**Open Access**-
**Total Downloads**: 5 -
**Authors :**John Ngaya Mukabi -
**Paper ID :**IJERTV8IS030257 -
**Volume & Issue :**Volume 08, Issue 03 (March – 2019) -
**Published (First Online):**30-03-2019 -
**ISSN (Online) :**2278-0181 -
**Publisher Name :**IJERT -
**License:**This work is licensed under a Creative Commons Attribution 4.0 International License

#### 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.

INTRODUCTION

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.

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].

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).

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).

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..

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.

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).

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.

FUNDAMENTAL STRUCTURAL DESIGN PRINCIPLES

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].

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 (Ã—)

Substituting for in Equation (8) yields:

and,

= [0.7(6 ) 2]

(10)

= 2

(2)

03 (Ã—)

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] Ã— Ã— (13)

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

() = { ( = 0Â°) Ã— (2), (0Â° 45Â°) 0, (45Â° 90Â°)

Essentially therefore, considering = 0 and substituting

3

3

the same in Equation (3) yields:

(11) = 2

2

(14)

1

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] Ã— Ã— (16)

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] Ã— 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] Ã— 162 (20)

2

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

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.

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

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

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 Â±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] Ã— 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)

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].

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).

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.

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

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)]Ã— 2

) [4 1] Ã— { }

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

2()

()=1

(34)

the natural subgrade.

. = (6 Ã— 1052 + 0.078

1

) Ã—

(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 = Ã— = 0.8 Ã— 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)Ã—]1] Ã— { }

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] Ã— 16( + )2 Ã—

2()

2

1.455

[()>1] [10.1(1)Ã—]{ 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) Ã—

[()>1] [10.1(1)Ã—]}(37)

3

{

2()

2

[()=1](4 1)

= Ã—

2

[()>1] [10.1(1)Ã—]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 ) Ã— .

.,.

.

.

.

.

.

.

(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.

BASIC DESIGN CRITERIA

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.

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.

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-

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.

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

()Ã—()

=

=

.Ã—.

(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.

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

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)

(Ã—Ã—)

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

foundation and subgrade structural thickness.

TABLE VIII. PROPOSED PARTIAL (REDUCTION) FACTORS.

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).

DEVELOPMENT OF DESIGN CATALOGUES

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 = Ã— {[ ] Ã— [ ]}

(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 Ã— , (42)

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.

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].

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].

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

= {[ ] Ã— [ ]} = {[ ] Ã— [

]}

(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)

Ã—

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]

Methodology for developing standard pavement strucures

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

,

, Ã— 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) Ã—

: 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.

Gravel Wearing Course (GWC) thickness design

The required gravel wearing course thickness shall

, Ã— 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 gravelfactored 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.

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).

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,

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 Ã— .]0.9426 Ã— {[1.3685 Ã— 1052

,

[3.3Ã—1082 +2Ã—105+0.3409] 10.008 + 6.6505] Ã— ,

}

(50)

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).

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

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

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

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

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

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

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.

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.

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

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

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.

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.