Numerical Modeling of Flexible Pavement Constructed On ... · Mostafa Deep Hashem Civil Engineering...

European International Journal of Science and Technology Vol. 2 No. 10 December, 2013

19

Numerical Modeling of Flexible Pavement Constructed On

Expansive Soils

Mostafa Deep Hashem1, Ahmed Mousa Abu-Baker

2

1,2Associate Prof, Civil Engineering Department

Faculty of Engineering, Al-Minia University, EGYPT

*Corresponding author:

Mostafa Deep Hashem

Civil Engineering Department

Faculty of Engineering,

Al-Minia University, EGYPT

Email: [email protected].

Abstract

Expansive soils are the soils which swell significantly when come in contact with water and shrink when

water squeezes out. Roads constructed on these soils are subjected to large uplifting forces caused by the

swelling. These forces will induce heaving, cracking, and breakup of roads. This paper discusses the

findings on analysis results of a pavement structure constructed on dry and saturated expansive subgrade

soil through numerical analysis using the Finite Elements Method. Plaxis program v8.2 was used to model

the soil behavior. The structure was subjected to the loads from two trucks with dual wheel load of

350kN/m2

per axle. Modeling was performed by a static plain strain analysis and the element mesh consisted

of triangular elements each with 15 nodes. The results showed that the values of vertical displacement for

saturated drained subgrade and dry undrained subgrade were much higher than that occurs in dry drained

subgrade. The values of vertical displacement under the center of shoulder were very lower compared with

that occurs under the center of different wheel loads.

Keywords: Flexible pavements, expansive soil, finite elementmethod,plaxis v8.2, soil behavior.

1. Introduction

Expansive soils are the soils which swell significantly when come in contact with water and shrink when the

water squeezes out. The severity of damages done by expansive soil has been well documented in literature

worldwide (Chen, 1988; Nelson and Miller, 1992; Gourley et al., 1993).Expansive soil swellsduring rainy

seasons as they absorb water and shrink when this water evaporates. Because of this extreme volumechange,

it causes distress to many civil engineering structures. There are many plastic types of clay that swell

considerably when water is added to them and then shrink with the loss of water. Roads constructed on these

clays are subjected to large uplifting forces caused by the swelling. These forces will induce heaving,

European International Journal of Science and Technology ISSN: 2304-9693 www.eijst.org.uk

20

cracking and breakup of roads (Das, B. M., 2011).Expansive soils are typically clays that demonstrate

extensive volume and strength changes at varying moisture content due to their chemical composition. This

change in soil volume has shown through history to cause significant structural damage to foundations,

including pavements (West, 1995). (Andy, 1989) reported that the lateral swelling pressure might be twice

that of the vertical swelling pressure.(Joshi and Katti, 1980) reported that the lateral swelling pressure ten

times larger than the vertical swelling pressure at a depth of0.28m.Pavements on expansive soils are

common in manyparts of the world, particularly in semi-arid regions.Such soils are generally unsaturated

and contain alarge amount of clay. In the presenceof water after a dry state, these soils undergo asignificant

volume change (Snethen et al., 1975). (Prasad et al., 2010; Jones and Holtz, 1973) reported that the losses

due to extensive damageto highways running over expansive soil sub-gradesare estimated to be in billions of

dollars all over theworld. Several mitigating techniques are adopted to counteract theproblems posed by the

expansive soils either by modifying the properties of the soil by lime, cement, fly ash, calcium chlorideor by

adopting special foundation technique(SubbaRao and Satyadas,1980, Marienfeld and Baker, 1999,

Thompson and Robnett, 1976). The severity of damagesdone by expansive soil has been well documented in

literature worldwide (Chen, 1988,Nelsonand Miller, 1992,Gourley et al., 1993).(Adel Djellali et.al,

2012)investigated the behavior of flexible pavements on expansive soils consisting mainly of brown clayey

silt in Tebessa, Algeria. Computer code Plaxis 8.2 was used fornumerical simulation to check the behavior

of structure pavement with three models in pavement structure, and freeexpansion test was performed to

calibrate the soil sub-grade with Soft-Soil Model. The results showed that the combinedmodel Mohr-

Coulomb in the pavement structure and the Soft-Soil in sub-grade accord perfectly with deformationstaken

on the existing pavement. (N. V. Nayakand R. W. Christensen, 1970) made study for the prediction of

swelling behavior of compactedexpansive soils. The study is based on a semi-empirical approach in which a

model ofswelling behavior is developed leading to equations relating swelling potential or swelling pressure

of acompacted soil to its plasticity index, clay content and initial molding water content. The results showed

that the predicted values of the swelling potential and swelling pressure based onthe proposed model agree

closely the experimental results of this study and those reported in theliterature. (Ayman A. Abed, 2008)

made study to model the behavior of expansive soil in the framework of unsaturated soil mechanics. The

proposed model is used then to predict the displacementsassociated with the changes in soil suction. The

elasto-plasticity framework is used forconstitutive modeling.

This paper presents a study result of the behavior of flexible pavement constructed on dry and saturated

expansive sub-grade soil through numerical analysis using the Finite Elements Method (FEM).

Plaxisprogram version 8.2 was used to model the behavior for this research. Pavement structures have rarely

been analyzed with finite element programs under static loading.The structure was subjected to two trucks

load with dual wheel load of 350kN/m2per axle. Then a complete analysis of stress-strain was performed on

the pavement structure. First, one truck pass was simulated. Then, loading from two trucks at the same time

with dual wheel of 0.60m wide was studied. Modeling was done by a static plain strain analysis and the

element mesh consisted of triangular elements each with 15 nodes.

2. Numerical Modeling using Plaxis

The finite element method was used to analyze the flexible pavement section resting on dry and saturated

expansive sub-grade soils.The software Plaxisv8.2 was used. Plaxisv8.2 software is a two-dimensional FEM

computer program that is used for stability analysis and deformation of soils in different geotechnical

problems. In this method,analyzed structure is divided to smaller elements and displacements of any point

in these elements are related to nodal displacements. The pavement section was considered as a 2-D plain

strain problem and 15-noded structural solid element with medium refinements was used for the analysis.

Mohr-coulomb model are used for the simulation of soil behavior and linear elastic model is used for the


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simulation of asphalt concrete layer. The thickness of each layer in the pavement section resting on

expansive sub-grade soils, the material parameters and constitutive models used were shown in Table1. The

total thickness of the pavement was 0.5 m. 2m thickness clayey silt sub-grade was covered with a 0.20 m

layer of crushed gravel as sub-base, 0.20 m crushed gravel as base course and 0.1 m asphalt concrete on

top.The bottom of model was fixed in both vertical and horizontal directions. Both edges of the models were

restricted from horizontal movement. The structure was subjected to the loads from two trucks with dual

wheel load of 350kN/m2 per axle and distributed over a circular area of radius 30 cm. To model the surface

load of the dual wheel, the total load is transferred to the pavement surface through an average contact

pressure of 350 kPa as shown in Fig.1.At first, passing of just one truck was simulated. Then, loading from

two trucks at the same time with dual wheel of 0.60m wide was studied as shown in Fig.1. For case of

saturated expansive soil sub-grade, the ground water level was modeled as a phreatic level at the top surface

of sub-grade according to actual field ground water condition as shown in Fig.2.After defining the material

properties and boundary conditions the finite element mesh is generated as shown in Fig.3.

3. Results and Discussion

3.1 Deformation behaviors by the Finite Elements simulation

Fig.4showsthe deformed mesh and settlementbehavior of the Finite Elements models for dry and saturated

drained expansive sub-grade soil studied. The figureshows that the difference of deformation behavior

producedby dry and saturated drained sub-gradeis significant.As shown inFig.4.a, the value of total

displacement for dry expansive subgrade soil drained is4.96×10-3

m, whileits value for saturated expansive

sub-grade soil drained is45.82×10-3

m as shown inFig.4.b. Fig.5shows the deformed mesh and

settlementbehavior of the Finite Elements models for dry and saturated undrained expansive sub-grade soil

studied. The figureshows that the difference of deformation behavior producedby dry and saturated

undrained sub-grade is significant. As shown in Fig.5.a, the value of total displacement for dry expansive

sub-grade soil undrained is20.51×10-3

m, while for saturated expansive sub-grade soil,the soil body

collapsed as shown in Fig.5.b.

3.2 plastic points and tension cut-off

The modeling results have been presented in Fig.6. Linear Elastic model was appliedfor asphalt concrete

layer and Mohr-Coulomb model was appliedfor the other soil layers. Fig.6 shows the plastic points in sub-

grade and pavement in the model. It is observed that the plastic Coulomb points are concentrated in the sub-

grade under the wheel load 4 for dry sub-grade drained. For the dry sub-grade undrained, the plastic

Coulomb points are concentrated in the sub-grade underthe right side of wheel 2 till the end of road. The

tensile stresses (tension cut-off) are concentrated in the base course under the shoulder for dry sub-grade

drained. For saturated drained and dry undrained, the tensile stresses (tension cut-off) are concentrated in the

base course and sub-base under the shoulder andwheel load 4.

3.3 Deformation in the form of shading

Fig.7 illustrates the deformation after two cycles of loading. The figure depicts that for dry drained sub-

grade, the total displacement is 4.96x10-3

m, whilefor saturated sub-grade drained,the total displacement

is45.45x10-3

m. For dry undrained sub-grade, the total displacement is 16.53x10-3

m. On the other hand, it

was evidenced in the dry undrained sub-grade results that the movements had concentrated largely in sub-

grade beneath the wheel 4 with maximum displacement of 16.53x10-3

m.


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3.4 Comparisons between dry and saturated drained sub-grade

3.4.1 Vertical displacements distribution

The vertical displacements profiles from the Finite Element analysis for case of road structure rested on dry

drained and saturated drained sub-grade soil for one truck and two trucks at centersof wheels and at shoulder

are shown in Figs.8 and 9 respectively. It can be noticedfrom these figures that the difference in vertical

displacements producedby dry drained sub-grade and saturated drained sub-grade is significant.The values

of vertical displacement for saturated drained sub-gradeare much higher than those occur in dry drained sub-

grade for both cases; one and two truck.Referring to Fig.8, for one truck, the values of vertical displacement

under the center of wheel 1 areslightly higher than that valueoccurs under the center of wheel 2 for saturated

drained sub-grade. It is also noted that the values of vertical displacement under the center of shoulder are

very lower and occurs at up direction.

It can be seen from Fig.9, for two trucks thatno significant differences found in vertical displacement under

the center of different wheel loads in dry condition.Unlike, for saturation condition,slightly

signifieddifferences in vertical displacement under the center of different wheel loads are found.It is also

noted that the values of vertical displacement under the center of shoulder aremuch lower and occurs at up

direction compared with those occur under the center of different wheel loads for both one and two truck

cases.Furthermore,the values of vertical displacementdecrease with the depth increase from the top of the

roadfor both cases.

Fig.10 shows the vertical displacements profiles at road surface for dry drained and saturated drained sub-

grade soil using two trucks. It can be observed from the figure that the values of vertical displacement for

saturated drained sub-gradeare much higher than those occur in dry drained sub-grade. In addition, slightly

signified differences in values of vertical displacement along the horizontal distance from the left road edge

till the center of wheel load 4 for dry drained.Unlike, for saturation condition significant differences in

vertical displacement along the horizontal distance from the left road edge till the center of wheel load 4 are

found.At the end of the center of wheel load 4 for saturation condition, the values of vertical displacement

decrease with increasing the horizontal distance from the left road edge till reaching nearly zero and then

occur at up direction above the surface of the shoulder.

3.4.2 Vertical Strain

Fig.11shows the vertical strain profiles at different locations within the pavement structure for dry and

saturated drained for two trucks. It is clear thatthere is no variation in the vertical stain values for dry drained

condition with the horizontal distance from left road edge. This phenomenonis noticed in different layers

position (asphalt concrete surface, base course surface, sub-base surface and sub-grade surface).For case of

saturated drained above asphalt concrete surface and base course surface, the vertical stain valuesremain

constant with the horizontal distance from left road edge till the center of wheel load4,then theygo up

suddenly to the value of 50% and 14.7% respectively, then go down back to theprevious values. Above the

sub-base surface and the sub-grade surface,the vertical stain values are also constant with the horizontal

distance from left road edge. Furthermore, the vertical stain values for the two cases are the same above

bothsub-baseand sub-gradesurfaces.

3.4.3 Shear Strain

The shear strain distributions developed at the top of asphalt concrete layer, base course layer, sub-base

layer and sub-grade layer for dry and saturated drained are shown in Fig.12. In case of dry condition, the

shear strains development at the layers top surfaces are very small and constant along the horizontal distance

from left road edge. For case of saturated condition, it can be seen that the shear strains development at the

top of the asphalt concrete layerare very small and constant along the horizontal distance from left road edge


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till the left edge of shoulder thendecrease suddenly to the value of 13.9%,then increase to -22.6%and return

to nearly zero after that.At the top surface of the base course layer, the shear strains are very small and

constant along the horizontal distance from left road edge till the center of wheel load 3 and then increase to

the value of -8.5% at the road pavement edge.At the top of the sub-base layer and sub-grade layer, the shear

strains are also very small and constant along the horizontal distance.

3.5 Comparisons between dry drained and undrained sub-grade

3.5.1 Vertical displacements Distribution

Fig.13 shows the vertical displacements profiles at center of different wheel loads and shoulder predicted for

case of road structure rested on dry drained and undrained sub-grade soil for two trucks. It can be seen from

this figure that the difference in vertical displacements producedby dry drained sub-grade and undrained

sub-grade is significant.The values of vertical displacement for dryundrained sub-gradeare much higher than

those in dry drained sub-grade under the center of both wheel loads 1, 2, 4 and shoulder.For dry undrained

under the center of both wheel loads 1, 3and 4, the values of vertical displacement at the road surface are -

1.2%, -5% and -14.2% respectively.Unlike, for dry undrained condition under the centerof both wheel

loads2 and shoulder,the values of vertical displacement occur in the opposite direction comparing with

vertical displacement values occurunder the centerof both wheel loads 1, 3 and 4. The values of vertical

displacement at the road surface under the center of both wheel loads 2 and shoulder are 3.9% and 10.7%

respectively.It can be seen from Fig. 13, that no significant differences in vertical displacement values under

the center of different wheel loads in dry condition.It is also noted that the values of vertical

displacementdecrease with the increasein depth in bothcases.Fig.14shows the vertical displacements profiles

at road surface for dry drained and undrained sub-grade soil under two trucks load. It can be observed from

the figure that the values of vertical displacement for dry undrainedsub-gradearelower than those occur in

dry drained sub-grade along the horizontal distance from left road edge till the left edge of wheel loads 3,

then they increaseup to(-14.3) mm and then they decrease to zero at the begin of shoulder.Above shoulder

surface, the vertical displacement occurs in the opposite direction (up direction).

3.5.2 Vertical Strain

Fig.15shows the vertical strain profiles at different locations within the pavement structure for dry

drainedand undrained due to two trucks load. It is noted from this figure that approximately there is no

variation in the vertical stain values for dry drained condition with the horizontal distance from left road

edge. For case of dry undrained above asphalt concrete surface, the vertical stain values arealmost constant

with the horizontal distance from left road edge till the center of wheel load4 then theyincrease suddenly to

the value of 5.45% and they return back to the previous values after that. Otherwise, above sub-grade

surface for case of dry undrained, the vertical stain values are constant with the horizontal distance from left

road edge till the center of wheel load 3, thenincrease to the value of (-1.52)% andreturn to the constant

previous values later.

3.5.3Shear Strain

The shear strain distributions developed at the top of asphalt concrete layer and sub-grade layer for dry

drainedand undrained are shown in Fig.16. In case of dry undrained condition, it can be seen that the shear

strains developed at the top of the asphalt concrete layerare very small and constant along the horizontal

distance from left road edge till the shoulder thendecrease suddenly to the value of 1.26% and increase at the

center of shoulder surface to the value of (-5.2) %. For case of dry drained condition, the shear strains

developed at the top of the asphalt concrete layerare very small and constant along the horizontal distance

from left road edge. The shear strain distributions developed at the top of sub-grade layer vary and increase


24

along the horizontal distance till the value 0f (-11.6) % at the left side of wheel load 4, and then decrease

again.

3.6 Total displacement by the applied loading

The values of total displacement for different cases and calculation states are shown in Table 2. Considering

Table 2, models in case of both dry drained, dry undrainedand saturated drained development could bear all

of the loading phases (Phase 1 one truck, Phase 2 two trucks).Whereas, the models in case of saturated

undrained subgrade could not bear the applied loading and collapsed in 1st phase stage 15.

4. Conclusion

Based on the result and analysis had been done for this research, the following conclusions are drawn:

1.The Mohr-Coulomb model reveals that the deformations are concentrated exclusively in the pavement

situated in direct contact with traffic loads, with the appearance of plastic tension cut-off points in base

course under the shoulder for dry subgrade drained. For saturated drained and dry undrained, the tension

cut-off are concentrated in the base course and subbase under the shoulder andwheel load 4.

2.The plastic Coulomb points are concentrated in the subgrade under the wheel load 4 for dry sub-grade

drained. For the dry sub-grade undrained, the plastic Coulomb points are concentrated in the sub-grade

under the right side of wheel 2 till the end of road.

3.The values of vertical displacement for saturated drained and dry undrained sub-grade were much higher

than that occurs in dry drained sub-grade.

4.No significant differences are found in vertical displacement under the center of different wheel loads in

dry condition.Unlike, for saturation condition, significant differences in vertical displacement under the

center of different wheel loads were found.

5.The values of vertical displacement under the center of shoulder were much lower compared with

thatoccurs under the center of different wheel loads for both one and two trucks load.

6.The values of vertical displacement decrease with the increase in the depth from the top of the road for

both one and two truck loads.

7.There was no variation in the vertical stain values for dry drained condition with the horizontal distance

from left road edge.

8.For case of saturated drained above asphalt concrete surface and base course surface , the vertical stain

values were approximately constant with the horizontal distance from left road edge till the center of

wheel load 4 then they increased suddenly. Above the sub-base surface and the sub-grade surface, the

vertical stain values were also constant with the horizontal distance from left road edge.

9.For case of saturated drained,the shear strains developed at the top of the asphalt concrete layerwere very

small and constant along the horizontal distance from left road edge till the left edge of shoulder, then

they decreased suddenly. At the top of base course layer, the shear strains were very small and constant

along the horizontal distance from left road edge till the center of wheel load 3 and then increased.The

shear strain distributions developed at the top of the sub-base layerand sub-grade layer were also very

small and constant along the horizontal distancefor dry and saturated drained condition.

10.The values of vertical displacement for dry undrained sub-grade were lower than those occurred in dry

drained sub-grade along the horizontal distance from left road edge till the left edge of wheel loads 3

then they increased to the value of (-14.3) mm and then they decreased again to zero at the begin of

shoulder. Above shoulder surface, the vertical displacement occurred in the opposite direction (up

direction).


25

11.For case of dry undrained above asphalt concrete surface, the vertical stain values were approximately

constant with the horizontal distance from left road edge till the center of wheel load4 then they

increasedsuddenly to the value of 5.45% before returning back to the constant previous values.

12. In case of dry undrained condition,the shear strains developed at the top of the asphalt concrete

layerwere very small and constant along the horizontal distance from left road edge till the shoulder

wherethey decreased suddenly. At the top of sub-grade layer they increased along the horizontal distance

till the value 0f (-11.6) % at the left side of wheel load 4 and then they decreased again.

13.The models in case of both dry drained, dry undrained and saturated drained sub-grade could bear all of

the loading phases (Phase 1 one truck, Phase 2 two trucks). Whereas, the models in case of saturated

undrained sub-grade could not bear the applied loading and collapsed in 1st phase stage 15.

5. References

Chen, F.H.(1988) Foundations on expansive soils, Elsevier Science publication, Newyork.

Nelson, D.J., and Miller, D.J. (1992) Expansive soils, problems and practice in foundation and pavement

engineering, John wiley and Sons, Newyork.

Gourley, C.S., Newill, D., and Shreiner, H.D.(1993) “Expansive soils:TRL’s research strategy, ” Proc.Int.

Symposium on engineering characteristics of arid soils.

Das, B. M. Principles of Foundation Engineering. (2011).7th edition.Cengage Learning.

West, T R (1995), Geology Applied to Engineering, Prentice Hall.

Andy, B.F.,(1989), "Laboratory evaluation of lateral swelling pressure,"Journal ofGeotechnical Engineering

. ASCE, Vol. 115, No.lO, pp. 1481-1486.

JoshiR.P.,andKatti,R.K.,(1980),"Lateral pressure development under surcharges,"proceedings , 4th

International Conference on expansive soils, Denver, CO, pp. 227-241

Snethen, D. R., Townsend, F. C., Johnson, L. D., Patrick, D. M. and Vedros, S. P. J. (1975) “Review of

engineeringexperiences with expansive soils in highwaysubgrades”, US Army Engineer Water Ways

ExperimentStation, FHWA, USA.

Prasad, D. S. V., Kumar, M. and Prasadaraju, G.V. R.(2010) “Behavior of reinforced subbases on

expansivesoil subgrade”, Global Journal of Researches in Engineering,Vol. 10, pp. 225-235.

Jones, D. E. and Holtz, W. G. (1973) “Expansive soilsthehidden disaster” , Civil Engineering : American

Societyof Civil Engineers, Vol. 43, No. 8, pp. 49-51.

Subaraob, K. S. and Satyadas, G. C. (1980) “Prewettedand overloaded expansive soil”, Proceedings

ofGeotech. 80, Bombay, pp. 29-32.

Marienfeld, M. L. and Baker, T. L. (1999) “Pavingfabric interlayer as a pavement moisture

barrier”,Transportation Research Circular, E-C006, ISSN 0097-8515.

Thompson, M. R. and Robnett, Q. L. (1976) “Pressureinjected lime for treatment of swelling soils”. In:One

of the 4 reports Prepared for the 54th Annual meetingof the TRB, TRR-568, pp. 24-34.

Djellali A., Ounis A. and SaghafiB., (2012), “Behavior of Flexible Pavements on Expansive Soils”,

International Journal of Transportation Engineering, Vol.1/ No.1/ Winter 2012, PP 1-14.

Nayak,N. V. and Christensen,R. W., “swelling characteristics of compacted, expansive soils”, 1970, Clays

and Clay Minerals, 1971, Vol. 19, pp. 251-261.

AymanA. Abed, (2008), “Numerical Modeling ofExpansive Soil Behavior”, Ph.D thesis, Institute for

geotechnical, Stuttgart University, Germany.


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Figures and Tables:

Table (1) Input Parameter of the Model

Material Asphalt

Concrete

Base Course

(Crushed

Gravel)

Subbase

Course

(Crushed

Gravel)

Expansive

Subgrade

Soil Dry

Expansive

Subgrade

Soil

Saturated

Model

Thickness, cm

Young’s modulus,

KN/m2

Poisson’s Ratio ν

Dry density KN/m3

Saturated density

KN/m3

Cohesion KN/m2

Friction angle ϕ (°)

Dilatation angle (°)

kx[m/day]

ky[m/day]

LE

10

5400×103

0.35

25.0

-

-

-

-

-

-

MC

20

250×103

0.35

21.20

23.20

30

43

13

1.000

1.000

MC

20

120×103

0.35

22

24

20

44

14

1.000

1.000

MC

200

50×103

0.30

16

18

10

25

0.0

0.0001

0.0001

MC

200

10×103

0.30

16

18

5

13

0.0

0.0001

0.0001

LE : Linear Elastic MC : Mohr-Coulomb

Table 2 Numerical modeling results for different cases of studied model.

Drained

Case

Saturation Calculation state No. of

truck

Total displacement

(mm)

Drained

Drained

Dry

Saturated

Fully reached

Fully reached

One Truck

One Truck

One Truck

One Truck

4.53×10-3

26.57×10-3

Undrained

Undrained

Dry

Saturated

Fully reached

Failed in Phase 1 stage

15

4.20×10-3

Failed

Drained

Drained

Dry

Saturated

Fully reached

Fully reached

Two Truck

Two Truck

Two Truck

Two Truck

4.96×10-3

45.82×10-3

Undrained

Undrained

Dry

Saturated

Fully reached

Failed in Phase 1 stage

15

20.51×10-3

Failed

Fig. 1: Modeling of flexible pavement resting on dry expansive sub-grade soils in Plaxis 2D.


27

Fig. 2: Modeling of flexible pavement resting on saturated expansive sub-grade soils in Plaxis 2D.

Fig. 3: Meshed geometry of the model

a) Dry drained expansive soil sub-grade.

b) Saturated drained expansive soil sub-grade.

Fig. 4: Deformed mesh of studied model for two trucks 350 KN/m2 dual wheel load case expansive soil sub-

grade drained.


28

a) Dry undrained expansive soil sub-grade.

b) Saturated undrained expansive soil sub-grade (Soil body collapses).

Fig. 5: Deformed mesh of studied model for two truck350 KN/m2 dual wheel load case expansive soil sub-

grade undrained.




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c) Dry undrained expansive soil sub-grade.

Fig. 6: Plastic, tension-cut-off.



c) Dry undrained expansive soil sub-grade.

Fig. 7:Deformation in the form of shading.


30

Fig. 8: vertical displacements profile of dry and saturated drained sub-grade for one truck.

Fig. 9:vertical displacements profile of dry and saturated drained sub-grade for two trucks.


31

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

0 1 2 3 4 5 6 7 8 9

Ve

rtic

al d

isp

lace

me

nt

(mm

) Distance from left road edge (m)

Dry Drained

Saturated Drained

Fig.10: Vertical displacement profiles above AC layer for dry drained and saturated drained sub-grade

-5

0

5

10

15

20

25

30

35

40

45

50

0 1 2 3 4 5 6 7 8 9

Ve

rtic

al s

tra

in (

%)

Distance from left road edge (m)

Dry Drained

Saturated Drained

a) Above asphalt concrete surface.

-5

0

5

10

15

20

25

30

35

40

45

50

0 1 2 3 4 5 6 7 8 9

Ve

rtic

al str

ain

(%

)


Dry Drained

Saturated Drained

b) Above base course surface.

-5

0

5

10

15

20

25

30

35

40

45

50

0 1 2 3 4 5 6 7 8 9

Ve

rtic

al str

ain

(%

)


Dry Drained

Saturated Drained

c) Above sub-base surface.

-5

0

5

10

15

20

25

30

35

40

45

50

0 1 2 3 4 5 6 7 8 9

Ve

rtic

al str

ain

(%

)


Dry Drained

Saturated Drained

d) Above sub-grade surface.

Fig. 11 Vertical strain profiles for dry drained and saturated drained sub-grade.


32

-25

-20

-15

-10

-5

0

5

10

15

0 1 2 3 4 5 6 7 8 9

Sh

ea

r S

tra

in (

%)


Dry Drained

Saturated Drained


-25

-20

-15

-10

-5

0

5

10

15

0 1 2 3 4 5 6 7 8 9

Sh

air

Str

ain

s %


Dry Drained

Saturated Drained

b) Above base course surface.

-25

-20

-15

-10

-5

0

5

10

15

0 1 2 3 4 5 6 7 8 9

Sh

air

Str

ain

s %


Dry Drained

Saturated Drained

c) Above sub-base surface.

-25

-20

-15

-10

-5

0

5

10

15

0 1 2 3 4 5 6 7 8 9

Sh

air

Str

ain

s % Distance from left road edge (m)

Dry Drained

Saturated Drained

d) Above sub-grade surface.

Fig.12 Shear Strain Profiles for dry drained and saturated drained subgrade.


33

Fig.13 Vertical displacements profile of dry drained and undrained sub-grade in case of two trucks.

-15

-10

-5

0

5

10

15

0 1 2 3 4 5 6 7 8 9

Ve

rtic

al D

isp

lace

me

nt

mm

)


Dry Drained

Dry undrained

Fig. 14Vertical displacement profiles above AC layer for dry drained and undrained sub-grade.

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9

Ve

rtic

al

stra

in (

%)


Dry Drained

Dry undrained



34

-2

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9

Ve

rti

ca

l str

ain

(%

)


Dry Drained

Saturated Drained

b) Above subgrade surface.

Fig.15 Vertical Strain Profiles for dry drained and undrained subgrade.

-13

-10

-7

-4

-1

2

0 1 2 3 4 5 6 7 8 9

Sh

ea

r stra

in (

%)


Dry Drained

Dry undrained


-13

-10

-7

-4

-1

2

0 1 2 3 4 5 6 7 8 9

Sh

air

Str

ain

s %


Dry Drained

Dry undrained

b) Above sub-grade surface.

Fig.16 Shear strain profiles for dry drained and undrained sub-grade.

Numerical Modeling of Flexible Pavement Constructed On ... · Mostafa Deep Hashem Civil Engineering...

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