Studying the effect of soft clay layer with different ...

CSCE 2013 General Conference - Congrès général 2013 de la SCGC

Montréal, Québec May 29 to June 1, 2013 / 29 mai au 1 juin 2013

Studying the effect of soft clay layer with different thicknesses on piled raft considering the superstructure. W. H. El Kamash* *

Dept. of civil Engineering, Suez Canal University, Egypt

Abstract: Many cities over the world such as Frankfurt, Shinghai and Port-Said contain soft clay layers underlain sand layers. That soft clay layer which exists with different positions and thicknesses presents a geotechnical challenge for deep foundation. Herein, a continuum model was developed to analyze such problem depending on Mindlins’ solutions. That model was incorporated into a computer program ASTN3 which was developed by the author in order to study the behavior of a layer of soft clay with different hypothetical positions and thicknesses. Based on finite element method, ASTN3 was used to analyze three dimensional buildings on piled raft in a parametric study. The study was extended to include the effect of the position and thickness of the soft clay in addition to the geometry of the superstructure. Discussions on the numerical results were performed and conclusions were drawn. 1.

Introduction

Differential settlement has a severe effect on buildings especially in cases of coastal cities which have a soft soil such as Port-Said as shown in Fig. 1. Traditional shallow foundation cannot control settlement while the cost of constructing piles group is rather expensive. For that reason, piled raft which employs both of piles and the raft simultaneously is considered a hot topic to be focally studied due to its economical impact. Early researches focused on homogeneous soil in the analysis, however, in the practical life, soil is always composed of different layers. Some of software programs were presented based on both of finite element and finite difference methods to analyze piled raft. Most of those did not consider 3D superstructure. El Kamash (2012) presented a model for analysis 3D-structures on piled raft against vertical and lateral loads using a computer program called ASTNII. The effect of superstructure on the analysis of piled raft was considered to worth the study. Moreover, El Kamash et al. (2012) developed software ASTN3 to examine the effect of 3D-structures with shear wall over piled raft against gravity and earthquake loads. Pile groups which are embedded in nonhomogeneous soil were analyzed by Chow (2009) based on elasticity theory against gravity and lateral loads. The finite approach method was used to determine the flexibility coefficients. The stiffness matrices of the soil were formulated by considering the variation of the soil stiffness into the numerical integration process in order to model the nonhomogeneity of the soil. Chow (2009) used Hankel and Fourier transforms based on the equations of Small and Booker (1984) to develop a software computer called APRILS in order to analyze piled raft against lateral and vertical loads. Analytical models were performed to GEN-269-1

simulate heterogeneous elastic properties of layers in vertical and horizontal directions for multilayered grounds and improved ground was presented by Hirai (2007). He proposed an equivalent elastic method to determine settlements and stresses of multi-layered. A numerical procedure was investigated by Maheshwari and Madhav (2006) to describe the analysis of the vertical deformation and the stress distribution of the strip footings on layered soil media with middle thin layer which has a high stiffness. Framework Analogy was presented to model the raft as plate element by Baz (1987).

Figure 1: Failure of structures in the gas station “Temsah” on the northwest of Port-Said due to deferential settlement That technique was used to model the raft and slabs by the same type of beam element in order to achieve the compatibility in the whole structure. El Gendy (1999) examined a threedimensional continuum model which considers any number of irregular layers and the nonlinearity of soil medium using FEM. Moreover, El Gendy (2007) introduced the composed coefficient technique to reduce the size of the stiffness matrix which increases the efficiency of finite element method to deal with huge problems. The software ASTN3 which was used in this study was proposed to analyze different shapes of 3-D buildings over piled raft embedded in nonhomogeneous soil. The response of each pile, slabs and the raft was modeled using continuum model, while the interaction among elements; pile–soil pile, raft–soil–raft and pile–soil– raft was calculated on the bases of integration of Mindlin’s solutions, Basile (2002). ASTN3 considered the elastic perfect plastic characteristic of the soil. The nonlinearity of the soil was considered in ASTN3 by incorporating Equivalent Stiffness technique which was developed by El Gendy (2007). The objective of this study is to reflect the effect of the presence of a very soft clay layer is in between comparatively stiff soil layers. Such cases occur in coastal area like Port-Said which lies on the eastern side of the Nile delta at the north entrance of the Suez Canal on the Mediterranean Sea. Golder Associates (1979) performed geotechnical study for the source of soil data of Port-Said. Reda (2009) studied the comparison between different foundation systems for Port-Said area with using the source data which was performed by Golder Associates (1979). The study presented the piled raft as the suitable system for Port-Said soil medium as well as considering the piled raft as settlement controller to avoid any excess differential settlement. 2.

Mathematical Model

The soft soil bore log of Prot-Said was performed by Golder Associates (1979). Based on equations presented by Nishida (1956), modulus of compressibility may be expressed as follows.

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[1]

 σ  σ  1 Cc σH  log  o H Es (1  eo )  σo 

Where, Es is the modulus of compressibility of Port-Said clay, (kN/m2), Δσ is the average vertical 2 stress increase in clay, (kN/m ), H is the layer thickness, (m) and σo is the initial overburden 2 pressure in a layer, (kN/m ). .

Figure 2: Typical soil properties of Port-Said area. Reda (2009) investigated the modulus of compressibility of the soil as shown in the Fig. 2 based on the following formula.

[2]

E s = E so 1+ 0.06 z 

Where, Eso is initial modulus of compressibility, Eso=2.7*103 (kN/m2) and z is the depth measured from the clay surface, m. Many sites consist of a soft intermediate soil layer between a relatively stiff soil layers. Fig. 2 presents a typical soil profile for Port-Said soil medium. The sand stratum is under the surface clay. The average thickness of the sand is 6.5 (m) ranges from 4.2 (m) to 10 (m). The transition zone exists under the sand stratum, at an elevation of about 7 (m). The lower clay is firm, becoming stiff, dark grey, organic and micaceous. The case of transition zone which varies in thickness and depth has a considerable effect. However, the study focally that effect on the behavior of piled raft was performed here. The soil deposit was modeled as shown in Fig.3(a) to include three layers (I), (II) and (III) of thicknesses, h1, h2, and h3, respectively. The modulus of elasticity and Poisson’s ratios of the layers are (E1, m1), (E2, m2) and (E3, m3) respectively, and GEN-269-3

these layers are underlain by a rigid base. Uniform load of intensity, q, was applied over a width, 2B, at the ground level, on the top of the layer (I). The second layer (II) was the soft layer, while the both of first and third layers (I) and (III) respectively were comparatively stiff layers. Values of (E1, m1) were computed as average values for Port-Said soil medium, while (E2, m2) was modeled to simulate a hypothetical soft layer based on Maheshwari and Madhav (2006). Soil was modeled as a three dimensional continuum medium based on integrations of Mindlin’s solutions. For the soil; modulus of the elasticity may be expressed as function of the modulus of the compressibility as follows, Reda (2009).

[3]

E=

1   s  2 s2 Es 1  s

Where, E is the modulus of the elasticity of the soil. It is well known from the theory of elasticity that Poisson’s ratio has not mentioned influence on stresses, while it has slightly more influence on displacements. Therefore, to simplify the analysis, the Poisson ratio for the soft layer was assumed to be the double value of the remained stiff layers for all cases. A 3D finite element method, incorporated in the analysis of structures resting on nonlinear soil (ASTN) version 3, El Kamash (2012), was adopted in this study. Herein, piles, beams and columns were represented by frame elements, while the raft and slabs were represented as plate elements by Framework Analogy, Baz (1987) as shown in Fig. 3(b). An elastic perfect plastic model of the soil was performed based on hyperbolic function. The composed coefficient technique was employed in the numerical model in order to save time of proceeding with reasonable accuracy. The nonslipped conditions were applied between the soil and piles. The interaction was completely performed between all soil elements adjacent to elements of piled raft based on integrations of Mindlin’s solutions which was introduced by Basile (2002). The surface between the raft and the soil was assumed to be smooth and the shear strain due to vertical loads was not considered. The elastic settlement beneath the corner of the rectangular element (B * L) which represents the dimension of each discretised element in FEM may be used to express the flexible coefficient of the raft’s element as presented by Boussinesq, Das (1999) as follows.

[4]

f rii 

B (1   2 )I 5  2 AE s

where, Es is the modulus of elasticity of the soil and  is Poisson ratio of the soil. I5 in Eq. (4) can be written in the following manner:

[5]

I5 

 1  m 2  1  1   1  m 2  m   ln  m ln   1  m 2  1     1  m 2  m    

where, m is a ratio factor between the length L and the width B of each element in the raft. The flexible coefficient for shear resistance, fshii, tends to be singular and the solution for such case can be gotten using the integration of Mindlin’s solutions based on Basile (2002) as follows.

[6]

w(i)  t ( j )



G (i, j ) dS ( j )

S

where, t is the uniform distributed tractions over the surface area of the shaft denoted by the surface S at any element j, w is the vertical displacement at any element i. G(i,j) represents the flexible coefficient of point load embedded in the soil based on Poulos and Davis (1980). G(i,j) is the integration of shear stress over the surface of pile element and it can be formulated as follows. GEN-269-4

[7 ]

G(i, j ) 

2

ro

0

0

 

f ij r dr d

where, fij is the flexible coefficient which represents the settlement at any arbitrary point i due to unit load at point j beneath the earth surface and ro is the radius of the pile. Herein, Steinbrenner’s approximation was incorporated to Mindlin’s solution in order to consider the nonhomogeneity of the soil by approximate solutions.

(a) Defined sketch of the soil. Figure 3: Modeling the supported soil.

(b) 3D-Space raft–pile–soil modeling.

Fig.3(b) shows number of layers n, and the layer which contains i is denoted by ‘’, settlement at i due to the effect of a point load at j can be calculated as follows.

[8]

[9]

the

k k f kj  f ( z top )  f ( z Bottom )

n

f

f ij  \

k 1,

where

kj

 ( f ij  f ( z Bottom ))

k  

where, fij\ is the modified flexible factor for the case of layered soil, fkj is the flexible coefficient representing the settlement at k due to unit load at j and f(Zktop) and f(ZkBottom) are flexible coefficients representing the settlement at the upper boundary and the lower boundary of layer k due to unite load at point j respectively. In addition, an average technique suggested by Poulos and Davis (1980) and Poulos (1990) is involved into the model as following equations.

[10]

E s (ij ) 

[11]

E s (1 j ) 

( E s (i )  E s (i 1) )  ( E s ( j )  E s ( j 1) ) 4 2 E s (1)  ( E s ( j )  E s ( j 1) ) 4

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where Es (ij) is the average Young’s modulus of the soil at the depths Zi and Zj, Es(i) and Es(j) are moduli of elasticity for soil layer numbers i and j. Based on above model, the stiffness matrix can be built for both of the substructure and the superstructure to be solved simultaneously. Moreover, continuous conditions were applied considering the interaction for all of substructure elements; pile-soil-pile, raft-soil-raft and pile-soil-raft. 3.

Verification

A 3D finite element method for Analysis of Structures resting on Nonlinear soil (ASTN) version 3 was developed in this study in order to perform the parametric study. To verify the validity of ASTN3, El Kamash (2012) showed that results obtained by the present approach ASTN3 are in a reasonably good agreement with those results which presented previously by researchers using different methods of analysis such as Poulos (1979), Poulos and Davis (1980), Das (1999), Poulos (1990), and Sommer et al. (1985). Moreover, Results of pile group which have been analyzed by ASTN3 and presented by El Kamash et al. (2012) showed a good agreement with other computer programs such as PIGLET, GEPAN and PGROUPN. 4.

Parametric study

4.1 Description of the model Herein, 3D-12 storeys-space structures of square and rectangular typical floors models were analyzed using ASTN3. Source data of soil which was shown in Fig.3(a) was considered. Groundwater was assumed to be directly below the raft which is 2.0 (m) below the ground surface. The square model has 4 bays in each of X- and Y-directions, while the rectangular one has 3 bays in X- direction and 6 bays in Y-direction as shown in Fig. 4. Both of two models have nearly the same area. Heights of ground and typical floors are 4.00 (m) and 3.00 (m), respectively. The structural system of all roofs is a flat slab type of 20 (cm) thickness subjected to a total uniform load of 10 (kN/m2). Dimensions of columns were listed in Table 1. The raft has 1.25 (m) thicknesses. The estimated total vertical load on both square and rectangular rafts is 101.265 (MN). A total of 25 piles are located under the raft for each model as shown in Fig. 5. In the analysis, the interaction between different elements of the foundation was achieved based on Mindlins’ solutions, while he raft was treated as an elastic plate supported on elastic piles considering the effect of the superstructure. Reda (2009) showed that lengths of piles in the piled raft system resting on Port-Said soil range from 16 to 24 (m). So that, piles were assumed as identical piles with length of 20 (m), and the effective depth of the soil layers under the raft was taken 40 (m). Two main parameters were studied in the analysis for both cases of structures; square- and rectangular-shapes. Herein, eight cases were examined; they can be illustrated as follows. 1) Change in the position of the soft clay layer for a square-shape structure resting on piled raft. 2) Change in the position of the soft clay layer for a square-shape structure resting on pile group. 3) Change in the position of the soft clay layer for a rectangular-shape structure resting on piled raft. 4) Change in the position of the soft clay layer for a rectangular-shape structure resting on pile group. 5) Change in the thickness of the soft clay layer for a square-shape structure resting on piled raft. 6) Change in the thickness of the soft clay layer for a square-shape structure resting on pile group. 7) Change in the thickness of the soft clay layer for a rectangular-shape structure resting on piled raft. GEN-269-6

8) Change in the thickness of the soft clay layer for a rectangular-shape structure resting on pile group. Young's modulus Eb for slabs, columns and the raft is 3.4*107 (kN/m2), while Eb for piles is 2.35*107 (kN/m2). Unite weight γb for all elements is 25 (kN/m3) and Poisson ratio b is 0.2. Each case of change in the position of the soft clay layer was analyzed five times with varying the ratio h/L of the soft clay layer. Moreover, the model was analyzed three times with varying the ratio t/L of the soft clay layer for each case of change in the thickness of the soft clay layer beside the case which considers the case without soft clay.

Figure 4: Typical floors for the two models with column arrangement

Figure 5: Piled rafts of the two shape models 4.2. Vertical Displacements Settlements at centers of the building floor roofs of rectangular- and square- models resting on piled raft decrease as the soft clay layer moves down by increasing the value of h till reaching the half of L as shown in Figs 6(a) and 8(a). By increasing the ratio h/L over 0.5, settlements come back to increase extremely. Min. and Max. settlements are recorded at h/L=0.5 and h/L=0.93 respectively for all cases of changing the position of the soft clay layer. This GEN-269-7

difference in settlement was increased dramatically with increasing the ratio h/L over 0.5 to range from 2 to 3.5 times of h/L=0.5 at h/L=0.79 and h/L=0.93 for both cases of the rectangular- model resting on piled raft and piles group as shown in Figs. 7(b) and 9(b) respectively. The increment in the case of change the thickness of the soft clay layer is extrusive for both cases of square- and rectangular-models for all cases as shown in Figs. 7 and 10. As the thickness of soft clay layer increases from t/L=0.14 to t/L=0.43, settlements increase by percentages of 40% and 60% for square- and rectangular-models as shown in Figs. 8(a) and 10(a) respectively in the case of piled raft. Those percentages reach to 115% and 100% for square- and rectangular-models as shown in Figs. 7(b) and 9(b) respectively for the case of piles group. The increment of thickness of the soft layer has a strong effect on settlements; it increases dramatically, as the thickness of the soft layer increases and it may be represented by an exponential form as shown in Fig. 10.

Settlement s [cm]

Settlement s [cm] 2

4

6

8

0

10

40

40

35

35

30

30

Floor Height [m]

Floor Height [m]

0

25 without clay layer Ratio h/L=0.07 Ratio h/L=0.21 Ratio h/L=0.5

20 15 10

0

4

6

8

10

12

25 without cla y la yer Ra tio h/L=0.07 Ra tio h/L=0.21 Ra tio h/L=0.5

20 15 10

Ratio h/L=0.79 Ratio h/L=0.93

5

2

Ra tio h/L=0.79 Ra tio h/L=0.93

5 0

a) Piled raft (b) piles group Figure 6: Settlements at the centres of the building of rectangular-shape resting on the piled raft due to the change in the position of the soft layer Settlement s [cm]

Settlement s [cm] 0

2

4

6

8

10

0

12

2

3

4

5

6

40

40

without clay layer

35

Floor Height [m]

30

Floor Height [m]

1

25 20

35

thickness ratio=0.14

30

thickness ratio=0.43

25 20 15

15 without clay layer

10

10

thickness ratio=0.14 thickness ratio=0.43

5

5

thickness ratio=0.71

0

0

(a) Piled raft

(b) piles group

Figure 7: Settlements at the centres of the building of rectangular-shape resting due to the change in the thickness of the soft layer 4.3. Bearing Factors

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The bearing factor is defined as the percentage of loads which is resisted by piles of total loads and it can be considered as indication of the performance of piled raft. As bearing factor decreases, the contribution of the raft increases in resisting loads. Bearing factors change due to the change of the position of the soft clay layer depending on the ratio of h/L related to periodic behaviour for both cases of rectangular- and square- models. That periodic behaviour leads bearing factor to decrease by a percentage of 28% as the soft clay layer moves down till reaching the minimum value, then the value comes back to increase again by a percentage of 47% as shown in Fig. 11. That phenomenon can be due to the interaction between elements of piles and the raft. As soft layer far from the raft the bearing factor increases. Settlement s [cm] 0

2

4

6

8

Settlement s [cm]

10

0

40

4

6

8

10

40

35

35

30

without cla y la yer

25

Ra tio h/L=0.07

20

Ra tio h/L=0.21

15

Ra tio h/L=0.5

10

Ra tio h/L=0.79

10

5

Ra tio h/L=0.93

5

30

Floor Height [m]

Floor Height [m]

2

25 without clay layer Ratio h/L=0.07 Ratio h/L=0.21 Ratio h/L=0.5

20 15

0

Ratio h/L=0.79 Ratio h/L=0.93

0

(a) Piled raft (b) piles group Figure 8: Settlements at the centres of the building of square-shape due to the change in the position of the soft layer Settlement s [cm] 0

2

4

6

Settlement s [cm] 8

10

12

0

35

35

30

30

25 20 15 10

2

3

4

5

6

40

Floor Height [m]

Floor Height [m]

40

1

without clay layer thickness ratio=0.14 thickness ratio=0.43

25 20 15

without clay layer

10

thickness ratio=0.14

5

thickness ratio=0.43

5

thickness ratio=0.71

0

0

(a) Piled raft (b) piles group Figure 9: Settlements at the centres of the building of square-shape due to the change in the thickness of the soft layer.

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12

rectangular-shape square shape Expon. (rectangular-shape) Expon. (square shape)

10

y = 1.6204e2.6373x

Settlement s (cm)

8

6 y = 0.833e3.3385x

4

2

0 0.00

0.20

0.40

0.60

0.80

1.00

ratio t /L

Figure 10: Settlements for buildings resting on piled raft due to change in the thickness of the soft layer As the soft layer moves down, it affects negatively again on the bearing factor due to its position in the pile in spite of increasing the distance to the raft. On the contrary, the change of bearing factor decreases linearly as the thickness of the soft clay layer increases. Bearing factors differs by a percentage of 51% between maximum and minimum values recorded at t/L=0.14 and t/L=0.71 in respectively, for both cases of rectangular- and square- models as shown in Fig. 12. 120

100 90

100

Bearing factor kpp [%]

Bearing factor kpp [%]

80

80

60

40

70 60

50 40 30 20

20

10

0

0

h/L=0.07

h/L=0.21

h/L=0.50

h/L=0.79

h/L=0.93

without soft layer

Normalized ratio h/L

t/L=0.14

t/L=0.43

t/L=0.71

Normalized ratio t/L

(a) change in the position

(b) change in thickness

Figure 11: Bearing factor for rectangular-shape due to the change in the position of the soft clay 120

100 90 80

Bearing factor kpp [%]

Bearing factor kpp [%]

100

80

60

40

70 60

50 40 30 20

20

10

0

0 h/L=0.07

h/L=0.21

h/L=0.50

h/L=0.79

h/L=0.93

without soft clay

t/L=0.14

t/L=0.43

Normalized ratio t/L

Normalized ratio h/L

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t/L=0.71

(a) change in the position

(b) change in thickness

Figure 12: Bearing factor for square-shape due to the change in the position of the soft clay 5. CONCLUSIONS This paper employed a 3D-numerical procedure to analyze the superstructure supported by piled raft or piles stand-alone systems taking into the consideration pile-soil-pile, raft-soil-raft and pilesoil-raft interactions. A parametric study has been carried out to examine the effect of a soft clay layer with different positions and thicknesses on different shapes of 3D-buildings resting on piled raft and piles stand alone under gravity loads. The parametric study showed that, in the case of soft clay layer in a comparatively stiff soil, the position of middle soft layer recorded lowest values of settlements. The change of the position of soft clay layer during the top half depth of layers had not a significant effect on settlements. While, as much the depth of the soft clay layer increases after the middle depth, settlements increase dramatically till reaching at the base of layer depth regardless piled raft or piles stand-alone cases. Maximum bearing factors recorded changes in periodic behavior due to the change of position of the soft clay layer. Bearing factors decrease, as much maximum moments increase regardless the geometric type. However, piled raft system had a good effect on reducing maximum moment by more than piles stand-alone system. The increment of thickness of the soft layer had a strong effect to reduce settlements and may be put easily in an exponential form. Moreover, the increment of the thickness of soft clay layer had more effect than the change in the position of it on settlements in all cases. Maximum bearing factor was recorded at which the soft layer in the mid-depth position. References Basile, F. 2002. Integrated form of singular., Proc. 10th ACME Conference, Swansea: 191-194. Baz, M. 1987. Plates on nonlinear subgrade. M.Sc. Thesis, El-Mansoura University, Egypt. Chow, H. 2007. Analysis of piled-raft foundations with piles of different lengths and diameters., PhD. Thesis, University of Sydney, Australia. Das, B.M. 1999. Shallow foundations bearing capacity and settlement., CRC Press. El Gendy M.M. 2007. Formulation of a composed coefficient technique for analyzing large piled raft., Journal of Ain Shams university, 42(1). El Gendy, M.M. 1999. An iterative procedure for foundation-superstructure interaction problem., Port-Said Engineering Research Journal, 3(I): 1-19, Egypt. El Kamash, W.H. 2012. The positioning and thickness effect for soft clay layer on 3D-building resting on piled raft., Journal of Ain Shams Elsevier, 3(1): 17–26. El Kamash, W.H., El Gendy M.M, and Salib R.A., Kandil M. 2012. Analysis of Shear Walls on Piled Raft under Earthquake Excitations., conference 2012CSCE Canadian society of Civil Engineering, Edmonton, Canada. Golder Associates 1979. Geotechnical report for Port-Said area., Port-Said, Egypt. Hirai, H., 2007. Settlements and stresses of multi-layered grounds and improved grounds by equivalent elastic method., J Appl Geotech:409–1502. Maheshwari, P., and Madhav, M. R. 2006. Analysis of a rigid footing lying on three-layered soil using the finite difference method., Journal of Geotechnical and Geological Engineering, 24: 851–869. Nishida, Y. 1956. A brief note on compression index of soils., Journal of SMFE Div., ASCE, July, 1027: 1-14. Poulos, H.G. 1990. User's guide to program DEFPIG -Deformation Analysis of Pile. Poulos, H.G., 1979 Settlement of single piles in non-homogeneous soil., Journal of Geotechnical Engineering ASCE, 105(5): 627–641. Poulos, H.G., and Davis, E.H. 1980. Pile foundation analysis and design., Jhon Wiley & Sons Inc., New York.

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Reda, A. 2009, Optimization of piled raft in Port-Said., M.Sc. Thesis, Faculty of Engineering, Suez Canal University, Port-said, Egypt. Small, J., and Booker, J. 1984. Finite Layer Analysis of Layered Elastic Materials Using Flexibility Approach. Part I. – Strip Loadings., Int. Jl. for Numerical Methods. Sommer, H., Wittmann, P., and Ripper, P. 1985, Piled raft foundation of a tall building in Frankfurt clay., Proc. 11th Int. Conf. Soil Mech. Found. Eng, San Francisco, 4: 2253-2257.

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