    0.009

    0.042

    0.228

    0.648

    445

    799

    603

    660

    423

    1008000

    0.092

    0.132

    0.187

    0.020

    0.054

    0.245

    0.676

    492

    837

    634

    686

    437

    1176000

    0.103

    0.144

    0.201

    0.029

    0.064

    0.260

    0.699

    536

    873

    663

    711

    451

    3192000

    0.174

    0.221

    0.286

    0.088

    0.128

    0.354

    0.849

    568

    901

    687

    732

    463

    9998800

    0.256

    0.310

    0.385

    0.156

    0.202

    0.462

    1.021

    594

    923

    707

    749

    474

    Equivalent Dynamic Strength (kPa)

    594

    923

    707

    823

    765

    749

    474

    Static Strength, UCS (kPa)

    483

    1086

    627

    1070

    852

    701

    169

    CBR (%)

    20

    45

    26

    44

    35

    29

    7

    Plasticity Index, PI (%)

    10

    11

    12

    8

    9

    13

    18

  5. VDL CHARACTERISTICS OF CLAYEY GEOMATERIALS Simulation of the Afmadow silty clay foundation ground is

    undertaken by comparatively evaluating the dynamic loading characteristics of clayey subgrade geomaterials. This involves the comparative analysis of: i) load impact (maximum impact

    upon contact) characteristics depicting the effects of lime stabilization on black cotton soil (BC) subjected to vibrational dynamic loading; ii) dynamic loading impact on the modulus of deformation of non-stabilized clayey geomaterials; iii) decay characteristics of secant stress as a result of cumulative dynamic loading effects; iv) deformation characteristics of clayey geomaterials under dynamic loading; and, v) cumulative stress- strain characteristics of neat clayey geomaterials subjected to vibrational dynamic loading.

    1. Analysis of load impact characteristics of natural and hydraulically stabilized clayey geomaterials

      A summary of the results of the impact of vibrational dynamic loading (VDL) on the characteristics of natural, lime and lime-conaid treated black cotton soil (BCS) and natural Afmadow silty clay is presented in Table IX, whilst the corresponding deformation characteristics are graphically depicted in Figures 8 and 9 for VD loadings within the range of 10 million and 1 million cycles, respectively.

      The characteristic curves in these graphs show that: i) notwithstanding the geomaterial type, deformation is significantly impacted by the cumulative cycles of the VDL; ii) in conformity with their bearing strengths (CBRs), the Baraawe silty clay quantitatively exhibits the lowest deformation, whilst the BCS registers the highest (4 days soaked CBRs: Baraawe=7%; Afmadow=2% BCS=1.5%); ii) lime stabilization enhances deformation resistance of the BCS; and

      iii) the Afmadow silty clay subgrade requires in-situ ground improvement.

      TABLE IX. COMPARISON OF NATURAL AND STABILIZED CLAYEY GEOMATERIALS SUBJECTED TO VIBRATIONAL DYNAMIC LOADING RESULTS.

      Comparison of Vibrational Dynamic Loading Effects on Deformation Characteristics of Clayey Geomaterials

      Loading Cycles (No.)

      Neat BCS: Measured

      Neat BCS: Predicted

      Neat Baraawe Silty Clay

      Neat Afmadow Expansive Clay

      Neat BCS: Predicted from Measured Values

      Neat BCS: Predicted

      Neat Baraawe Silty Clay

      Neat Afmadow Expansive Clay

      Vertical Deformation, a (%)

      Resulting Modulus of Deformation, ED (kPa)

      2800

      1.15

      1.315

      0.564

      876

      706

      2764

      5600

      1.703

      0.831

      466

      1481

      8400

      1.929

      0.986

      381

      1122

      11200

      2.22

      2.090

      1.097

      304

      334

      945

      14000

      2.215

      0.031

      1.183

      305

      295015

      837

      28000

      2.603

      0.136

      1.450

      235

      27510

      603

      42000

      3.16

      2.830

      0.197

      1.605

      172

      205

      15102

      512

      56000

      2.991

      0.240

      1.716

      188

      10954

      460

      70000

      3.116

      0.274/p>

      1.802

      176

      8867

      425

      84000

      3.28

      3.218

      0.301

      1.872

      162

      167

      7600

      400

      112000

      3.505

      3.379

      0.344

      1.983

      145

      154

      6118

      364

      140000

      3.503

      0.378

      2.069

      145

      5265

      340

      168000

      3.605

      0.406

      2.139

      139

      4702

      322

      196000

      3.692

      0.429

      2.198

      134

      4299

      308

      224000

      3.766

      0.449

      2.249

      129

      3992

      297

      252000

      3.832

      0.467

      2.295

      126

      3750

      288

      336000

      3.83

      3.993

      0.510

      2.405

      126

      118

      3250

      267

      383600

      5.33

      4.068

      0.530

      2.457

      74

      114

      3054

      258

      504000

      4.220

      0.571

      2.561

      108

      2708

      241

      672000

      4.381

      0.614

      2.672

      101

      2407

      225

      840000

      4.506

      0.648

      2.758

      97

      2209

      214

      1008000

      4.608

      0.676

      2.828

      94

      2066

      205

      1176000

      4.694

      0.699

      2.887

      91

      1956

      199

      3192000

      5.253

      0.849

      3.271

      76

      1429

      162

      9998800

      5.892

      1.021

      3.710

      63

      1061

      133

      4.5

      4

      3.5

      Axial Strain, a (%)

      Axial Strain, a (%)

      3

      Comparison of Impact of Vibrational Dynamic Loading on Deformation of Clayey

      Geomaterials

      Neat BCS Failed @ Nvd=384000 Cycles

      The results in Figure 10 show that: i) the mode and rate of secant deviatoric stress decay as a result of cumulative VDL is dependent upon the nature and stiffness of the clayey geomaterial; and ii) a very good agreement exists between the measured and modelled (predicted) results.

      Figure 11 depicts the superimposed VDL stress-strain

      2.5

      = . . ×

      . .

      curves for varying clays. The graph also includes a comparison

      2

      1.5

      1

      0.5

      0

      of measured and predicted results for BCS. As was deduced form Figure 10, the Baraawe silty clay has the highest resistance to stress decay, whilst the BCS registers the lowest. Measured vs. predicted BCS results show quasi-perfect superimposition.

      Comparison of Impact of Vibrational Dynamic Loading on Deformation of Clayey

      Geomaterials Including Meausred vs. Predicted Results for BCS

      Comparison of Impact of Vibrational Dynamic Loading on Deformation of Clayey

      Geomaterials Including Meausred vs. Predicted Results for BCS

      = . . × . .

      = . . × . .

      0 2000000 4000000 6000000 8000000 10000000

      100

      100

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      = . .

      90

      = . .

      90

      80

      70

      60

      50

      40

      30

      20

      10

      0

      80

      70

      60

      50

      40

      30

      20

      10

      0

      Neat BCS 2% Lime Stabilized Con Aid + 2% Lime Stabilized

      Secant Deviatoric Stress, d (kPa)

      Secant Deviatoric Stress, d (kPa)

      5% Lime Stabilized Baraawe Silty Clay Afmadow Expansive Clay

      Axial Strain, a (%)

      Axial Strain, a (%)

      Fig. 8. Comparison of impact of dynamic loading on natural and stabilized clays [ = 10].

      4.5

      Comparison of Impact of Vibrational Dynamic Loading on Deformation of Clayey

      Geomaterials

      = . . × . .

      4.5

      Comparison of Impact of Vibrational Dynamic Loading on Deformation of Clayey

      Geomaterials

      = . . × . .

      4

      Neat BCS Failed @ Nvd=384000 Cycles

      4

      Neat BCS Failed @ Nvd=384000 Cycles

      0.01

      0.1

      1

      10

      0.01

      0.1

      1

      10

      Axial Strain, a (%)

      Axial Strain, a (%)

      Neat BCS: Measured

      Neat BCS: Predicted

      Baraawe Silty Clay

      Afmadow Expansive Clay

      Neat BCS: Measured

      Neat BCS: Predicted

      Baraawe Silty Clay

      Afmadow Expansive Clay

      0

      200000

      400000

      600000

      800000

      1000000

      0

      200000

      400000

      600000

      800000

      1000000

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      Neat BCS

      5% Lime Stabilized

      2% Lime Stabilized

      Baraawe Silty Clay

      Con Aid + 2% Lime Stabilized

      Afmadow Expansive Clay

      Neat BCS

      5% Lime Stabilized

      2% Lime Stabilized

      Baraawe Silty Clay

      Con Aid + 2% Lime Stabilized

      Afmadow Expansive Clay

      3.5

      3

      2.5

      2

      1.5

      1

      0.5

      0

      3.5

      3

      2.5

      2

      1.5

      1

      0.5

      0

      Fig. 9. Comparison of impact of dynamic loading on natural and stabilized clays [ = 1].

    2. Analysis of secant stress decay resulting from cumulative dynamic load impact on natural clayey geomaterials

      × + . + .

      × + . + .

      15

      10

      5

      15

      10

      5

      Secant Deviatoric Stress, kPa)

      Secant Deviatoric Stress, kPa)

      Modelled decay characteristics of the secant deviator stress of natural black cotton soil, Afmadow silty clay and Baraawe silty clay are graphically depicted in Figure 10 for loadings up to 1 million with comparison to measured data.

      Secant Stress Decay resulting from Impact of Vibrational Dynamic Loading on Clayey

      Geomaterials Including Meausred vs. Predicted Characteristic Curve for BCS

      Secant Stress Decay resulting from Impact of Vibrational Dynamic Loading on Clayey

      Geomaterials Including Meausred vs. Predicted Characteristic Curve for BCS

      30

      25

      20

      = . + . + . ×

      30

      25

      20

      = . + . + . ×

      Neat BCS Failed @ Nvd=384000 Cycles

      Neat BCS Failed @ Nvd=384000 Cycles

      0

      1000

      10000

      100000

      1000000

      0

      1000

      10000

      p>100000

      1000000

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      Neat BCS: Measured

      Neat BCS: Predicted

      Baraawe Silty Clay

      Afmadow Expansive Clay

      Neat BCS: Measured

      Neat BCS: Predicted

      Baraawe Silty Clay

      Afmadow Expansive Clay

      Fig. 10. Decay characteristics of secant deviator stress under dynamic loading

      [ = 10].

      Fig. 11. Stress-strain characteristics under dynamic loading [ = 10].

    3. Deformation characteristics of natural clayey geomaterials subjected to VDL

      Axial Strain, a (%)

      Axial Strain, a (%)

      Deformation characteristics under dynamic loading of natural black cotton soil, Afmadow silty clay and Baraawe silty clay are graphically depicted in Figures 12 and 13 for loadings up to 3.2 million and 100,000 (one hundred thousand) cycles, respectively; with a comparison of measured and predicted results for BCS. The results from these figures clearly indicate that: i) deformation, defined in terms of axial (vertical) strain is significantly influenced by the nature and stiffness of the clayey geomaterials; and ii) the impact of VDL is more intense within the initial phase of loading tending to a residual state with increased cumulative loading (Figure 13).

      4.5

      Comparison of Impact of Vibrational Dynamic Loading on Deformation of Clayey Geomaterials

      Including Meausred vs. Predicted Characteristic Curves for Black Cotton Soil

      4.5

      Comparison of Impact of Vibrational Dynamic Loading on Deformation of Clayey Geomaterials

      Including Meausred vs. Predicted Characteristic Curves for Black Cotton Soil

      Neat

      4 BCS

      Failed @

      Nvd=384000

      3.5 Cycles

      3

      2.5

      2

      = . . × . .

      Neat

      4 BCS

      Failed @

      Nvd=384000

      3.5 Cycles

      3

      2.5

      2

      = . . × . .

      0

      500000 1000000 1500000 2000000 2500000 3000000 3500000

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      0

      500000 1000000 1500000 2000000 2500000 3000000 3500000

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      Neat BCS: Measured

      Neat BCS: Predicted

      Baraawe Silty Clay

      Afmadow Expansive Clay

      Neat BCS: Measured

      Neat BCS: Predicted

      Baraawe Silty Clay

      Afmadow Expansive Clay

      1.5

      1

      0.5

      0

      1.5

      1

      0.5

      0

      Fig. 12. Deformation characteristics of clays under dynamic loading

      [ = 3.2].

      Neat BCS: Measured

      Neat BCS: Predicted

      Baraawe Silty Clay

      Afmadow Expansive Clay

      Baraawe Silty Clay: PI=18%

      Afmadow Expansive Clay: PI=28%

      Neat BCS:PI=32%

      3.5

      3

      3.5

      3

      Comparison of Impact of Vibrational Dynamic Loading on Deformation of Clayey Geomaterials

      Including Meausred vs. Predicted Characteristic Curves for Black Cotton Soil

      Neat BCS

      Failed @ Nvd=384000

      Cycles

      Comparison of Impact of Vibrational Dynamic Loading on Deformation of Clayey Geomaterials

      Including Meausred vs. Predicted Characteristic Curves for Black Cotton Soil

      Neat BCS

      Failed @ Nvd=384000

      Cycles

      2.5

      2

      1.5

      1 = . . × . .

      0.5

      0

      0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      2.5

      2

      1.5

      1 = . . × . .

      0.5

      0

      0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      Effects of Cumulative Impact Stress on Deformation Characteristics of Clayey Geomaterials

      Effects of Cumulative Impact Stress on Deformation Characteristics of Clayey Geomaterials

      = × . + . × . + . . + .

      = × . + . × . + . . + .

      500

      450

      400

      500

      450

      400

      Cumulative Impact Stress @ Failure:

      =135.6kPa @ 383,600Cycles Strain @ Critical State: =3.83% Strain @ Failure: =5.33%

      Cumulative Impact Stress @ Failure:

      =135.6kPa @ 383,600Cycles Strain @ Critical State: =3.83% Strain @ Failure: =5.33%

      350

      300

      250

      200

      150

      100

      50

      0

      350

      300

      250

      200

      150

      100

      50

      0

      0

      0

      1

      1

      2

      2

      3

      Axial Strain, a(%)

      3

      Axial Strain, a(%)

      4

      4

      5

      5

      6

      6

      7

      7

      Axial Strain, a (%)

      Axial Strain, a (%)

      Cumulative Impact Stress, ci (kPa)

      Cumulative Impact Stress, ci (kPa)

      Neat BCS: Measured

      Neat BCS: Predicted

      Baraawe Silty Clay

      Afmadow Expansive Clay

      Baraawe Silty Clay: PI=18%

      Afmadow Expansive Clay: PI=28%

      Neat BCS:PI=32%

      Fig. 13. Deformation characteristics of clays under dynamic loading

      [ = 100000].

    4. Analysis of cumulative stress-strain characteristics of natural clayey geomaterials subjected to VDL

    The influence of dynamic loading on cumulative impact stress, for [. = 3.2] is depicted in Figure 14 for natural Baraawe and Afmadow silty clays as well as natural black cotton soil (BCS). It can be observed that the Baraawe silty clay exhibits the highest impact stress; a state that is

    Influence of Vibrational Dynamic Loading on Cumulative Impact Stress of Clayey

    Geomaterials

    500

    Cumulative Impact Stress @ Failure:

    450 =135.6kPa @ 383,600Cycles

    Strain @ Critical State: =3.83%

    400 Strain @ Failure: =5.33%

    350

    300

    250

    200

    150

    Influence of Vibrational Dynamic Loading on Cumulative Impact Stress of Clayey

    Geomaterials

    500

    Cumulative Impact Stress @ Failure:

    450 =135.6kPa @ 383,600Cycles

    Strain @ Critical State: =3.83%

    400 Strain @ Failure: =5.33%

    350

    300

    250

    200

    150

    Cumulative Impact Stress, cid (kPa)

    Cumulative Impact Stress, cid (kPa)

    attributable to its lower plasticity index and higher stiffness (4 days soaked resilient moduli in : = 39; = 12 = 9).

    Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

    Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

    Baraawe Silty Clay: PI=18%

    Afmadow Expansive Clay:PI=28%

    Neat BCS:PI=32%

    Baraawe Silty Clay: PI=18%

    Afmadow Expansive Clay:PI=28%

    Neat BCS:PI=32%

    100

    50

    0

    1000

    100

    50

    0

    1000

    10000

    10000

    100000

    100000

    1000000

    1000000

    10000000

    10000000

    Fig. 14. Influence of dynamic loading on cumulative impact stress

    [. = 3.2].

    On the other hand, the characteristics of the cumulative impact stress plotted against axial strain under vibrational dynamic loading are depicted in Figure 15. The results in these figures show that: i) the Afmadow silty clay subgrade requires ground improvement to enhance its resistance to impact stress and reduce the magnitude of deformation; and, ii) black cotton soil (BCS) exhibits the highest deformation strain due to its lower resistance to impact stress [lower stiffness (deformation resistance)].

    Fig. 15. Cumulative impact stress-strain characteristics under dynamic loading.

    • Implication of results from this Section V: Simulation of foundation/subgrade ground characteristics for design

    1.

    Vibrational dynamic loading (VDL) has distinctly significant

    1.

    Vibrational dynamic loading (VDL) has distinctly significant

    impact on the geotechnical engineering properties, characteristics and geotechnical quantities of clayey subgrade geomaterials.

    1. As the dynaic loading increases, the deformation and impact stress resistance of the clayey subgrade geomaterials reduces exponentially with the most drastic reduction exhibited within the initial (primary) phase of loading.

    2. The Afmadow silty clay subgrade requires in-situ ground improvement preferably using ND (Non-Destructive) GI techniques and/or replacement.

    3. Designs based on comprehensive subgrade geomaterials and in- situ ground property analysis as well as high standards of QCA are imperative in ensuring achievement of Performance Based Value Engineering (PB-VE) pavement structures.

    4. Both Afmadow and Hudur gravels require OPMC (Optimum Mechanical & Chemical) stabilization in order to achieve the geotechnical engineering properties required for the design & construction specifications for the designated design aircraft.

    impact on the geotechnical engineering properties, characteristics and geotechnical quantities of clayey subgrade geomaterials.

    1. As the dynamic loading increases, the deformation and impact stress resistance of the clayey subgrade geomaterials reduces exponentially with the most drastic reduction exhibited within the initial (primary) phase of loading.

    2. The Afmadow silty clay subgrade requires in-situ ground improvement preferably using ND (Non-Destructive) GI techniques and/or replacement.

    3. Designs based on comprehensive subgrade geomaterials and in- situ ground property analysis as well as high standards of QCA are imperative in ensuring achievement of Performance Based Value Engineering (PB-VE) pavement structures.

    4. Both Afmadow and Hudur gravels require OPMC (Optimum Mechanical & Chemical) stabilization in order to achieve the geotechnical engineering properties required for the design & construction specifications for the designated design aircraft.

  6. VDL EFFECTS ON GRAVELLY GEOMATERIALS The effects of vibrational dynamic loading on the

    characteristics of gravelly geomaterials are analyzed in this Section VI. Essentially, this involves the analysis of: i) dynamic loading impact on the modulus of deformation of non-stabilized gravelly geomaterials; ii) decay characteristics of secant stress as a result of cumulative dynamic loading effects; iii) deformation characteristics of gravelly geomaterials under dynamic loading; and, v) cumulative stress-strain characteristics of neat gravelly geomaterials subjected to vibrational dynamic loading.

    1. Analysis of VDL impact on modulus of deformation and axial strain of gravelly geomaterials: Comparative simulation of pre- and post-conctruction charatceristics

      Simulated Pre-Construction (PrC) and Post-Construction (PoC) characteristics of the modulus of deformation and cumulative strain subjected to VDL on some typical Somalia gravels are graphically depicted and compared in Figures 16 and 17 for cumulative loadings of up to 10 million cycles.

      500

      Decay of Modulus of Deformation Due to Impact of Vibrational Dynamic Loading on Gravel

      Geomaterials

      Secant Stress Decay resulting from Impact of Vibrational Dynamic Loading on Gravel

      Geomaterials

      500

      Decay of Modulus of Deformation Due to Impact of Vibrational Dynamic Loading on Gravel

      Geomaterials

      Secant Stress Decay resulting from Impact of Vibrational Dynamic Loading on Gravel

      Geomaterials

      450

      = . .

      140

      = . .

      450

      = . .

      140

      = . .

      400

      350

      PrC: Pre-Construction

      PoC: Post-Construction

      400

      350

      PrC: Pre-Construction

      PoC: Post-Construction

      300

      250

      200

      150

      100

      50

      0

      100000

      300

      250

      200

      150

      100

      50

      0

      100000

      1000000

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      1000000

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      10000000

      10000000

      Hudur PrC Afmadow PrC Bardhere PrC Bardhere PoC Diinsoor PrC Diinsoor PoC

      Hudur PrC Afmadow PrC Bardhere PrC Bardhere PoC Diinsoor PrC Diinsoor PoC

      120

      100

      80

      60

      40

      20

      0

      100000

      120

      100

      80

      60

      40

      20

      0

      100000

      1000000

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      1000000

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      10000000

      10000000

      Modlus of Deformation, ED (MPa)

      Modlus of Deformation, ED (MPa)

      Deviatoric Stress, kPa)

      Deviatoric Stress, kPa)

      Fig. 16. Impact of dynamic loading on modulus of deformation of gravels

      0.30

      0.25

      0.20

      0.15

      0.10

      0.05

      0.00

      0.30

      0.25

      0.20

      0.15

      0.10

      0.05

      0.00

      Axial Strain, a (%)

      Axial Strain, a (%)

      [. = 10].

      Deformation Characteristics of Somalia Gravel Geomaterials Under Vibrational Dynamic Loading

      Deformation Characteristics of Somalia Gravel Geomaterials Under Vibrational Dynamic Loading

      0.50

      0.50

      0.45

      0.40

      = . . × . .

      0.45

      0.40

      = . . × . .

      0.35

      PrC: Pre-Construction

      PoC: Post-Construction

      0.35

      PrC: Pre-Construction

      PoC: Post-Construction

      0

      2000000

      4000000

      6000000

      8000000

      10000000

      0

      2000000

      4000000

      6000000

      8000000

      10000000

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

      Hudur PrC

      Afmadow PrC

      Bardhere PrC

      Bardhere PoC

      Diinsoor PrC

      Diinsoor PoC

      Hudur PrC

      Afmadow PrC

      Bardhere PrC

      Bardhere PoC

      Diinsoor PrC

      Diinsoor PoC

      Fig. 17. Cumulative strain characteristics of gravels under dynamic loading

      [. = 10].

      It can be observed and derived, from Figures 16 and 17 that:

      i) the rate of decay of the modulus of deformation is more drastic for the post-construction gravels implying that effects of reconstitution/remolding are visibly apparent and that these geomaterials may have been in varying degrees of weathered states culminating in the increase in fines contents, which implies loss in bearing capacity and stiffness; ii) resistance to deformation under dynamic loading is dependent on the magnitude of both plasticity index and the bearing strengths; iii) the mode of decay is influenced by both the magitude of the initial stiffness and number of cumulative loading cycles, whereas the charcteristic curves in Figure 17 show that the axial deformation (straining) is almost entirely dependent only on the initial stiffness; and iv) both stiffness dacay and straining are more acute within the initial stage of loading. Refer to Tables VII and VIII for further data correlation and verification.

    2. Analysis of cumulative deviator stress decay resulting from cumulative VDL impact on gravelly geomaterials

      Decay characteristics of the secant deviator stress of some

      Hudur Gravel

      Afmadow Gravel

      Bardhere Gravel

      Diinsoor Gravel

      Hudur Gravel

      Afmadow Gravel

      Bardhere Gravel

      Diinsoor Gravel

      Fig. 18. Deviator stress decay characteristics of gravels under dynamic loading [. = 10].

    3. Influence of VDL and axial strain level on the cumulative impact stress of gravelly geomaterials

    The influence of cumulative VDL on the cumulative impact stress is demonstrated in Figure 19, whilst its strain level dependency is depicted in Figure 20 for loadings of up to 10 million cumulative cycles. In both cases it can be observed that the cumulative impact stress increases with both cumulative loading and straining tending towards a residual state after approximately one million (1,00,000) loading cycles. However, it can be inferred that, whereas the threshold for the initiation of the residual state tendency is virtually clearly defined at this level, that of cumulative deformation occurs at varying strain levels depending on the magnitude of the initial stiffness, plasticity index as well as compressive and bearing strength (refer to Tables VII and VIII).

    It can further be derived that reconstitution/remolding reduces the levels/thresholds of both cumulative loading and deformation resistance of the cumulative impact stress (compare Pre-Construction (PrC) and Post-Construction (PoC) characteristic curves in Figures 19 and 20).

    Influence of Vibrational Dynamic Loading on Cumulative Impact Stress of Somalia Geomaterials

    PrC:

    PoC

    Pre-Construction St

    : Post-Construction S

    age

    tage (Reco

    nstituted

    /Rem

    olded

    Stat

    e)

    PrC:

    PoC

    Pre-Construction St

    : Post-Construction S

    age

    tage (Reco

    nstituted

    /Rem

    olded

    Stat

    e)

    1000

    900

    Cumulative Impact Stress, ci kPa)

    Cumulative Impact Stress, ci kPa)

    800

    700

    600

    500

    400

    300

    200

    100

    0

    100000 1000000 10000000

    Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

    typical Somalia gravels are graphically depicted in Figure 18

    Hudur PrC Afmadow PrC Bardhere PrC Diinsoor PrC Bardhere PoC Diinsoor PoC

    for loadings of up to 10 million cumulative cycles. That drastic deviator stress decay occurs within the zone of initial loading can very well be observed from this figure.

    Fig. 19. Cumulative impact stress characteristics of gravels under vibrational dynamic loading.

    Effects of Cumulative Impact Stress on Deformation Characteristics of Somalia Gravel Geomaterials

    Effects of Cumulative Impact Stress on Deformation Characteristics of Somalia Gravel Geomaterials

    Degradation of Gravelly Geomaterial Stiffness Resulting from Cumulative Dynamic Loading Progression

    1000

    900

    800

    700

    600

    500

    400

    300

    200

    100

    0

    1000

    900

    800

    700

    600

    500

    400

    300

    200

    100

    0

    140

    = . . × . + . ×

    Zone of Erratic Data

    . . × . × + .

    Cumulative Impact Stress, cid kPa)

    Cumulative Impact Stress, cid kPa)

    Secant Modulus of Deformation, Es (MPa)

    Secant Modulus of Deformation, Es (MPa)

    120

    100

    80

    60

    40

    Due to Bedding Errors and System Compliance

    MR: Resilient Modulus in MPa

    20

    PrC: Pre-Construction Stage

    PoC: Post-Construction Stage (Reconstituted/Remolded State)

    PrC: Pre-Construction Stage

    PoC: Post-Construction Stage (Reconstituted/Remolded State)

    0

    1000 10000 100000 1000000 10000000 100000000

    0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

    Axial Strain, a (%)

    0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

    Axial Strain, a (%)

    Vibrational Dynamic Loading, NA,VL (Cumulative No. of Cycles)

    Diinsoor: Eoi = 44 Afmadow: Eoi = 58 Bardhere: Eoi = 87 Baraawe: Eoi = 91 Hudur: Eoi = 95 Diinsoor PC: Eoi = 63 Bardhere PC: Eoi = 133

    Hudur PrC

    Afmadow PrC

    Bardhere PrC

    Diinsoor PrC

    Bardhere PoC

    Diinsoor PoC

    Hudur PrC

    Afmadow PrC

    Bardhere PrC

    Diinsoor PrC

    Bardhere PoC

    Diinsoor PoC

    Fig. 20. Cumulative impact stress-strain characteristics of gravels under vibrational dynamic loading.

    the geotechnical engineering properties, characteristics and geotechnical quantities of the gravelly geomaterials designated for use in pavement construction.

    1. As the dynamic loading increases, the deformation and impact stress resistance of thegravelly geomaterials reduces exponentially with the most drastic reduction exhibited within the initial (primary) phase of loading.

    2. Both Afmadow and Hudur gravels require mechanical as well as chemical stabilization in order to meet design and construction specification requirements.

    3. Designs based on comprehensive pavement geomaterials analysis of the effects of vibrational dynamic loading in retrospect to the maintenance of high standards of QCA are imperative in ensuring achievement of Performance Based Value Engineering (PB-VE) pavement structures.

    4. Both Afmadow and Hudur gravels require OPMC stabilization in order to achieve the geotechnical engineering properties required for design & construction specifications of the designated design aircraft.

    the geotechnical engineering properties, characteristics and geotechnical quantities of the gravelly geomaterials designated for use in pavement construction.

    1. As the dynamic loading increases, the deformation and impact stress resistance of thegravelly geomaterials reduces exponentially with the most drastic reduction exhibited within the initial (primary) phase of loading.

    2. Both Afmadow and Hudur gravels require mechanical as well as chemical stabilization in order to meet design and construction specification requirements.

    3. Designs based on comprehensive pavement geomaterials analysis of the effects of vibrational dynamic loading in retrospect to the maintenance of high standards of QCA are imperative in ensuring achievement of Performance Based Value Engineering (PB-VE) pavement structures.

    4. Both Afmadow and Hudur gravels require OPMC stabilization in order to achieve the geotechnical engineering properties required for design & construction specifications of the designated design aircraft.

    • Implication of results in this Section VI: Stress-strain and deformation resistance (geotechnical engineering) characteristics for design.

    1.

    Vibrational dynamic loading has distinctly significant impact on

    1.

    Vibrational dynamic loading has distinctly significant impact on

    Fig. 21. Impact of vibrational dynamic loading on secant modulus of deformation of Somalia gravels [. = 30].

    Impact of Dynamic Loading on Gravelly Geomaterials with Varying Resilient Moduli

    7

    MR: Resilient Modulus in MPa

    Deformation (Axial Strain), a (%)

    Deformation (Axial Strain), a (%)

    6

    5

    4

    3

    2

    1 = . . × . + . ×

    . . × . × + .

    0

    0 5000000 10000000 15000000 20000000 25000000 30000000

    Vibrational Dynamic Loading, NA,VL (Cumulative No. of Cycles)

    MR= 100MPa Diinsoor: Eoi = 44 Afmadow: Eoi = 58 Bardhere: Eoi = 87 Baraawe: Eoi = 91 Hudur: Eoi = 95 Diinsoor PC: Eoi = 63 Bardhere PC: Eoi = 133

  7. ANALYSIS OF STIFFNESS DECAY AND DEFORMATION OF

    TYPICAL SOMALIA GRAVELS UNDER CUMULATIVE VDL

    1. Decay and deformation characteristics

      The impact of vibrational dynamic loading on the decay

      Fig. 22. Deformation characteristics of Somalia gravels under dynamic loading [ = 30].

    2. Analysis of VDL impact on modulusof deformation within the initial phase of loading

    The characteristic curves depicting stiffness degradation resulting from progressive cumulative vibrational dynamic loading within the initial phase of loading [1000 100000 ] are graphically plotted in Figure 23.

    Degradation of Gravelly Geomaterial Stiffness Resulting from Cumulative Dynamic Loading Progression

    characteristics of secant modulus of deformation and the strain

    = . . × . + .

    ×

    deformation of Somalia gravels is depicted in Figures 21 and 22, respectively; for VDLs of up to 30 million cumulative cycles. It can be deduced that both the stiffness decay and straining deformation resistance largely depend on the magnitude of the initial stiffness (elastic modulus).

    The results in these figures further make a comparison of the Pre-Construction and Post-Construction characteristics, which show that the Pre-Construction (PrC) Bardhere gravel with the highest initial elastic modulus [0 = 133] exhibits the highest resistance to deformation (note that the maximum strain

    250

    Secant Modulus of Deformation, Es (MPa)

    Secant Modulus of Deformation, Es (MPa)

    200

    150

    100

    50

    0

    . . × . × + .

    Zone of Erratic Data Due to Bedding Errors, System Compliance and Low Load Intensity

    Eo: Elastic Modulus in MPa

    for this gravel is; [] = 1.8%.

    1000 10000 100000

    Vibrational Dynamic Loading, NA,VL (Cumulative No. of Cycles)

    Diinsoor: Eoi = 72 Bardhere: Eoi = 133 Hudur: Eoi = 163 Afmadow: Eoi = 232

    Baraawe: Eoi = 278 Diinsoor PC: Eoi = 153 Bardhere PC: Eoi = 197

    Fig. 23. Modulus of deformation decay characteristics Somalia gravels under dynamic loading [1000 100000].

    Cumulative Impact Stress, ci (kPa)

    Cumulative Impact Stress, ci (kPa)

    The following observations and/or derivations can be made from the modelled results graphically plotted in Figure 23: i) there exists a zone of erratic data (within the region of very small strains), the causes of which may be attributable to bedding errors, system compliance and low load intensity (limitation of transducer resolution); ii) it can be explicitly confirmed that the mode and magnitude of impact of VDL is predominantly dependent upon the initial stffness of the geomaterial; iii) application of the TACH-MD VDL models, which were developed within a mechanistic-empirical framework based on experimental testing data, is limited within this zone; and iv) the limiting factor, which is the number of cumulative load cycles, depends on the magnitude of the initial stiffness with geomaterials of higher stiffness registering higher cyclic limits possibly due to the fact that bedding error correction requires higher load intensity for stiffer specimens.

    • Implication of Results in this Section VII: Simulation of pavement gravel characteristics within initial phase of VDL for design and construction

    1.

    Deformation resistance is predominantly dependent upon the

    1.

    Deformation resistance is predominantly dependent upon the

    magnitudes of the initial/original stiffness (elastic modulus) and the plasticity characteristics.

    1. Vibrational dynamic loading has distinctly significant impact on the geotechnical engineering properties, characteristics and geotechnical quantities of the gravelly geomaterials designated for use in pavement construction.

    2. As the dynamic loading increases, the deformation and impact stress resistance of thegravelly geomaterials reduces exponentially with the most drastic reduction exhibited within the initial (primary) phase of loading.

    3. Further research is required in order to determine a sustainable solution to the data collection and processing within the erratic zone which occurs within the region of very small strains (initial phase of the vibrational dynamic loading [ < 10000].

    magnitudes of the initial/original stiffness (elastic modulus) and the plasticity characteristics.

    1. Vibrational dynamic loading has distinctly significant impact on the geotechnical engineering properties, characteristics and geotechnical quantities of the gravelly geomaterials designated for use in pavement construction.

    2. As the dynamic loading increases, the deformation and impact stress resistance of thegravelly geomaterials reduces exponentially with the most drastic reduction exhibited within the initial (primary) phase of loading.

    3. Further research is required in order to determine a sustainable solution to the data collection and processing within the erratic zone which occurs within the region of very small strains (initial phase of the vibrational dynamic loading [ < 10000].

    errors, system compliance, low load intensity (limitation of transducer resolution) and environmental factors (Sec. IX) during VDL testing.

    errors, system compliance, low load intensity (limitation of transducer resolution) and environmental factors (Sec. IX) during VDL testing.

    5.

    5.

    Both Afmadow and Hudur gravels require OPMC stabilization in order to achieve the geotechnical engineering properties required for design & construction specifications of the ATR72 design aircraft.

    6.

    Both Afmadow and Hudur gravels require OPMC stabilization in order to achieve the geotechnical engineering properties required for design & construction specifications of the ATR72 design aircraft.

    6.

    It is crucially vital to consider the adverse effects of bedding

    It is crucially vital to consider the adverse effects of bedding

  8. ANALYSIS OF CUMULATIVE STRESS-STRAIN CHARACTERISTICS OF CLAYS AND GRAVELS UNDER

PROGRESSIVE VDL

Under this Section VIII, cumulative stress-strain characteristics of specimens subjected to dynamic loading are analyzed. The analysis includes evaluation of the effects of reconstitution/remolding, which are outlined under several preceding sub-Sections. This is achieved by comparing Pre- Construction (PrC) and Post-Constrution (PoC) results.

  1. Cumulative impact stress-strain characteristics of clayey geomaterials

    Figure 24 shows the impact of vibrational dynamic loading on cumulative impact stress of clays subjected to dynamic loading [ = 3.2 ] . It can be noted that clayey geomaterials with lower plasticity indices (PIs) exhibit

    higher cumulative impact stresses and that the Afmadow silty clay subgrade certainly requires ground improvement.

    Influence of Vibrational Dynamic Loading on Cumulative Impact Stress of Clayey Geomaterials

    Influence of Vibrational Dynamic Loading on Cumulative Impact Stress of Clayey Geomaterials

    500

    Cumulative Impact Stress @ Failure:

    450 =135.6kPa @ 383,600Cycles

    Strain @ Critical State: =3.83%

    400 Strain @ Failure: =5.33%

    350

    300

    250

    200

    150

    100

    50

    500

    Cumulative Impact Stress @ Failure:

    450 =135.6kPa @ 383,600Cycles

    Strain @ Critical State: =3.83%

    400 Strain @ Failure: =5.33%

    350

    300

    250

    200

    150

    100

    50

    0

    1000

    10000

    100000

    Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

    1000000

    10000000

    0

    1000

    10000

    100000

    Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

    1000000

    10000000

    Baraawe Silty Clay: PI=18%

    Afmadow Expansive Clay:PI=28%

    Neat BCS:PI=32%

    Baraawe Silty Clay: PI=18%

    Afmadow Expansive Clay:PI=28%

    Neat BCS:PI=32%

    Fig. 24. Impact of dynamic loading on cumulative impact stress of Clays

    [ = 3.2].

    The characteristics of the cumulative impact stress versus strain of clayey geomaterials are graphically depicted in Figure

    Cumulative Impact Stress, ci (kPa)

    Cumulative Impact Stress, ci (kPa)

    25. It can be noted that the Baraawe silty clay with the lowest PI exhibits the highest resistance to deformation.

    Effects of Cumulative Impact Stress on Deformation Characteristics of Clayey Geomaterials

    Effects of Cumulative Impact Stress on Deformation Characteristics of Clayey Geomaterials

    = × . + . × . + . . + .

    = × . + . × . + . . +.

    500

    500

    Cumulative Impact Stress @ Failure:

    =135.6kPa @ 383,600Cycles Strain @ Critical State: =3.83% Strain @ Failure: =5.33%

    450

    400

    350

    300

    250

    200

    150

    100

    50

    Cumulative Impact Stress @ Failure:

    =135.6kPa @ 383,600Cycles Strain @ Critical State: =3.83% Strain @ Failure: =5.33%

    450

    400

    350

    300

    250

    200

    150

    100

    50

    0.010

    0.100

    0

    1.000

    10.000

    0.010

    0.100

    0

    1.000

    10.000

    Axial Strain, a(%)

    Axial Strain, a(%)

    Baraawe Silty Clay: PI=18%

    Afmadow Expansive Clay: PI=28%

    Neat BCS:PI=32%

    Baraawe Silty Clay: PI=18%

    Afmadow Expansive Clay: PI=28%

    Neat BCS:PI=32%

    Fig. 25. Cumulative impact stress-strain characteristics of clays under dynamic loading.

  2. Cumulative impact stress-strain characteristics of gravelly geomaterials

    The impact of VDL on cumulative impact stress of gravels is graphically demonstrated in Figure 26 for loadings of up to [ = 10 ] . It can be noted that gravelly geomaterials with higher strengths and stiffness exhibit higher cumulative impact stresses (refer to results tabulated in Tables

    VII & VII in Section IV). It can further be observed that the influence of cumulative VDL on the impact stress is more pronounced within the loading zone of 100,000 ~ 1000,000 (one hundred thousand to one million) cycles, after which practically all modelled curves tend to a residual state with increased loading. On the other hand, the characteristics of the cumulative impact stress versus strain for gravels are depicted in Figure 27. It can be noted that the gravels with lower PIs and higher strengths and stiffness (elastic moduli) exhibit the highest resistance to deformation (refer to summary results in Tables VII & VII in Section IV).

    Influence of Vibrational Dynamic Loading on Cumulative Impact Stress of Somalia Gravels

    Influence of Vibrational Dynamic Loading on Cumulative Impact Stress of Somalia Gravels

    1000

    900

    800

    700

    600

    500

    400

    300

    200

    100

    0

    100000

    1000000

    Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

    10000000

    1000

    900

    800

    700

    600

    500

    400

    300

    200

    100

    0

    100000

    1000000

    Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

    10000000

    Hudur Gravel

    Afmadow Gravel

    Bardhere Gravel

    Diinsoor Gravel

    Hudur Gravel

    Afmadow Gravel

    Bardhere Gravel

    Diinsoor Gravel

    Cumulative Impact Stress, ci kPa)

    Cumulative Impact Stress, ci kPa)

    Cumulative Impact Stress, ci kPa)

    Cumulative Impact Stress, ci kPa)

    Fig. 26. Impact of dynamic loading on cumulative impact stress of Somalia gravels [ = 10].

    Effects of Cumulative Impact Stress on Deformation Characteristics of Somalia Gravel Geomaterials

    Effects of Cumulative Impact Stress on Deformation Characteristics of Somalia Gravel Geomaterials

    1000

    900

    800

    700

    600

    500

    400

    300

    200

    100

    0

    1000

    900

    800

    700

    600

    500

    400

    300

    200

    100

    0

    0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

    Axial Strain, a (%)

    0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

    Axial Strain, a (%)

    Hudur Gravel

    Afmadow Gravel

    Bardhere Gravel

    Diinsoor Gravel

    Hudur Gravel

    Afmadow Gravel

    Bardhere Gravel

    Diinsoor Gravel

    Fig. 27. Cumulative stress-strain characteristics of Somalia gravels under vibrational dynamic loading.

  3. Cumulative impact stress-strain characteristics of typical Somalia gravels under VDL: Effects of reconstitution/remolding

    Cumulative Impact Stress, ci kPa)

    Cumulative Impact Stress, ci kPa)

    The effects of reconstitution/remolding are analyzed through the comparison of the Pre-Construction (PrC) and Post- Construction (PoC) results shown in Figures 28 and 29.

    Influence of Vibrational Dynamic Loading on Cumulative Impact Stress of Somalia Geomaterials

    Influence of Vibrational Dynamic Loading on Cumulative Impact Stress of Somalia Geomaterials

    1000

    900

    800

    700

    600

    500

    400

    300

    200

    100

    PrC: Pre-Construction Stage

    PoC: Post-Construction Stage (Reconstituted/Remolded State)

    1000

    900

    800

    700

    600

    500

    400

    300

    200

    100

    PrC: Pre-Construction Stage

    PoC: Post-Construction Stage (Reconstituted/Remolded State)

    0

    100000

    1000000

    Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

    10000000

    0

    100000

    1000000

    Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

    10000000

    Hudur PrC

    Afmadow PrC Bardhere PrC Diinsoor PrC Bardhere PoC Diinsoor PoC

    Hudur PrC

    Afmadow PrC Bardhere PrC Diinsoor PrC Bardhere PoC Diinsoor PoC

    Fig. 28. Impact of dynamic loading on cumulative impact stress of gravels

    Figure 28 and the correlation between cumulative impact stress and cumulative progressive strain depicted in Figure 29 clearly show that reconstitution of the gravelly geomaterials reduces strength/stiffness and that the magnitude of this reduction is dependent upon the original strength, stiffness and plasticity index (refer to summary Tables VII & VII in Section IV).

    Effects of Cumulative Impact Stress on Deformation Characteristics of Somalia Gravel Geomaterials

    1000

    900

    800

    700

    600

    500

    400

    300

    200

    100

    0

    Effects of Cumulative Impact Stress on Deformation Characteristics of Somalia Gravel Geomaterials

    1000

    900

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    700

    600

    500

    400

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    100

    0

    0.01

    0.10

    Axial Strain, a (%)

    1.00

    0.01

    0.10

    Axial Strain, a (%)

    1.00

    Hudur Gravel

    Afmadow Gravel

    Bardhere Gravel

    Diinsoor Gravel

    Hudur Gravel

    Afmadow Gravel

    Bardhere Gravel

    Diinsoor Gravel

    Cumulative Impact Stress, ci kPa)

    Cumulative Impact Stress, ci kPa)

    Fig. 29. Cumulative impact stress-strain of Somalia gravels: LS

    [ = 10]: Comparison of Pre-Construction (PrC) and Post-construction (PoC) characteristics

    On the other hand, Figures 30 and 31 show the impact of progressive loading on the magnitude of axial strain (deformation) graphically plotted both in arithmetic and semi- log scale for clarity of comparison of this VDL impact on Pre- Construction (PrC) and Post-construction (PoC) characteristics simulating the effects of reconstitution/remolding and to enable proper analysis thereof.

    0.30

    0.25

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    0.05

    0.00

    0.30

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    0.00

    Axial Strain, a (%)

    Axial Strain, a (%)

    It can also be inferred from these figures that: i) reconstitution reduces the deformation resistance of gravelly geomaterials; and ii) the magnitude of resistance is proportional to the magnitude of the initial stiffness.

    Deformation Characteristics of Somalia Gravel Geomaterials Under Vibrational Dynamic Loading

    Deformation Characteristics of Somalia Gravel Geomaterials Under Vibrational Dynamic Loading

    0.50

    0.50

    0.45

    0.40

    = . . × . .

    0.45

    0.40

    = . . × . .

    0.35

    PrC: Pre-Construction

    PoC: Post-Construction

    0.35

    PrC: Pre-Construction

    PoC: Post-Construction

    0

    2000000

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    0

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    Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

    Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

    Hudur PrC

    Afmadow PrC

    Bardhere PrC

    Bardhere PoC

    Diinsoor PrC

    Diinsoor PoC

    Hudur PrC

    Afmadow PrC

    Bardhere PrC

    Bardhere PoC

    Diinsoor PrC

    Diinsoor PoC

    Fig. 30. Impact of dynamic loading on cumulative axial strain of Somalia

    [

    = 10]: Comparison of Pre-Construction (PrC) and Post-construction

    (PoC) characteristics

    gravels [ = 10]: Comparison of Pre-Construction (PrC) and Post- construction (PoC) characteristics.

    Comparison of Impact of Vibrational Dynamic Loading on Deformation of Gravel Geomaterials

    Comparison of Impact of Vibrational Dynamic Loading on Deformation of Gravel Geomaterials

    1. Influence of moisture-suction variation

1.200

1.200

= . . × . .

= . . × . .

1.000

1.000

Axial Strain, a (%)

Axial Strain, a (%)

As can be observed from Figures 32 and 33, plasticity index and mechanical stability (particle size and distribution) have significant influence on both static and dynamic strengths of clayey geomaterials as well as gravels.

0.800

0.800

0.600

0.600

0.400

0.400

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0.200

0.000

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1000000

10000000

0.000

10000

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1000000

10000000

Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)

Hudur Gravel

Afmadow Gravel

Bardhere Gravel

Diinsoor Gravel

Baraawe Silty Clay

Hudur Gravel

Afmadow Gravel

Bardhere Gravel

Diinsoor Gravel

Baraawe Silty Clay

Fig. 31. Impact of dynamic loading on cumulative axial strain of Somalia gravels [ = 10]: Log Scale (LS): Comparison of Pre-Construction (PrC) and Post-construction (PoC) characteristics.

500

Unconfined Compressive Strength, UCS (kPa)

Unconfined Compressive Strength, UCS (kPa)

450

400

350

300

250

200

150

100

50

0

Comparison of Static and Dynamic Strength of Clayey Geomaterials

Baraawe Silty Clay

Afmadow Silty Clay

Black Cotton Soil

18 20 22 24 26 28 30 32

Plasticity Index, PI (%)

Static Dynamic

  • Implication of Results in Section VIII: Simulation of pavement gravel characteristics subjected to VDL

1.

Reconstitution/remolding impacts adversely on the geotechnical

1.

Reconstitution/remolding impacts adversely on the geotechnical

Fig. 32. Impact plasticity index on static and dynamic strengths of clayey geomaterials.

Comparison of Static and Dynamic Strength of Somalia Gravels

engineering properties of gravelly geomaterials by reducing strength and deformation resistance (stiffness) making the geomaterials more susceptible to the impact of dynamic loading.

  1. Deformation resistance is predominantly dependent upon the magnitudes of the initial/original stiffness (elastic modulus) and the plasticity characteristics, particularly under dynamic loading.

  2. Vibrational dynamic loading has distinctly significant impact on the geotechnical engineering properties, characteristics and geotechnical quantities of the gravelly geomaterials designated for use in pavement construction.

  3. It is imperative to carry out further comprehensive analyses of the vibrational dynamic loading characteristics during the design stage in order to generate appropriate design parameters.

engineering properties of gravelly geomaterials by reducing strength and deformation resistance (stiffness) making the geomaterials more susceptible to the impact of dynamic loading.

  1. Deformation resistance is predominantly dependent upon the magnitudes of the initial/original stiffness (elastic modulus) and the plasticity characteristics, particularly under dynamic loading.

  2. Vibrational dynamic loading has distinctly significant impact on the geotechnical engineering properties, characteristics and geotechnical quantities of the gravelly geomaterials designated for use in pavement construction.

  3. It is imperative to carry out further comprehensive analyses of the vibrational dynamic loading characteristics during the design stage in order to generate appropriate design parameters.

Unconfined Compressive Strength, UCS (kPa)

Unconfined Compressive Strength, UCS (kPa)

1200

1100

1000

900

Hudur: Bardhere: Afmadow: Diinsoor:

Afmadow Coarse Particle Effect:

D60 = 10.5mm; D10 = 4.5mm

  1. PERFORMANCE EVALUATION OF VDL EFFECTS

    800

    700

    600

    500

    400

    Pre-Construction Data: Bardhere & Diinsoor

    Hudur, Bardhee & Diinsoor: D60 < 9mm; D10 < 0.1mm

    Structural performance simulation of subgrade and pavement geomaterials as well as discrete layers and composite pavement subjected to the effects of vibrational dynamic loading is to be carried out in [10] mainly in consideration of extreme changes in environmental conditions and factors in retrospect to the limiting design parameters.

    Based on the prevailing climatic conditions in Afmadow and

    8 9 10 11 12 13

    Plasticity Index, PI (%)

    Static Dynamic

    Fig. 33. Impact plasticity index on static and dynamic strengths of Somalia gravels: Without consideration of particle size effect

    Unconfined Compressive Strength, UCS (kPa)

    Unconfined Compressive Strength, UCS (kPa)

    Comparison of Static and Dynamic Strength of Somalia Gravels

    Hudur, locations of the aerodromes to be designed in Somalia, it was deemed imperative that moisture ~ suction variation be analyzed for both suction and dilatancy characteristics under dynamic loading conditions; the comprehensive testing regime of which is included in the testing matrix, modules defining basic protocols and main testing procedure presented in Section

    4.6 of Chapter 4 of [1].

    One of the main influencing factors with regard to the impact of moisture ~ suction variation is the PI (plasticity index); refer to [10] for the functional and applicable models as well as validation and comprehensive analytical discussions. An introductory example of influence of PI and correlation with mode of loading (dynamic static) is subsequently provided.

    1100

    1000

    900

    800

    700

    600

    500

    400

    8 9 10 11 12 13

    Plasticity Index, PI (%)

    Static Dynamic

    Fig. 34. Impact plasticity index on static and dynamic strengths of Somalia gravels: Corrected particle size effect.

    It can also be noted from these figures that, in general, the dynamic strengths are higher than static strengths for geomaterials with strengths lower than 700kPa ( 700). It can also be noted that whereas both static and

    dynamic strengths (UCS) reduce consistently for clayey geomaterials (Figure 32), the characteristic curves in Figure 33 are rather sinusoidal. This is attributable to the effect of mechanical stability (particle size fines content) as indicated in Figure 33. This fact is verified in Figure 34, which depicts the characteristic curves corrected for particle size effects.

    Simulation is therefore carried out, in [10], taking the effects of plasticity index, particle size, mechanical stability, agglomeration, among other factors, into account.

    1. Overall performance evaluation

      The overall structural performance evaluation of discrete layers and composite pavements is undertaken in [10].

  2. CONCLUSIONS

    1. Vibrational dynamic loading has distinctly significant impact on the geotechnical engineering properties, characteristics and geotechnical quantities of clayey subgrade and gravelly geomaterials for pavements.

    2. As the dynamic loading increases, the deformation and impact stress resistance of the clayey and gravelly geomaterials reduces exponentially with the most drastic reduction exhibited within the initial (primary) phase of loading.

    3. Designs based on comprehensive subgrade geomaterials, in- situ ground property and pavement geomaterials analyses of the effects of vibrational dynamic loading in retrospect to the maintenance of high standards of QCA are imperative in ensuring achievement of Performance Based Value Engineering (PB-VE) pavement structures.

    4. Deformation resistance is predominantly dependent upon the magnitudes of the initial/original stiffness (elastic modulus) and the plasticity characteristics.

    5. Reconstitution/remolding impacts adversely on the geotechnical engineering properties of gravelly geomaterials by reducing strength and deformation resistance (stiffness) making the geomaterials more susceptible to the impact of dynamic loading and environmental conditions/factors.

    6. Deformation resistance is predominantly dependent upon the magnitudes of the initial/original stiffness (elastic modulus) and the plasticity characteristics, particularly under vibrational dynamic loading.

    7. It is imperative to carry out further comprehensive analyses of the vibrational dynamic loading characteristics during the design stage in order to generate appropriate design parameters.

ACKNOWLEDGMENT

The author wishes to acknowledge, with utmost gratitude, the Japan International Cooperation Agency and Kajima Corporation (JICA) for substantially funding the initial stage of this research, the Materials Testing & Research Division (MTRD), Ministry of Transport, Infrastructure, Housing & Urban Development in Kenya, the University of Nairobi and Norconsult for carrying out the initial phase of testing as well as the Research Teams of Kensetsu Kaihatsu Engineering Consultants Limited and the Kenya Geotechnical Society (KGS) for their relentless efforts in providing the due assistance that culminated in the successful compilation of this paper.

REFERENCES

  1. Mukabi, J.N. & Sirmoi, F.W. Comprehensive Geomaterials Characterization for Design of Aerodrome Pavement Structures:Geotechnical Engineering Report, March 2019. Technical Report No. MFCR-AH-SOM01.

  2. Wichtmann, T., & Trantafyllidis, Th. Influence of a Cyclic and dynamic Loading History on Dynamic Properties of Dry Sand, Part I: Cyclic and Dynamic Torsional Prestraining, Journal of Soil Dynamics and Earthquake Engineering.

  3. Enomoto, T., Qureshi, O.H., Sato, T., and Koseki, J. Strength and Deformation Characteristics and Small Strain Properties of Undisturbed Gravelly Soils, Japanese Geotechnical Society, Soils and Foundations 2013, 53(6): pp. 951 965.

  4. Gabrys, K., Wojciech, S. & Sobol, E. Dynamic and Cyclic Static Loading Behavior of Silty-Sandy Clay at Small and Moderate Strains, Acta Sci. Pol. Architectura; 15(4) 2016: pp. 43 55.

  5. Mukabi, J.N. Characterization of consolidation stress-strain-time histories on the pre-failure behavior of natural clayey geomaterials, Proceedings of the VIth International Symosium on Deformation Characteristics on Geomaterials, Buenos Aires, 2015.

  6. Mukabi, J.N. Unique Analytical Models for Deriving Fundamental Quasi-Mechanistic Design Parameters for Highway and Airport Pavements:, International Journal of Engineering Research & Technology, Vol. 5 Issue 09, September-2016, pp. 61 77.

  7. Mukabi, J.N. & Wekesa, S.F. Case examples of successful application of a new PB-VE design approach for runway pavements in East Africa, Proceedings of the World Road Congress Workshop on Airfields, Seoul, South Korea, CD ROM; November 2015.

  8. Mukabi, J.N. & Hossain, Z. Characterization and Modeling of Various Aspects of Pre-failure Deformation of Clayey Geomaterials Fundamental Theories and Analyses, First International Conference on Geotechnique, Construction Materials and Environment GEOMAT, Mie, Japan, November, 2011.

  9. Mukabi, J.N. Characterization and Modeling of Various Aspects of Pre- failure Deformation of Clayey Geomaterials Application of Models, First International Conference on Geotechnique, Construction Materials and Environment GEOMAT, Mie, Japan, November, 2011.

  10. Mukabi, J.N. Comprehensive Quasi-Mechanistic Analytical Approach for Evaluating Structural Performance of Highway and Aerodrome Pavements Under Vibrational Dynamic Loading, unpublished.

  11. US Army Engineer Waterways Experimental Station, Corps of Engineers. A Procedure for Determining Elastic Moduli of Soils by Field Vibratory Techniques, Miscellaneous Paper No. 4-577; June, 1963.

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