Functional Analytical Models for Characterizing Wholly Encapsulated Confinement Systems for Design of Geo-Structures

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Functional Analytical Models for Characterizing Wholly Encapsulated Confinement Systems for Design of Geo-Structures

John Ngaya Mukabi

R&D/Design Dept.

Kensetsu Kaihatsu Consulting Engineers Ltd.

Nairobi, Kenya

Abstract Although wholly encapsulated confinement systems (WECS) typically utilizing steel mesh for gabions and polymeric/soilbag encapsulation are established technologies in terms of application for temporary structures, the theory and its employment for permanent structures has only recently been inducted. The analytical models introduced in this paper are developed on the premise that the associated scientific theories and structural/geotechnical engineering concepts are explicated and that further advances are to be made in R&D (research & development) supported by comprehensive investigations based on rigorous laboratory and in-situ (field) testing, full-scale model testing, analytical modelling, numerical simulation as well as monitoring and evaluation. Examples of parameters generated using the proposed analytical models that can be adopted for developing design catalogues for structural foundations and full-depth pavements structures for unpaved and paved (sealed) LVRs (low volume roads) are provided. Possible functions and attested applications are also introduced.

Keywords Encapsulated confinement system, WECS, analytical models, design, geo-structures, fill geomaterial.

  1. INTRODUCTION

    1. Background for developing analytical models

      For a long time, wholly encapsulated confinement systems (WECS) such as soilbags (do-nou in Japanese) have been used to prevent flow of soils from floodwaters and building temporary structures in cases of emergency. However, until as recent as 1991 no application of soilbags had been made for building permanent structures {[1], [2], [3]}. This might have been due to lack of knowledge about the mechanical behaviour of soilbags and the deterioration thereof after an extended period of exposure to sunlight, especially the polyethylene made soilbags which are very sensitive to ultraviolet rays (sunlight). Findings of research trials carried out in Kenya inspired the development of the application of the WECS earth reinforcement technology for road foundation. In Japan, for example, this reinforcing method has been successfully applied in such cases as for the reinforcement of ballast foundation under railway sleepers, reinforcement for soft building foundations and the construction of embankments and retaining walls [3]. In these applications, attention was paid to protect soilbags from sunlight by either embedding them in the ground or using thin facing concrete slabs/columns.

      Essentially, external loading on the WECS enables mobilization of the tensile strength of the fabric of the bag,

      which enhances the bearing capacity of the soil by several times depending on the tensile strength/stiffness of the soilbag fabric and properties of the fill geomaterials. Experimental testing and investigations have indicated the possible increase of the bearing capacity (load) of a soft building foundation by as high as 5-10 times [2]. In this Study, the WECS considered is predominantly a system of geomaterials encapsulated within varying types of polymeric bags.

      The analytical models developed in this Study can be applied in a wide range of encapsulated units of geo- structures including foundations, pavements, embankments, reinforced earth retaining walls, among others.

    2. Theoretical and conceptual considerations

      As depicted in Figures 1 ~ 5, when WECS are progressively subjected to external loading, varying modes of encapsulation, cellular and laminated confinement/reinforcement mechanisms become prevalent depending on the stage and/or conditions of loading. The considerations in this respect include: (a) fully encapsulated; (b) partially encapsulated; (c) cellular confinement; (d) discrete planar frictional/bonding confinement/resistance; and (e) laminated planar frictional/bonding confinement/resistance. As demonstrated in these figures, the number of nodes and encapsulating planes determine the degree of influence of the prevalent mechanisms on the magnitude of the tensile resistance and strength/stiffness developed.

      A comparison of Figures 1 and 2 explicitly shows the significantly enhanced efficacy resulting from the mechanisms of a fully encapsulated confinement system. The rupture of the loading plane is simulated in consideration of unpaved roads, whereby sections of the gravel wearing course are totally depleted resulting in exposure of the do-nou (soilbags) to tyre traction stresses and sunlight which end up causing the rupture of the soilbag. Theoretically, the fully encapsulated confinement system can be considered in terms of 3D planes, whilst the partially encapsulated confinement system consists of 2D planes.

      Tensile Stress Mobilization

      The following considerations define the modes presented in Figures 1 ~ 5. The examples are based on results reported in [4].

      1. Fully encapsulated (Fig. 1): Entails that all the three dimensional (3D) planes are triggered into the action of total confinement acting as a composite slab generating tensile stresses in all 3D planes to provide resistance to the external loading (Figure 6). This would occur during the advanced stages of pre-failure and at failure when the tensile stresses are fully mobilized. Note that full encapsulation involves all

        Fig. 1. Fully encapsulated confinement system tensile stresses highly mobilized due to external loading (Figure 6): Soil particles are densely packed resulting in reduced voids ratio, enhanced confining stress, density, shearing resistance, bearing strength/capacity and apparent cohesion.

        Rupture Plane of Exposed Do-nou

        Tensile Stress Mobilization

        Fig. 2. Partially encapsulated confinement system tensile stresses partially mobilized due to external loading (Figure 7): Increase in voids ratio resulting in decrease in confining stress, density, shearing resistance, bearing strength/capacity and apparent cohesion.

        Fig. 3. Cellular confinement: Tensile stress mobilization concentrated in the along the lateral 2D planes (Figure 8).

        .

        Fig. 4. Discrete planar frictional/bonding confinement/resistance: Surface acting as a geotextile

        Fig. 5. Laminated planar frictional/bonding confinement/resistance: Surface acting as a laminated geotextile with enhanced tensile properties.

        the subsequent mechanisms explained from Figures 2 ~ 5.

        Fig. 6. Cross-sectional perspectives of single layer embedded do-nou (soilbags): (a) schematic of log profile; and (b) trial pit excavated during performance evaluation of the Kirima ~ Kianoe Road in Nakuru County (MTRD Evaluation Report No. 1314: April, 2018).

      2. Partially encapsulated (Fig. 2): This phenomenon would occur after total loss of the overlaying gravel wearing course when the upper plane (external loading stress recipient plane) of the soilbags is exposed as shown in Figure 7. In this case partial encapsulated confinement occurs due to the two lateral planes and the bottom horizontal plane in direct contact with the pavement foundation or subgrade.

        Fig. 7. Exposed do-nou (soilbags) resulting from total loss of overlaying gravel wearing course investigated during performance evaluation of the trial/improved sections in Embu County, Kenya (MTRD Evaluation Report No. 1314: April, 2018).

      3. Cellular confinement (Fig. 3): The phenomenon of cellular confinement systems is well illuminated by geocells in general and the loading and failue modes [5], geocell confinement geometry (Figure 8b) and the lateral confinement mechanisms depicted in Figure 8a. In this case,

        as can be derived from the LHS depiction in Figure 8, the geocell triggers tensile stress mobilization as a result of lateral confinement and stabilizes the subgrade reaction against external loading. With reference to WECS, the bottom, if intact (not depleted) would provide additional tensile resistance and further stabilization to the subgrade reaction. This would occur after total depletion of the overlaying gravel wearing course when the upper plane (external loading stress recipient plane) of the soilbags is exposed as shown in Figure 7 above.

        Fig. 8. Cellular confinement: a) tensile stress mobilization concentrated in the along the lateral 2D planes; and b) reinforcing geometry and mechanisms..

      4. Discrete planar frictional/bonding confinement/resistance (Fig. 4): This mechanism would be analogous to the one exhibited by a geotextile embedded within a pavement layer to act as a reinforcing element. The stabilization/reinforcement of the layer within which it is embedded results from the friction and bonding of the geotextile with the soil particles within the particular layer generating a zone of influence of specific interface thickness and characteristics.

        In consideration of the tensile strength/stiffness development of the WECS, the frictional/bonding confinement/resistance actually occurs in the initial stage of loading prior to the prevalence of full encapsulation mechanisms (vicinity of the loading surface in Figure 9b on the RHS). This action would be predominant within the elastic and elasto-plastic zones of the kinematic hardening framework.

        Fig. 9. Transformation of shear surface resulting in reinforcement of subgrade due to inclusion of frictional geotextile.

      5. Laminated planar frictional confinement/resistance (Fig. 5): Figure 10, which depicts cross-sectional perspectives of a log profile and trial pit, is an example of a multi-layer structural application of WECS soilbags (do-nou).

        t can be observed from Figure 10a that a laminated interface exists between the first and second layers of the

        WECS. As validated in sub-Sections II-E. and II-F., the tensile strength increases in proportion to the number of layers and lamination interfaces, respectively. Accordingly, therefore, it is essential that these characteristics are taken into account during the design and structural performance evaluation WECS geostructures

        Fig. 10. Cross-sectional perspectives of double layer embedded do-nou (soilbags): (a) schematic of log profile; and (b) trial pit excavated during performance evaluation of the Kerugoya ~ Kamondo Road in Kirinyaga County (MTRD Evaluation Report No. 1314: April, 2018).

    3. Fundamental considerations of design approach

    The fundamental considerations for choice of the appropriate design for WECS technology are mainly influenced by overlay thickness of layer covering the soilbags and type of surfacing, details of which are discussed in Section II and Section IV.

  2. FUNDAMENTAL STRUCTURAL DESIGN PRINCIPLES

    1. Criteria for development of structural design principles

      In deriving the structural design principles, consideration of the fundamental design aspects including philosophy/criteria, climatic and environmental conditions, mode of interpretation/evaluation of traffic/load factors, materials characterization and classification, analyses of vital mechanisms required for appropriate use of WECS soilbags and the effective evaluation thereof for purposes of advancing this technology were made accordingly. Methods of evaluation and optimization of the accruing benefits are also included as integral considerations.

      In particular, the following considerations have been made:

      i) the reinforcement/improvement/stabilization mechanisms resulting from the use of the WECS technology; ii) strength and stiffness development soil mechanics theories and geotechnical engineering concepts; iii) appropriate methods of evaluating the developed bearing capacity; iv) influence of the size and shape of the WECS (soilbags); v) encapsulation characteristics and contribution to deformation resistance; vi) performance evaluation of the possible functions associated with the use of do-nou; vii) the fundamental design criteria including loading characteristics and stress-strain behavior, failure criterion for the bags, composite WECS, WECS foundation and natural/existing subgrade, area coverage ratio, relevant and appropriate partial factors and design life; viii) evaluation of material properties and the appropriate selection criteria of the reinforcing elements and fill geomaterials; ix) characterization of encapsulated fill geomaterials; x) criteria for evaluation of applicability and benefits; xi) criteria for

      selected pavement structural configurations provided within the charts in Chapter 5 of this DG-4; and xii) criteria for the developed design catalogues that are presented in [6].

    2. Strength and stiffness development mechanisms

      Based on the theoretical and conceptual considerations elucidated in the preceding Section I, strength and stiffness development mechanisms prevail when soilbags are externally loaded and tensile stresses are mobilized as a result. This

      angle of internal friction/shearing resistance, , which is a significantly influential parameter, be appropriately determined from triaxial tests. However, given the complexity and the fact that it is scarcely available, the following model

      and Table I can be employed in converting the values determined from direct shear testing to equivalent values that would be obtained from triaxial tests.

      , = [0.72057(6.3196 0.9019)] (7)

      ,

      advantage is used to reinforce various geo-structures including Table I provides a summary of useful values for within

      soft foundations for pavements and buildings, embankments and retaining walls. In general, as shown in Figure 1, use of soilbags becomes effective when they are subjected to vertical forces from the upper structures. Figure 1 shows a soilbag subjected to principal stresses, at failure; 1 and 3 from a two dimensional perspective. Considering that the fill material within the soilbag is frictional and granular, to an appreciable extent, at constant volume condition and under the actions of 1 and 3 , the total perimeter of the bag would usually increase as a result of reduction in the height (thickness) due to the compaction/consolidation/compression effects on the fill geomaterial.

      Subsequently, the bag compacts vertically and a tensile force T is developed along the 3D planes of the soilbag fabric. The dilatancy occurring inside the bag helps to develop high tensile forces. The tensile force T produces additional stresses that act on the particles inside the soilbag whose vertical and horizontal (lateral) components are expressed as defined in

      the range that is typically encountered.

      Direct Shear, ds ()

      20

      25

      28

      30

      32

      34

      36

      38

      40

      42

      44

      46

      48

      50

      Triaxial Equivalent, tx ()

      26.5

      30.6

      32.9

      34.4

      35.9

      37.3

      38.8

      40.1

      41.5

      42.8

      44.2

      45.5

      46.7

      48.0

      42

      Direct Shear, ds ()

      20

      25

      28

      30

      32

      34

      36

      38

      40

      44

      46

      48

      50

      Triaxial Equivalent, tx ()

      26.5

      30.6

      32.9

      34.4

      35.9

      37.3

      38.8

      40.1

      41.5

      42.8

      44.2

      45.5

      46.7

      48.0

      TABLE I. CONVERSION OF VALUES FROM DIRECT SHEAR TESTS TO THE TRIAXIAL EQUIVALENTS.

      3

      3

      On the other hand, Equation (5) can be verified by considering the model adopted in defining and quantifying the apparent cohesion that prevails due to soilbags (geotextile) reinforcement as is expressed in Equation (8).

      = (8)

      3

      3

      where, is the apparent increase in confining stress as a result of WECS soilbags reinforcement, which is defined in Equation (9) with slight modification to account for the fully encapsulated confinement effects as exhibited by the WEC system.

      Equations (1) and (2), respectively.

      = 2

      (1)

      = 0.7(6 ) 2

      3

      3

      3

      3

      (9)

      01 (×)

      Substituting for in Equation (8) yields:

      and,

      = [0.7(6 ) 2]

      (10)

      = 2

      (2)

      03 (×)

      where and are the width and height of the soilbag, respectively and is the length which is considered to be unity ( = 1).

      1

      1

      Thus, as illustrated in Figure 1, the stresses acting on the particles are the combination of external stresses and stress caused by the tensile force (T) of the Do-nou fabric. At failure, the major effective principal stress can be calculated from Equation (3):

      Note that model Equations (9) and (10) account for the effects of intrinsic mechanical stability (gradation) of the fill geomaterial in terms of the average maximum particle size whose typical representative value for gravelly material is considered to be between: = 8 (0.008) and

      = 10 (0.01) based on the results from [4].

      Validation is achieved by comparing the apparent cohesion

      values computed using Equations (5) and (10) for varying quality of fill geomaterial defined in terms of the angle of

      = ( + 2)

      2

      (3)

      internal friction/shearing resistance and ultimate tensile

      1

      3

      strengths for the two typical polyethylene that can be available

      On the other hand, based on soil mechanics principles for

      cohesive-frictional geomaterial ( ) in general and

      in Kenya. The comparison is made in Table II and graphically

      demonstrated in Figure 11.

      pertinent stress ratio concepts in particular, 1 can be expressed in terms of strength @ failure as:

      = + 2 (4)

      Based on the virtually perfect superimposition of the characteristic curves depicted in Figure 11, it can be derived that Equation (5) is very well validated. Consequently, it is also

      1 3

      1

      1

      where, is the apparent cohesion resulting from the tensile stresses acting on and within the soilbag, Now, taking the RHS term in Equation (4), substituting in Equation (3),

      rearranging the terms and solving for yields:

      = ( 1) (5)

      verified that values for the apparent cohesion generated from either Equation (5) or Equation (10) that are summarized in Table II are applicable in design. The models shall be adopted directly in cases where there are changes in soilbag dimensions and/or maximum particle size of the fill geomaterial is

      significantly greater than 10mm. However, it should be noted

      1+( )

      = 1( )

      (6)

      that, for optimal results using the WECS soilbag technology, the UBL upper boundary limit of the maximum particle size is:

      From Figure 1, it is inferred that the soilbag can be considered to be under triaxial conditions. In order to better simulate these conditions therefore, it is advisable that the

      = 20 (0.02)

      Type of Fabric (Material)

      Polyethelene

      Polypropylene

      Polyester

      Tult. (kN/m)

      6.6

      11.2

      20

      Country of Ori gin

      China

      Kenya

      Japan

      AIF/ASR,

      tx

      Coefficient of Passive Earth Pressure, Kp

      Apparent Cohesion, cR (kPa)

      Eq. (5)

      Eq. (10)

      Eq. (5)

      Eq. (10)

      Eq. (5)

      Eq. (10)

      20

      2.040

      83

      90

      140

      152

      251

      272

      25

      2.464

      93

      99

      158

      167

      282

      299

      28

      2.770

      100

      104

      170

      177

      303

      317

      30

      3.000

      105

      109

      178

      185

      318

      330

      32

      3.255

      110

      113

      187

      192

      333

      343

      34

      3.537

      115

      118

      196

      200

      350

      358

      36

      3.852

      121

      123

      206

      209

      367

      373

      38

      4.204

      127

      129

      216

      218

      386

      390

      40

      4.599

      134

      135

      227

      228

      406

      408

      42

      5.045

      141

      141

      239

      239

      427

      427

      44

      5.550

      148

      148

      252

      251

      450

      448

      46

      6.126

      157

      155

      266

      264

      475

      471

      48

      6.786

      166

      164

      281

      278

      502

      496

      50

      7.549

      175

      173

      298

      293

      531

      523

      Type of Fabric (Material)

      Polyethelene

      Polypropylene

      Polyester

      Tult. (kN/m)

      6.6

      11.2

      20

      Country of Ori gin

      China

      Kenya

      Japan

      AIF/ASR,

      tx

      Coefficient of Passive Earth Pressure, Kp

      Apparent Cohesion, cR (kPa)

      Eq. (5)

      Eq. (10)

      Eq. (5)

      Eq. (10)

      Eq. (5)

      Eq. (10)

      20

      2.040

      83

      90

      140

      152

      251

      272

      25

      2.464

      93

      99

      158

      167

      282

      299

      28

      2.770

      100

      104

      170

      177

      303

      317

      30

      3.000

      105

      109

      178

      185

      318

      330

      32

      3.255

      110

      113

      187

      192

      333

      343

      34

      3.537

      115

      118

      196

      200

      350

      358

      36

      3.852

      121

      123

      206

      209

      367

      373

      38

      4.204

      127

      129

      216

      218

      386

      390

      40

      4.599

      134

      135

      227

      228

      406

      408

      42

      5.045

      141

      141

      239

      239

      427

      427

      44

      5.550

      148

      148

      252

      251

      450

      448

      46

      6.126

      157

      155

      266

      264

      475

      471

      48

      6.786

      166

      164

      281

      278

      502

      496

      50

      7.549

      175

      173

      298

      293

      531

      523

      TABLE II. SUMMARY OF APPARENT COHESION VALUES APPLICABLE IN DESIGN.

      summary of ranges of bearing capacity values determined from unconfined compression tests that can be applicable in the evaluation of bearing capacity of discrete WECS soilbags. It is important to note that the bearing capacity of the soilbags is mainly a function of the ultimate tensile strength as well as the apparent lateral/confining stress and apparent cohesion, which increase due to the mobilized tensile stresses as a result of the fully encapsulated confinement effect.

      S/N

      Type of Fabric Material

      Ultimate Tensile Strength (kN/m)

      Range of Load/ Strength/Stiffness

      Fill Geomateri als

      Load

      @ Failure (kN)

      Bearing Strength (Stiffness)

      @ Failure (MPa)

      1.

      Polyethylene (PE)

      12

      230 –

      280

      1.44 1.75

      (390 –

      625)

      Crushed Stone/Sand

      2.

      Polyester (PET)

      20

      540 –

      640

      3.375 4.0

      (4350 –

      7450)

      Crushed Stone/Sand

      3.

      Polypropylene (PP)

      6.6

      250 –

      300

      1.56 1.875 (470 – 750)

      Lateritic Gravel

      S/N

      Type of Fabric Material

      Ultimate Tensile Strength (kN/m)

      Range of Load/ Strength/Stiffness

      Fill Geomateri als

      Load

      @ Failure (kN)

      Bearing Strength (Stiffness)

      @ Failure (MPa)

      1.

      Polyethylene (PE)

      12

      230 –

      280

      1.44 1.75

      (390 –

      625)

      Crushed Stone/Sand

      2.

      Polyester (PET)

      20

      540 –

      640

      3.375 4.0

      (4350 –

      7450)

      Crushed Stone/Sand

      3.

      Polypropylene (PP)

      6.6

      250 –

      300

      1.56 1.875 (470 – 750)

      Lateritic Gravel

      TABLE III. APPLICABLE RANGE FOR BEARING CAPACITY.

      600

      Resulting Apparent Cohesion, cR (kPa)

      Resulting Apparent Cohesion, cR (kPa)

      500

      400

      Comparison of Apparent Cohesion Computed from Model Equations (5) and (10)

      300

      200

      100

      0

      20 25 30 35 40 45 50

      2) Mathematical models for estimating bearing capacity based on UCS testing

      Useful mathematical/analytical models for estimating the bearing strength/capacity of WECS soilbags are introduced. Under unconfined compression conditions, the minor principal stress, 3 does not take effect. In other words, 3 = 0 . Essentially therefore, considering 3 = 0 and substituting the same in Equation (3) and rearranging the terms, the major

      Angle of Internal Friction/Shearing Resistance, ' ()

      principal stress, can be predicted from Equation (12).

      T=6.6 Eq. (5) T=6.6 Eq. (10) T=11.2 Eq. (5) T=11.2 Eq. (10) T=20 Eq.(5) T=20 Eq.(10)

      1

      = (2) [() 1] (12)

      Fig. 11. Comparison of apparent cohesion values determined from analytical

      1

      model Equations 5 and 10.

      Note that the values summarized in Table II are for areas with

      The load at failure can be predicted by introducing the planar dimensions comprising of the width, and the length,

      of the soilbag as is expressed in Equation (13).

      flat terrain. In other words, the load is vertical without

      = (2) [()

      1] × × (13)

      inclination ( = 0), where is the angle of the slope. For sloppy areas these values are corrected using Equation (11).

      () = { ( = 0°) × (2), (0° 45°) 0, (45° 90°)

      Essentially therefore, considering = 0 and substituting

      3

      3

      the same in Equation (3) yields:

      (11) = 2

      2

      (14)

      1

    3. Analytical evaluation of strength and stiffness properties

      Key Standard methods of evaluating the bearing capacity of WECS do-nou include experimental testing and

      Multiplying the RHS of Equation (14) by to derive

      1

      1

      common terms and rearranging the terms enables the major principal stress, to be predicted from Equation (15).

      mathematical models. Standard methods of testing that have

      = (2) [()

      1] (15)

      been adopted to evaluate the bearing capacity include the UCS

      1

      (Unconfined Compressive Strength) in the laboratory and the PL/BT (Plate Loading/ Bearing Test).

      The load at failure can then be predicted by introducing the planar dimensions comprising of the width, and the length,

      of the soilbag as is expressed in Equation (16).

      = (2) [()

      1] × × (16)

      1. Guidance on range of bearing capacity and stiffness based on unconfined compression strength (UCS) tests.

        Laboratory tests, detailed in [4] and [7], carried out on WECS show strength improvement of up to ten times that of the unreinforced soil. On the other hand, Table III presents a

        Considering that the post-compaction dimensions of the WECS do-nou to be the same in all cases of application, it can be derived that = and = 4. Taking advanage of these relations, Equations (15) and (16) can be derivatively

        expressed to be dimensionally dependent on only the thickness (height), of the WECS soilbag by substituting for in Equations (15) and (16), Equations 17 and 18 are obtained.

        an average value determined from literature and in consideration of a yield strain of = 15% of the WECS do- nou (soilbag) fabric (refer to Table VII).

        = (2) [(4)

        1] (17)

        1

        4

        TABLE IV. PREDICTED PARAMETRIC VALUES APPLICABLE

        = (2) [(4)

        1] × 42 (18)

        FOR TESTING, DESIGN, CONSTRUCTION QCA AND STRUCTURAL

        1

        4

        PERFORMANCE FOR BEARING CAPACITIES @ FAILURE.

        Type of Fabric

        PE

        PP

        PET

        Tult. (kN/m)

        6.6

        11.2

        20

        Country of Origin

        China

        Kenya

        Japan

        AIF/ASR,

        tx

        Coefficient of Passive Earth Pressure, Kp

        Bearing Capacity, 1f (kPa)

        20

        2.040

        255

        433

        774

        25

        2.464

        316

        536

        957

        28

        2.770

        360

        610

        1090

        30

        3.000

        392

        666

        1189

        32

        3.255

        429

        728

        1299

        34

        3.537

        469

        796

        1421

        36

        3.852

        514

        872

        1558

        38

        4.204

        564

        957

        1710

        40

        4.599

        621

        1053

        1881

        42

        5.045

        684

        1161

        2073

        44

        5.550

        756

        1283

        2292

        46

        6.126

        839

        1423

        2541

        48

        6.786

        933

        1583

        2827

        50

        7.549

        1042

        1767

        3156

        Type of Fabric

        PE

        PP

        PET

        Tult. (kN/m)

        6.6

        11.2

        20

        Country of Origin

        China

        Kenya

        Japan

        AIF/ASR,

        tx

        Coefficient of Passive Earth Pressure, Kp

        Bearing Capacity, 1f (kPa)

        20

        2.040

        255

        433

        774

        25

        2.464

        316

        536

        957

        28

        2.770

        360

        610

        1090

        30

        3.000

        392

        666

        1189

        32

        3.255

        429

        728

        1299

        34

        3.537

        469

        796

        1421

        36

        3.852

        514

        872

        1558

        38

        4.204

        564

        957

        1710

        40

        4.599

        621

        1053

        1881

        42

        5.045

        684

        1161

        2073

        44

        5.550

        756

        1283

        2292

        46

        6.126

        839

        1423

        2541

        48

        6.786

        933

        1583

        2827

        50

        7.549

        1042

        1767

        3156

        The equations hence take the simplified form defined in model Equations (19) and (20).

        = (

        = (

        1

        2

        ) [4 1] (19)

        The load at failure can be predicted by introducing the planar dimensions of the soilbag as is expressed in Equation (20).

        = ( ) [4

        1] × 162 (20)

        2

        Note that these prediction equations are significantly important mainly due to the following advantages/facilitation.

        1. Enable estimation of the stresses and loads at failure which can be adopted in design in the absence of testing facilities. This is quite simply possible based on the magnitude of the ultimate tensile strength, of the soilbag material and the angle of internal friction/shearing resistance, of the fill

          geomaterials, parameters which are knowns or can be derived from simple tests and/or models.

        2. Enable design of appropriate loading capacities for the load components for UCS laboratory tests.

        3. Stiffness (elastic modulus) can be predicted by using these results and small strain sophisticated predictive models.

        4. The parameters can be adopted for the design of pre- construction trial sections, construction QCA and structural performance evaluation.

          It is essential, however, to note that Equations (14) ~ (20) do not take the deformation (change in the dimensions) of the

          Notes: PE Polyethylene; PP Polypropylene; PET Polyester.

          The predicted values show extremely good compatibility with experimental test results reported in international publications (deviation/difference within ±10% ). Application of these values is therefore recommended. Note that the model defined in Equation (21) should be adopted in cases where the soilbag fill geomaterial exhibits high shearing resistance.

          Influence of Coefficient of Passive Earth Pressure and Ultimate Tensile Strength on the Encapsulated Minor Principal (Confining) Stress

          WECS soilbags, which undergoes progressive loading to

          failure, into consideration. This influences the confidence level of the predicted parameters. In order to circumvent this problem, a deformation parameter, which is a function of the ultimate tensile strength, of the soilbag material, the angle of internal friction/shearing resistance, of the fill geomaterials

          and the soilbag initial thickness, , is introduced. The deformation parameter, can be computed from Equation

          (21) and introduced as a multiplier in Equations (14) ~ (20).

          3500

          Encapsulated Bearing Strength/Capacity, 3f (kPa)

          Encapsulated Bearing Strength/Capacity, 3f (kPa)

          3000

          2500

          2000

          1500

          1000

          500

          0

          T: U

          PE:

          PP:

          ltim Poly Pol

          ate T ethy yprop

          ensi lene yle

          le S

          ne

          treng

          th in

          kN/

          m

          PET

          : Po

          lyest

          er

          td/>

          1 2 3 4 5 6 7 8

          = 0.04251(0.0321 )

          (21)

          Coefficient of Passive Earth Pressure, Kp

          .

          T=6.6 (PE) T=11.2 (PP) T=20 (PET)

          On the other hand, where the deformation, can be

          estimated, then Equations (22) can be adopted based on the concept of constant volume associated with fully encapsulated confinement systems.

          Influence of Angle of Shearing Resistance/Internal Friction and Ultimate Tensile Strength on the Encapsulated Minor Principal (Confining) Stress

          Encapsulated Bearing Strength/Capacity, 1f (kPa)

          Encapsulated Bearing Strength/Capacity, 1f (kPa)

          3500

          T: Ultimate Tensile Strength in kN/m

          PE: Polyethylene

          = (

          ) [4

          1] (22)

          3000

          PP: Polypropylene

          PET: Polyester

          1

          2()

          2500

          The load at failure can be predicted by introducing the planar dimensions of the soilbag as is expressed in Equation (23).

          2000

          1500

          1000

          = (

          ) [4

          1] × 16( + )2 (23)

          500

          0

          0

          2()

          Equations (22) and (23) are employed in generating Table IV that is applicable for predicting bearing capacities and loads, for testing, design, construction QCA and structural performance evaluation. In this table, the deformation at failure is accounted for as: = 7.5(0.0075), which is

          10 15 20 25 30 35 40 45 50

          Angle of Shearing Resistance/Internal Friction, f ()

          T=6.6 (PE) T=11.2 (PP) T=20 (PET)

          Fig. 12. Effects of ultimate tensile strength of soilbag fabric on encapsulated bearing capacity with varying: a) coefficient of passive earth pressure; and,

          b) angle of shearing resistance.

          3

          3

          Thus Another integral factor to consider is that, as a result of the tensile stresses mobilized within the soilbag apparent intrinsic confining stress, and apparent intrinsic cohesion,

          3

          3

          will be progressively prevalent to failure. can be derived from Equation (3) as follows.

          On the other hand, the apparent intrinsic cohesion, is derived on the basis of Equations (4), (22) and (29) taking the effect of the apparent confining stress, into account.

          3

          3

          Rearranging the terms in Equation (4) as an expression defining , yields:

          2

          2

          ( + )

          3 = 1

          +

          (24)

          1

          3

          = 1 ( 2

          + 2) (25)

          =

          2

          (30)

          3

          1

          Substituting for and from Equations (22) and (29)

          1 3

          1

          1

          Substituting for in Equation (25) from the expression in

          the following expression is obtained.

          Equation (22) yields Equation (26).

          (41)

          =

          [1 ] (31)

          = 1 {[( ) (4

          1)] 2 + 2} (26)

          4()

          3 2()

          Consequently, the apparent intrinsic cohesion,

          can be

          Equation (26) can be rewritten as:

          quantitatively evaluated from Equation (32).

          =

          (4 1)

          [( ) (4

          1)] (27)

          (41)

          (32)

          3

          2

          ()

          4

          =

          =

          and further rearranged to:

          = (41) [ ( )]

          Note that Equations (19) ~ Equation (32) can further be simplified by considering the specified height/thickness as a

          3

          2()

          (28)

          constant value, = 0.1.

          3

          3

          Consequently, can be quantitatively evaluated from Equation (29).

          = (41) (29)

          1. Model and full-scale testing

            In order to advance the understanding and capacity to elucidate the mechanisms of fully encapsulated confinement

            3

            2()

            systems and establish standard methods of strength, stiffness and performance evaluation, it is imperative that innovative

            Encapsulated Apparent Cohesion, CR (kPa)

            Encapsulated Apparent Cohesion, CR (kPa)

            600

            500

            400

            300

            200

            100

            0

            Influence of Coefficient of Passive Earth Pressure and Ultimate Tensile

            Strength on the Encapsulated Apparent Cohesion

            T: U

            PE:

            PP:

            ltim Poly Poly

            ate ethy pro

            nsile ne lene

            Stre

            ngt

            h in

            kN/

            m

            PET

            : Pol

            yest

            r

            T: U

            PE:

            PP:

            ltim Poly Poly

            ate ethy pro

            nsile ne lene

            Stre

            ngt

            h in

            kN/

            m

            PET

            : Pol

            yest

            r

            Te le py e

            1 2 3 4 5 6 7 8

            Coefficient of Passive Earth Pressure, Kp

            T=6.6 (PE) T=11.2 (PP) T=20 (PET)

            modelling and full-scale testing is undertaken rigorously. Guidelines on the appropriate and innovative methods of testing are provided in [8].

          2. Field (in-situ) investigations

          The most pragmatic method of evaluating the strength, bearing capacity, stiffness and degree of performance enhancement is to perform field investigations and in-situ testing. The methods of in-situ testing that have been performed to evaluate the bearing capacity of do-nou improved road sections include the DCP (dynamic cone penetrometer) for determining the CBR (California Bearing Ratio) and the PB/LT (plate bearing/loading tests).

          Figure 14 depicts the recommended mode of determining stiffness (surface modulus) from PB/LT (plate bearing/loading) measurements.

          Encapsulated Apparent Cohesion, CR (kPa)

          Encapsulated Apparent Cohesion, CR (kPa)

          600

          500

          400

          300

          Influence of Angle of Shearing Resistance/Internal Friction and Ultimate

          td>

          ate T thyl prop

          T: U

          PE:

          PP:

          ltim Polye Poly

          ensil ene ylene

          e Stre

          ngth

          in k

          N/m

          PET:

          Poly

          este

          r

          T: U

          PE:

          PP:

          ltim Polye Poly

          ate T thyl prop

          ensil ene ylene

          e Stre

          ngth

          in k

          N/m

          PET:

          Poly

          este

          r

          Tensile Strength on the Encapsulated Apparent Cohesion

          GWC surface modulus

          GWC

          Do-nou layer surface modulus

          Subgrade modulus

          200

          100

          0

          10 15 20 25 30 35 40 45 50

          Angle of Shearing Resistance, f ()

          T=6.6 (PE) T=11.2 (PP) T=20 (PET)

          Subgrade

          Element modulus

          Fig. 14. Mode of determining stiffness (elastic modulus) from PB/LT (plate bearing/loading) measurements (MTRD Evaluation Report No. 1314 of April, 2018).

    4. Anaysis of size and shape effects

      Fig. 13. Effects of ultimate tensile strength of soilbag fabric on encapsulated apparent cohesion with varying: a) coefficient of passive earth pressure; and,

      b) angle of shearing resistance.

      As can be unequivocally inferred from practically all the foregoing Equations 1 ~ 32, the size and shape of the WECS soilbags has significant influence on the mobilization of tensile

      stresses hence the development of the strength and stiffness of the fill material. It is therefore imperative that the dimensions specified at the outset are strictly adhered to.

    5. Influence of number of layers

      It is imperative to determine the appropriate number of layers required. The number of do-nou layers required is, understandably, dependent on the tensile strength of the WECS bag, bearing strength/capacity/stiffness of the subgrade and the delineating geotechnical/environmental conditions.

      The influence of the number of do-nou stacked layers is to be quantified and incorporated in the design for cases whereby multiple layers are necessary as depicted in Figures 15 and 16.

      TABLE V. APPROPRIATE NUMBER OF WECS (SOILBAG) LAYERS REQUIRED BASED ON SUBGRADE STIFFNESS.

      Site Conditions

      Normal

      Critical

      Highly Critical

      Factor of Safety, Fs

      1.5

      1.75

      2

      Priority

      1

      2

      3

      Subgrade Resilient Modulus, MR (Mpa

      Equivalent CBR (%)

      Number of Do-nou Layers Required, ND L (No.)

      6

      1

      3.1

      3.6

      4.1

      12

      2

      1.6

      1.8

      2.1

      18

      3

      1.1

      1.3

      1.4

      24

      4

      0.8

      1.0

      1.1

      29

      5

      0.7

      0.8

      0.9

      34

      6

      0.6

      0.7

      0.8

      39

      7

      0.5

      0.6

      0.7

      44

      8

      N/A

      0.5

      0.6

      49

      9

      N/A

      0.5

      0.5

      54

      10

      N/A

      N/A

      0.5

      Notes: . = 0.5 to be rounded to: . 1 depending on the site

      Fig. 15. Various WECS do-nou cross-sectional layout configuration (Matsuoka and Liu, 2003).

      conditions @ Engineers judgement: N/A Not Applicable

    6. Quantitative evaluation of influence of number of vertically stacked layers

    2

    2

    Results from model experimental testing conducted on WECS indicate that the bearing capacity of do-nou basically increases by the square exponent of the ratio of the increased

    to the original area: ( .) , which applies both in plane and cross-sectional perspectives [2]. Based on this concept and taking the soilbag edge reduction and the effects of installation/construction deficiencies and ramification, the model defined in Equation (34) should be applied in the evaluation of the influence of stacked layers.

    The appropriate number of soilbag (do-nou) layers required,

    . can be computed from the model defined in Equation

    = (

    = (

    1

    () >1[10.1(1)]× 2

    ) [4 1] × { }

    (33), which takes into account the deformation resistance of

    2()

    ()=1

    (34)

    the natural subgrade.

    . = (6 × 1052 + 0.078

    1

    ) ×

    (33)

    where, = number of stacked layers and = partial factor to account for installation/construction deficiencies,

    ,

    where, is the resilient modulus of the natural (existing) subgrade prior to improvement and is the factor of safety to cater for site conditions, installation/construction deficiencies and ramification. It is recommended that the factor of safety is

    and ramification, whereby = × = 0.8 × 0.91 = 0.727. This implies the square exponent reduces to 1.455.

    Employing the ratio conversion concept, Equation (34) is simplified to:

    limited within the range: 1.5

    2 . Equation (33) is

    2 1.455

    adopted in generating Table V, w

    h is to be employed in

    = (

    ) [4

    [()>1] [10.1(1)×]

    1] × { }

    design.

    hic

    1

    2()

    2

    [()=1]

    (35)

    A similar principle is used in developing Equation (36), which mathematically defines the resulting loads at failure.

    = ( ) [4

    1] × 16( + )2 ×

    2()

    2

    1.455

    [()>1] [10.1(1)×]

    { 2 }

    [()=1]

    (36)

    Equations (35) and (36) are employed in generating Table VI, which summarize bearing capacity and load values, that areto be adopted in design of WECS do-nou foundations to a level of up to 3 (three) vertically stacked soilbag layers.

    Note that the ultimate tensile strength of the Kenyan manufactured polypropylene soilbag fabric (. = 11.2/

    ) is adopted in these computations.

    The apparent increase in intrinsic confining stress and intrinsic cohesion can be evaluated from Equations (37) and (38).

    p>2 1.455

    = (41) ×

    [()>1] [10.1(1)×]}

    (37)

    3

    {

    2()

    2

    [()=1]

    (4 1)

    = ×

    2

    [()>1] [10.1(1)×]

    1.455

    (38)

    4 { ( ) 2 }

    [ =1]

    where, = length of the WECS do-nou (soilbag). Note that these models are simplified based on the fact that the standard specifications stipulated are: = = 0.4 and = 0.1.

    TABLE VI. BEARING CAPACITIES FOR VARYING NUMBER OF VERTICALLY STACKED WECS LAYERS.

    Fig. 16. Example of laminated soilbags: Effect of lamination depending on number of WECS do-nou layers.

    The model defined in Equation (39), which is used in computing the values summarized in Table VII for two laminates (. = 2) enable the accounting for the influence of lamination in design.

    Ref. Bearing Capacity

    Tult. (kN/m)

    11.2

    Bearing Capacities for Varying Vertically Stacked Do-nou Layers

    No. of Stacked Layers

    1

    2

    3

    4

    5

    6

    7

    8

    9

    10

    Equiv. CBR (%)

    AIF/ASR,

    tx

    Coefficient of Passive Earth Pressure, Kp

    Bearing Capacity, 1f (kPa)

    10

    15

    1.698

    351

    927

    1610

    2354

    3129

    3916

    4698

    5463

    6200

    6901

    19

    20

    2.040

    433

    1145

    1989

    2908

    3866

    4838

    5805

    6750

    7661

    8527

    31

    25

    2.464

    536

    1417

    2461

    3597

    4783

    5985

    7181

    8350

    9477

    10549

    40

    28

    2.770

    610

    1612

    2801

    4095

    5444

    6813

    8173

    9504

    10787

    12006

    47

    30

    3.000

    666

    1760

    3057

    4469

    5941

    7435

    8920

    10372

    11772

    13103

    54

    32

    3.255

    728

    1923

    3340

    4882

    6491

    8123

    9746

    11333

    12862

    14316

    62

    34

    3.537

    796

    2103

    3654

    5341

    7101

    8887

    10662

    12398

    14072

    15662

    71

    36

    3.852

    872

    2305

    4003

    5853

    7781

    9738

    11683

    13585

    15419

    17162

    80

    38

    4.204

    957

    2530

    4395

    6425

    8542

    10689

    12824

    14913

    16925

    18839

    90

    40

    4.599

    1053

    2783

    4834

    7067

    9395

    11758

    14106

    16403

    18617

    20721

    100

    42

    5.045

    1161

    3068

    5329

    7791

    10358

    12963

    15552

    18084

    20525

    22845

    111

    44

    5.550

    1283

    3391

    5891

    8612

    11450

    14329

    17191

    19990

    22688

    25253

    123

    46

    6.126

    1423

    3760

    6531

    9548

    12695

    15886

    19060

    22163

    25154

    27998

    135

    48

    6.786

    1583

    4183

    7265

    10621

    14121

    17672

    21202

    24654

    27981

    31145

    148

    50

    7.549

    1767

    4670

    8112

    11860

    15768

    19732

    23674

    27529

    31244

    34776

    Ref. Bearing Capacity

    Tult. (kN/m)

    11.2

    Bearing Capacities for Varying Vertically Stacked Do-nou Layers

    No. of Stacked Layers

    1

    2

    3

    4

    5

    6

    7

    8

    9

    10

    Equiv. CBR (%)

    AIF/ASR,

    tx

    Coefficient of Passive Earth Pressure, Kp

    Bearing Capacity, 1f (kPa)

    10

    15

    1.698

    351

    927

    1610

    2354

    3129

    3916

    4698

    5463

    6200

    6901

    19

    20

    2.040

    433

    1145

    1989

    2908

    3866

    4838

    5805

    6750

    7661

    8527

    31

    25

    2.464

    536

    1417

    2461

    3597

    4783

    5985

    7181

    8350

    9477

    10549

    40

    28

    2.770

    610

    1612

    2801

    4095

    5444

    6813

    8173

    9504

    10787

    12006

    47

    30

    3.000

    666

    1760

    3057

    4469

    5941

    7435

    8920

    10372

    11772

    13103

    54

    32

    3.255

    728

    1923

    3340

    4882

    6491

    8123

    9746

    11333

    12862

    14316

    62

    34

    3.537

    796

    2103

    3654

    5341

    7101

    8887

    10662

    12398

    14072

    p>15662

    71

    36

    3.852

    872

    2305

    4003

    5853

    7781

    9738

    11683

    13585

    15419

    17162

    80

    38

    4.204

    957

    2530

    4395

    6425

    8542

    10689

    12824

    14913

    16925

    18839

    90

    40

    4.599

    1053

    2783

    4834

    7067

    9395

    11758

    14106

    16403

    18617

    20721

    100

    42

    5.045

    1161

    3068

    5329

    7791

    10358

    12963

    15552

    18084

    20525

    22845

    111

    44

    5.550

    1283

    3391

    5891

    8612

    11450

    14329

    17191

    19990

    22688

    25253

    123

    46

    6.126

    1423

    3760

    6531

    9548

    12695

    15886

    19060

    22163

    25154

    27998

    135

    48

    6.786

    1583

    4183

    7265

    10621

    14121

    17672

    21202

    24654

    27981

    31145

    148

    50

    7.549

    1767

    4670

    8112

    11860

    15768

    19732

    23674

    27529

    31244

    34776

    = (0.35950.97372+10.450.9916 ) × .

    .,.

    .

    .

    .

    .

    .

    .

    (39)

    where .,.

    and . = 70 are the resulting

    G. Effects of lamination in multi-layered WECS

    In most cases, for soft ground reinforcement/improvement, the WECS do-nou technology requires multi-layer piling as shown in Figure 16.

    Model and full-scale experimental testing results indicate that the effect of lamination is to increase the ultimate tensile strength, . by approximately the number of laminates depending on the axial strain at which the . is determined. Unless otherwise intentional modified, WECS do-nou laminates would usually be two faces notwithstanding the number of piled layers as can be derived from Figure 16. In this case it can be seen that the middle portion of the three layer pile on the RHS is laminated on both the top and bottom faces (two face lamination). This effect has yet to be investigated. This notwithstanding, the overlaying and under-laying layers are each single face laminated.

    laminated and the reference ultimate tensile strengths, respectively.

    TABLE VII. SUMMARY OF RESULTING ULTIMATE TENSILE STRENGTH DUE TO SINGLE FACE LAMINATION (. = 2).

    Ma te ri a l

    PE

    PP

    PET

    Tult. (kN/m)

    6.6

    11.2

    20

    Ori gi n

    Chi na

    Ke nya

    Ja pa n

    Axial Strain, (%)

    Resulting Ultimate Tensile Strength Due to Single Face Lamination Effect, Tult .la m . (kN/m)

    3

    5.3

    9.0

    16.0

    4

    6.8

    11.5

    20.5

    6

    9.4

    15.9

    28.4

    8

    11.4

    19.4

    34.6

    10

    12.9

    21.9

    39.2

    11

    13.5

    22.9

    40.9

    12

    13.9

    23.6

    42.2

    13

    14.2

    24.1

    43.1

    14

    14.4

    24.4

    43.6

    15

    14.4

    24.5

    43.7

    16

    14.3

    24.3

    43.3

    17

    14.1

    23.9

    42.6

    18

    13.7

    23.2

    41.5

    19

    13.2

    22.4

    40.0

    20

    12.6

    21.3

    38.0

    Notes: PE Polyethylene; PP Polypropylene; Polyester

    It is recommended that the values .,. highlighted in grey be adopted since they are the maximum values determined @ = 15%, which is almost a standard value for determining the ultimate tensile strengths for woven geotextiles.

  3. BASIC DESIGN CRITERIA

    1. Structural design criteria

      The conceptual basis of the structural design criteria developed is focused on the effective characterization of the WECS do-nou (soilbag) encapsulation characteristics based on

      the soil mechanics theories and geotechnical engineering concepts introduced in the preceding Section II. In particular, the following considerations and attributes constitute the structural design criteria: i) under dynamic loading, the wheel loading applied to a soilbag reinforced layer will usually be multi-directional; ii) a wheel passage over a single soilbag impacts force vectors through the Mechanically Stabilized Layer (MSL) which vary in time, direction and magnitude; iii) vertical stresses impacted predominantly by live load surcharges from traffic dynamic loading are dispersed in the mode and pattern portrayed in a Westergaard model; iv) stress

      ~ strain distribution primarily depends on the index characteristics of soilbag product, the intrinsic mechanical; strength and stiffness (elastic modulus) properties of the fill geomaterials and the degree/extent of the encapsulation confinement effect; v) lateral restraint/confinement of the base and subgrade is achieved through friction and bonding of the layer geomaterials and the WECS; vi) increase in the system bearing capacity is gained by diverting the potential bearing capacity failure surface to develop along alternate, higher shear strength surfaces both for the soilbag fill g and the pavement and subgrade layer geomaterials; and vii) membrane support of the wheel loads is only achievable under considerably high strain conditions within the soilbag hence its application should be limited to temporary road pavements.

    2. Failure criteria

      The The failure criterion of the composite do-nou consisting of the soil and the bag is based on the Limit State philosophy entailing ultimate and serviceability states.

      1. Failure criterion based on shear strength

        It has been explicitly demonstrated in the preceding Section II that WECS soilbags exhibit both compressive and tensile characteristics. It was also shown that the compressive strength decreases with a corresponding decrease in the apparent cohesion, () when subjected to inclined external loading ( > 0) [Equation (11)].

        As shown in Figure 17, the failure criterion of the composite soilbags is based on Mohrs strss diagram [2]. As can be inferred from this schematic representation, failure assumes two major conditions including: i) the confining stress is non-prevalent (3 = 0); and ii) both the soilbag fabric and fill geomaterial fail simultaneously. In this case, the soilbags will exhibit tensile strength when connected (refer to sub-

      2. Serviceability criterion based on rut depth

        The serviceability criterion deemed to be the maximum rut depth. In this case, a maximum rut depth of 15mm is considered the allowable value hence non-serviceability compliance is designated when , 15.

    3. Area coverage ratio

    As can be observed from Figures 18 and 19, soilbags are installed as discrete reinforcing elements in this case. It has been evident from various trials and road sections improved using the Do-nou technology that the 5cm spacing provided as a tolerance or compaction is never closed perfectly.

    Edge Effects

    Gap between Do-nou (Soilbags) = 5cm (0.005m)

    Fig. 18. Gap provision for compaction tolerance of WECS soilbags.

    Fig. 19. Installation, compaction and filling of gaps between WECS soilbags.

    In order to account for these gaps, the area coverage ratio is introduced as a reduction factor to be applied to the effective bearing strength/capacity and strength parameters, which are highly dependent on the area coverage of the soilbags. In consideration of the gaps and edge effects, the area coverage ratio shall be computed on the basis of Equation (40).

    Section D). The integral parameters that delineate the failure

    ()×()

    =

    =

    .×.

    (40)

    criterion are the vertical stress, angle of shearing resistance and the apparent cohesion.

    Fig. 17. Failure criterion of composite WECS soilbags (Matsuoka and Liu, 2003).

    Based on the WECS soilbag dimensional specifications provided in this paper, which are standard and remain constant, the area coverage ratio is designated at = 0.81.

    1. Connectivity of WECS bags

      The effects of connection on tensile strength and their contribution to yield strength and the failure criterion can be derived from Figure 17. It has also been derived from the analysis and structural performance evaluation of the trial and road sections improved using the Do-nou technology in Kenya that these gaps culminate in drifting of the soilbags particularly in areas predominated with problematic soils.

      On the other hand, it can be derived from Figure 24 that for permanent structures constructed in Japan using the Do-nou technology, the soilbags are connected. Although further investigations are necessary in order to develop appropriate

      Surface Dressing

      Surface Dressing

      guidelines regarding this aspect, it is advisable that the soilbags are connected through seaming in the field.

      Base Layer

      Thickness

      Base Layer

      Thickness

    2. Applicable partial factors

      Full-depth

      Structural Pavement Thickness

      Full-depth

      Structural Pavement Thickness

      Do-nou Layer

      Thickness

      Structural Subgrade

      Layer Thickness

      Do-nou Layer

      Thickness

      Structural Subgrade

      Layer Thickness

      Do-nou

      Foundation

      Do-nou

      Foundation

      In designing geo-structures with do-nou application, reduction factors have to be employed to mainly account for durability, installation damage/construction deficiencies, creep reduction and uncertainties in consideration of the do- nou material properties and soil interaction characteristics [7]. The partial (reduction) factors to be employed for the Long- Term Design Strength (LTDS) of soilbags reinforced/improved embankments and pavements are presented in Table VIII.

      The data in Table VIII is then used to determine the allowable working stress of the soilbag reinforcement from the expression in the following Equation 41. The values in brackets are the equivalent partial factors.

      = () (41)

      (××)

      Fig. 20. Depiction of various layer types and definition of WECS (Do-nou)

      foundation and subgrade structural thickness.

      TABLE VIII. PROPOSED PARTIAL (REDUCTION) FACTORS.

    3. Design life

    The design life shall be equivalent to the in-service life and shall be designated at a period that is compatible to the LTDS (long-term design strength).

  4. DEVELOPMENT OF DESIGN CATALOGUES

  1. Foundation structural configuration

    The WECS do-nou foundation, as per the definition of this paper, consists of the structural subgrade thickness and the soilbag layer(s) as depicted in Figure 20.

    The integral criteria of adopting the WECS Do-nou technology is to ensure the achievement of a sound foundation that will effectively support the pavement structure over an extended period comprising of the design life and rehabilitation extension. It is therefore imperative to determine the appropriate number of do-nou layers required. As demonstrated in the preceding sections, the number of do-nou layers required is, understandably, dependent on the bearing strength/capacity/stiffness of the subgrade and the delineating geotechnical/environmental conditions.

    The influence of the number of vertically stacked do-nou layers is to be quantified and incorporated in the design for cases whereby multiple layers are necessary.

    The appropriate number of do-nou layers required, . as computed from the model defined in Equations (33) and (42), which take into account the deformation resistance of the natural subgrade, are summarized in Table V.

    S/N

    Particulars

    Typical Values

    Proposed Values

    1.

    Durability Reduction Factor,

    1.2 (0.833)

    1.2 (0.833)

    2.

    Installation Damage Reduction Factor,

    1.25 (0.8)

    1.25 (0.8)

    3.

    Creep Reduction Factor,

    1.66 (0.6)

    1.5 (0.667)

    4.

    Factor of Safety against Uncertainties,

    1.5 (0.667)

    1.1 (0.909)

    S/N

    Particulars

    Typical Values

    Proposed Values

    1.

    Durability Reduction Factor,

    1.2 (0.833)

    1.2 (0.833)

    2.

    Installation Damage Reduction Factor,

    1.25 (0.8)

    1.25 (0.8)

    3.

    Creep Reduction Factor,

    1.66 (0.6)

    1.5 (0.667)

    4.

    Factor of Safety against Uncertainties,

    1.5 (0.667)

    1.1 (0.909)

    In cases whereby it is deemed by the Engineer that the site conditions are critically problematic, additional do-nou layers based on a design review may be incorporated upon review and approval by the Chief Engineer.

    Note that Table V is generated based on the specifications stipulated in [6] considering Class G8 natural material with an initial target improvement to Foundation Class F3 (Equivalent Subgrade Class S5) whereby the fill geomaterial is reinforced to Class G22, at a relative compaction of 95%MDD using a soilbag fabric with an ultimate tensile strength of 11.2kN/m (. = = 11.2) . In this case, the initial target surface (composite) modulusis 125MPa. Table IX provides computational details. Note that further improvement/reinforcement is anticipated with progressive consolidation in the initial stages of traffic loading.

    Do-nou Natural Fill Material Calssification and Reference Bearing Capacity

    Tult. (kN/m)

    6.60

    11.20

    20.00

    Tall. (kN/m)

    2.67

    4.53

    8.08

    Elastic Modulus (Stiffness) for Varying Vertically Stacked Do-nou CompositeStructural Layers

    No. of Stacked Layers

    1

    2

    3

    1

    2

    3

    1

    2

    3

    4

    PDG 1

    Designation

    Equiv. CBR (%)

    AIF/ASR,

    tx

    Coefficient of Passive Earth Pressure, Kp

    Elastic Modulus (Stiffness) Values for Donou Composite Structural Layers, E0 (MPa)

    G5

    5

    11

    1.472

    18

    43

    68

    29

    67

    106

    48

    108

    196

    387

    G8

    8

    14

    1.638

    20

    48

    76

    32

    74

    118

    54

    121

    239

    521

    G10

    10

    15

    1.698

    21

    50

    79

    34

    77

    123

    56

    126

    257

    579

    G15

    15

    18

    1.894

    23

    55

    87

    38

    85

    140

    62

    144

    326

    809

    G20

    20

    21

    2.078

    26

    60

    95

    41

    93

    157

    68

    162

    408

    1088

    G25

    25

    23

    2.257

    28

    65

    103

    45

    101

    176

    73

    182

    507

    1430

    G30

    30

    25

    2.417

    30

    70

    110

    48

    108

    195

    78

    202

    614

    1800

    G50

    50

    31

    3.124

    39

    88

    144

    61

    141

    312

    98

    330

    1345

    4325

    G60

    60

    34

    3.464

    43

    96

    163

    67

    159

    394

    108

    419

    1880

    6161

    G80

    80

    38

    4.204

    51

    115

    216

    79

    209

    649

    131

    698

    3571

    7980

    90

    40

    4.599

    55

    125

    253

    86

    243

    838

    144

    905

    4823

    8485

    100

    42

    5.045

    60

    138

    302

    93

    289

    1103

    161

    1195

    6572

    9035

    111

    44

    5.550

    65

    154

    370

    101

    352

    1480

    182

    1607

    7546

    9638

    123

    46

    6.126

    71

    174

    467

    110

    442

    2020

    210

    2199

    8065

    10301

    135

    48

    6.786

    77

    201

    607

    121

    572

    2806

    249

    3059

    8638

    11033

    148

    50

    7.549

    85

    238

    813

    135

    763

    3965

    305

    4326

    9274

    11845

    45

    Do-nou Natural Fill Material Calssification and Reference Bearing Capacity

    Tult. (kN/m)

    6.60

    11.20

    20.00

    Tall. (kN/m)

    2.67

    4.53

    8.08

    Elastic Modulus (Stiffness) for Varying Vertically Stacked Do-nou CompositeStructural Layers

    No. of Stacked Layers

    1

    2

    3

    1

    2

    3

    1

    2

    3

    4

    PDG 1

    Designation

    Equiv. CBR (%)

    AIF/ASR,

    tx

    Coefficient of Passive Earth Pressure, Kp

    Elastic Modulus (Stiffness) Values for Donou Composite Structural Layers, E0 (MPa)

    G5

    5

    11

    1.472

    18

    43

    68

    29

    67

    106

    48

    108

    196

    387

    G8

    8

    14

    1.638

    20

    48

    76

    32

    74

    118

    54

    121

    239

    521

    G10

    10

    15

    1.698

    21

    50

    79

    34

    77

    123

    56

    126

    257

    579

    G15

    15

    18

    1.894

    23

    55

    87

    38

    85

    140

    62

    144

    326

    809

    G20

    20

    21

    2.078

    26

    60

    95

    41

    93

    157

    68

    162

    408

    1088

    G25

    25

    23

    2.257

    28

    65

    103

    101

    176

    73

    182

    507

    1430

    G30

    30

    25

    2.417

    30

    70

    110

    48

    108

    195

    78

    202

    614

    1800

    G50

    50

    31

    3.124

    39

    88

    144

    61

    141

    312

    98

    330

    1345

    4325

    G60

    60

    34

    3.464

    43

    96

    163

    67

    159

    394

    108

    419

    1880

    6161

    G80

    80

    38

    4.204

    51

    115

    216

    79

    209

    649

    131

    698

    3571

    7980

    90

    40

    4.599

    55

    125

    253

    86

    243

    838

    144

    905

    4823

    8485

    100

    42

    5.045

    60

    138

    302

    93

    289

    1103

    161

    1195

    6572

    9035

    111

    44

    5.550

    65

    154

    370

    101

    352

    1480

    182

    1607

    7546

    9638

    123

    46

    6.126

    71

    174

    467

    110

    442

    2020

    210

    2199

    8065

    10301

    135

    48

    6.786

    77

    201

    607

    121

    572

    2806

    249

    3059

    8638

    11033

    148

    50

    7.549

    85

    238

    813

    135

    763

    3965

    305

    4326

    9274

    11845

    TABLE IX. ELASTIC MODULUS (STIFFNESS) VALUES FOR THE WECS COMPOSITE STRUCTURAL LAYERS.

    4.5

    Number of Do-nou Layers Required, NDL (No.)

    Number of Do-nou Layers Required, NDL (No.)

    4.0

    Determination of Number of Do-nou Layers Required Based on Subgrade Resilient Modulus

    FS: Factor of Safety

    = 0.063(0,) + 0.864 (44)

    where; ; ; = WECS Do-nou Foundation layer

    3.5 = . . .

    thickness/elastic modulus/Poissons ratio,

    ;

    ; =

    ,

    3.0

    2.5

    2.0

    1.5

    Base Course layer thickness/elastic modulus/Poissons ratio, and , = subgrade resilient modulus, whilst denotes pavement layer.

    To determine the appropriate or required base course thickness, Equation (45) can be rewritten as:

    1.0

    (12 )

    13

    0.5 = × {[ ] × [ ]}

    (45)

    (12 )

    0.0

    5 10 15 20 25 30 35 40 45 50 55

    Subgrade Resilient Modulus, MR,SG (MPa)

    FS=1.5 FS=1.75 FS=2.0

    Fig. 21. Graphical method of determining number of WECS soilbag (do-nou) layers required based on subgrade stiffness.

    On the other hand, Figure 21. depicts the graphical method of determining the number of do-nou layers required based on subgrade stiffness, which is defined in terms of the resilient modulus. The main model is defined in Equation (33). An alternative counter-check model is expressed in Equation (42).

    ,

    ,

    = 12.4011.000180.982 × , (42)

  2. Full-depth structural configuration

    As outlined under Section II of this paper and [6], the pavement structural configurations selected and provided within the Standard Pavement Structure Type, which define the Design Catalogues, are developed on the basis of the thickness-modulus ratio concepts that ensure the achievement of a balanced pavement structure. In so doing, due consideration has been made to the following: i) a structurally balanced pavement is realized; ii) achievement of enhanced strength, stiffness and deformation resistance as a result of increasing the vertically stacked WECS soilbags (do-nou) layers; iii) influence of cross-sectional layout configuration as shown in Figure 15, is taken into account; and iv) the subbase layer is wholly expunged from the pavement structural configuration as part of the VE (value engineering benefit.

  3. Application of the thickness-modulus ratio concept

    When a pavement structure undergoes vibrational dynamic loading under heavy and/or progressively continuous traffic, it experiences prolonged residual vibrations. The intensity of such residual vibrations highly depends on the absorbent capacity of the flexible pavement, which is defined by the reciprocal balance between the stiffness (elastic modulus) of the neighbouring layers. Prolonged reverberation of such stress can have detrimental effects on the structural soundness of the pavement. The thickness-modulus ratio concepts are employed as a geotechnical engineering means of mitigating this problem by ensuring reciprocal compensation between the thickness and the elastic modulus (stiffness) of the neighbouring layers as can be derived from the model defined in Equation (43).

    Application of the thickness-modulus ratio concepts is

    particularly essential when the Do-nou encapsulated confinement system is applied in multiple layers due to the significant increase in stiffness. The integral part of the results applied in the development of the pavement structural configurations presented in the Design Catalogues summarized in [6].

  4. Structural concepts adopted

    A QM (Quasi-Mechanistic) approach is applied in deriving structural layer thickness equations used in developing Catalogues for Standard Pavement Structure Type for WECS do-nou (soilbag) pavement foundations. The range of the ultimate tensile strength, = . and radial (secant) stiffness at 2% strain, @2%, of the do-nou (soilbag) fabrics considered was:

    6 . 20 .

    and for ultimate tensile strength, = . and within the range indicated below for secant stiffness at 2% strain, @2%,

    57 . 153 .

    The standard pavement structures developed and the

    applicable traffic and subgrade classes are presented in the Design Catalogues provided in the charts format in Section 5.7 and Section 5.8 of [6]. Basically, the design for the applicable class of soil and traffic is discreetly presented in a single chart. Brief comments on the peculiarities, advantages, and disadvantages of each type of pavement structural type are provided accordingly [7]. The pavement materials required for use in each chart have been indicated and referenced to the Material Specification Charts, which include a summary of construction procedures provided under Section 5.13 of Chapter 5 of the [8].

  5. Methodology for developing standard pavement strucures The methodology of developing the standard pavement structures is summarized as follows: i) the subgrade resilient modulus (stiffness) is determined from in-situ mechanical and/or geophysical tests; ii) based on the magnitude of the subgrade stiffness,the required number of do-nou layers is

determined from Table V and/or computed using Equation (33) and counter-checked employing Equation (42); alternatively, the nomograph presented in Figure 21 can also be adopted; iii)

3

(12 )

(12 )

13

the bearing capacity and elastic modulus (stiffness) of the

= {[ ] × [ ]} = {[ ] × [

]}

(43)

(12 )

(12 )

natural do-nou fill material is determined from the tables

On the other hand, the layer Poissons ratios, can be computed from the respective pavement layer stiffness based on the model defined in Equation (44).

provided in Appendix A4 of [6]; iv) the data and information from 1) and 2) above is then applied to derive the appropriate composite do-nou foundation layer stiffness from Table A4-10

in Appendix A4.5 of [6]; v) the appropriate composite do-nou

,. = [924.66() + 3624.2]

(0.68030.0322)

×

foundation layer thickness is determined from the Tables provided in [6]; vi) by considering the standard overlying thickness of the gravel wearing and base courses as:

= = 125, the full-depth pavement and discrete layer thicknesses are determined; vii) gravel loss prediction for the unpaved roads is undertaken by adopting Equations (46); and viii) selection of the most appropriate standard pavement structural configuration can now be made from the Catalogue Design Charts provided in [6]

  1. Methodology for developing standard pavement strucures

    1. Gravel loss prediction

      Climate has a fundamental influence on road materials and performance particularly for unpaved (gravel wearing course) roads. In this regard therefore, the gravel loss prediction model considers this diversity in terms of intensity of precipitation

      ,

      , × 0, (47a) where, is the cumulative equivalent single axles,

      , is the structural thickness ratio factor defined in

      Equation (47b). The , factor is derived from do-nou layer thickness and the factored elastic modulus of the do- nou fill, 0, and 0, is the elastic modulus (stiffness) factor defined in Equation (47c). Fundamentally, the 0, factor represents/describes the quality of geomaterials used for the GWC (gravel wearing course). Note that a ramification reduction factor, = 0.833 ( = 1.2) is applied on both the elastic modulus for the do-nou foundation and gravel wearing course geomaterials.

      0,

      0,

      , = 2.70220.276 (47b)

      and gradients. It is therefore prudent to consider, in general, two zones consisting of wet and dry defined in [9].

      0,

      = 3.51850.276 (47c)

      0,

      0,

      In developing the design catalogues for gravel wearing

      = +

      (48)

      surfaces, gravel loss prediction is performed for the unpaved

      ,.

      ,.

      roads based on model Equation (46a), which should distinctly be in consideration of two (dry and wet) zones.

      Pending further modification, the recommended gravel loss

      G. Full-Depth and base course thickness design for LVSRs

      The models adopted for determining and/or counter- checking the appropriate full-depth, . and base course,

      model is defined in Equation (46a) The gravel loss,

      model,

      .

      developed by TRRL based on R&D carried out in

      ya, is:

      structural thicknesses as functions of subgrade stiffness

      = (

      = (

      2

      2

      Ken

      ) [4.2 + 0.092 + 3.502 + 1.88]

      (resilient modulus), cumulative traffic loading and elastic modulus of the do-nou fill geomaterial are provided in

      where,

      +50

      (46a)

      Equations (49) and (50), respectively. The thickness determined from these models and the thickness-modulus ratio

      : Gravel loss in mm; : Constant depending on type of gravel; for Kenyan gravel; = 1.29 for lateritic gravel; = 1.51 for quartztic gravel; = 0.96 for volcanic gravel; and = 1.38 for coral gravel; : Annual traffic in both directions measured in thousands of vehicles;

      models defined in Equations (43) ~ (45) are employed in generating the pavement structural configurations presented in the Design Catalogues in [6].

      =

      =

      .

      ,

      [2786.4(0.557)(0.0535(,N)0.0591) ×

      : Annual average rainfall in measured in metres; :

      ,

      ,N

      ,

      Gradient (rise and fall) expressed in percentage of m/km;

      : Correction factor correlating to actual measurements defined in Equation (46b).

      = 0.149772 + 0.21884 + 0.009978 (46b) where, = elapsed post-construction time or regravelling intervening periods.

    2. Gravel Wearing Course (GWC) thickness design

      The required gravel wearing course thickness shall

      , × 0,] , (49a)

      where, , and , are factors that account for thickness-modulus ratios of low volume sealed roads defined in Equation (49b) and Equation (49c), , is the resilient modulus of the natural (native) subgrade prior to improvement,

      , is the cumulative traffic loading defined in terms of ESALs (equivalent single axles) and , is the structural thickness ratio factor of the do-nou fill geomaterial. The , factor is derived from Equation (49b), whilst 0, is the

      constitute of the structural,

      [Equations (47)] and gravel

      factored elastic modulus (stiffness) factor defined in Equation

      ,.

      loss, portions, yielding the total gravel thickness [10],

      ,., as defined in Equation (48).

      Essentially, the GWC thickness shall be derived as follows.

      1. Determine the minimum structural thickness

        (49d). Fundamentally, the 0, factor represents/describes the quality of geomaterials used for the BC (base course). Note that a ramification reduction factor, = 0.833 ( = 1.2) is applied on the elastic modulus for the base course.

        ,

        ,

        necessary to avoid excessive compressive strain in the subgrade [11], ,. from the Catalogue

        ,

        = 357761.193 (49b)

        Design Charts or by applying Equation (47).

      2. Determine the extra thickness needed to compensate for the gravel loss, , during the design life or period

        ,

        = 3221121.343 (49c)

        ,

        ,

        = 3.70450.276 (49d)

        between regravelling from model Equation (46a).

        0,

        0,

      3. Determine the total gravel thickness required by addition of the above two thicknesses [11] as depicted in Equation (48).

The optimum base course layer thickness, . is, on the

other hand, determined from the model defined in Equation (50).

. = 2.7[0.336 × .]0.9426 × {[1.3685 × 1052

,

[3.3×1082 +2×105+0.3409] 1

0.008 + 6.6505] × ,

}

(50)

  1. POSSIBLE FUNCTIONS AND ATTESTED APPLICATIONS

    The Possible functions and attested applications are introduced [5]. The possible functions, depending on the quality, type and properties of the do-nou fill geomaterials, may include: i) Separation: the prevention from intermixing of adjacent issimilar soils and or materials; ii) Filtration: the retaining of soil or other particles subject to hydrodynamic forces while allowing the passage of fluids into or through the soilbag; iii) Drainage: the collecting and transmitting of precipitation, ground water and or other liquids or gases along the plane of the soilbag; iv) Reinforcement: the use of the properties of a soilbag to imprve the mechanical properties of soil or other construction materials; v) Barrier: the prevention or reduction of the movement of any fluid through a construction by the use of a soilbag barrier; vi) Protection: the use of a soilbag material as a localised stress reduction or dissipation layer to prevent or reduce damage to a given surface, material or layer; vii) Surface erosion control: the use of a soilbag to prevent soil or other particle movements on the surface of a slope; viii) Stabilization: improvement of the mechanical behaviour of an unbound granular material by including one or more soilbag layers such that deformation under applied loads is reduced by minimizing movement of the unbound granular material.

    Attested applications of the WECS include: i) reinforcement of road subgrades/foundations; ii) reinforcement of building foundations (see Figure 1-5); iii) reinforcement of railway foundations; iv) construction of retaining walls; v) construction of embankments; vi) piling; vii) reduction in settlement; and viii) reduction in vibrations/noise.

    In Kenya, WECS was initially introduced as a labour based Do-nou (soilbags) technology. Below are the advantages of the WECS including Do-nou that make it unique as a useful technology [2]: i) does not involve use of any cement or chemical agents thus it is environment-friendly; ii) no special construction equipment is needed; iii) the materials inside soil bags may be any construction wastes such as concrete, asphalt, tire and tile wastes as well as granular remains after garbage treatment; iv) thus soil bags can also contribute to the recycle of waste materials; v) the soil bag itself has a high compressive strength; vi) it has an effect of reducing traffic- or machine- induced vibration; implicitly/retrospectively, it may also have the inherent propensity to reduce earthquake vibration; vii) it has an effect of preventing heave if course granular are filled in the bags; viii) as demonstrated in Figure waterlogged soft ground may also be effectively reinforced.

    A typical cross section for WECS (do-nou) rut improvement is shown in Figure 22.

    Fig. 22. Typical WECS Do-nou cross sections for improvement of ruts.

    Condition of the road: Water Logged Subgrade

    Before

    After

    Condition of the road: Problematic (Expansive) Black Cotton Soil Subgrade

    Before

    After

    Fig. 23. Application of the WECS soilbag (do-nou) technology for the construction of the roads constructed within: a) water logged sections; and b) problematic(expansive) black cotton soils

    Fig. 24. Application of the Do-nou WECS technology for improvement of building foundations (Matsuoka and Liu, 2003).

  2. CONCLUSIONS

In this paper, it has been demonstrated that the proposed analytical models equipped with a variety of application modules are unique functional and effectively applicable for the design of wholly encapsulated confinement systems (WECS) comprising of polymeric soilbags (do-nou). Application of the proposed models has also been practically manifested through graphical examples for the characterization of the influence factors and material properties as well generation of imperative design parameters. The design characteristic curves and parametric values generated based on the application of these models distinctly confirm the validity, lucidity and rationality of the proposed analytical models.

ACKNOWLEDGMENT

The author wishes to acknowledge, with utmost gratitude, the Materials Testing & Research Department, Ministry of Transport, Infrastructure, Housing & Urban Development in Kenya, the International Labour Organization (ILO), the Community Road Empowerment (CORE), the Japan International Cooperation Agency 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. Matsuoka H. and Liu, S., New Earth Reinforcement Method by Soilbags (Donow), Soils and Foundations, Japanese Geotechnical Society, Vol. 43(6), pp.173-188, 2003

  2. Yoshinori Fukubayashi and Makoto Kimura, Improvement of Rural Access Roads in Developing Countries with Initiative for Self-reliance of Communities, June 2013

  3. Matsuoka H. and Liu, S. A New Earth Reinforcement Method using Soilbags, London, Taylor & Francis Group, 2006

  4. Materials Testing and Research Department (MTRD), Ministry of Transport, Infrastructure, Housing and Urban Development: Do-nou Technology Evaluation Report No. 1314 of April, 2018

  5. US-FHWA-NHI (United States Federal Highway Authority-National Highway Institute), Geosynthetic Design Guidelines Reference Manual, FHWA-NHI-07-092: August, 2008.

  6. Materials Testing and Research Department (MTRD), Ministry of Transport, Infrastructure, Housing and Urban Development: PDG 4: Daft Interim Guideline for Design and Structural Improvement of Low Volume Roads Using Do-nou Technology, March, 2018.

  7. J .N. Mukabi, Profound methodology for prediction and evaluation of performance of GRE walls for road embankment and bridge abutments, Proceedings of the XXVth World Road Congress, Seoul, South Korea, November 2015, CD-Rom.

  8. Ministry of Transport, Infrastructure, Housing and Urban Development, PDG 1: Pavement Design Guideline for Low Volume Sealed Roads; April, 2017.

  9. Kenya Road Design Manual Part III. Materials and Pavement Design for new roads, Roads Department Ministry of Roads and Public works,1987

  10. J.N. Mukabi, Proposed unique quasi-mechanistic models for advanced design of GMSE and GRS retaining wall geo-structures, Proceedings of the 3rd World Congress on Civil, Structural and Environmental Engineering, Budapest, Hungary, 2018.

  11. J.N. Mukabi, Inimitable Approach to design of foundations for GMSE and GRS retaining walls based on a case example, Proceedings of the 3rd World Congress on Civil, Structural and Environmental Engineering, Budapest, Hungary, 2018.

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