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Finite element analysis of short piles in expansive soils
Computers and Geotechnics 24 (1999) 231±243
Finite element analysis of short piles in expansive soils Yahia E-A. Mohamedzein*, Muzamil G. Mohamed, Ahmed M. El Sharief Building and Road Research Institute, University of Khartoum, PO Box 321, Khartoum, Sudan Received 10 September 1998; received in revised form 24 March 1999; accepted 26 March 1999
Abstract A two dimensional axisymmetric ®nite element based model for analysis of a soil±pile system in expansive soils is developed. The pile is assumed to behave as linearly elastic while the soil is modelled as nonlinear elastic material. Swelling and shrinkage of the soil are related to change in soil suction. The predictions of the model are compared to the results of ®eld experiments from two expansive soil sites in Sudan, Wad Madani and Elfao. The predictions of the numerical model are in good agreement with ®eld results. Parametric studies are performed using the model. The study shows that increase in pile length decreases the upward vertical movement of the pile. As the axial load increases, both the upward vertical movement and the tensile stress decreases and eventually the pile may be subjected only to downward movement and compressive stresses. Tensile stresses for loaded piles occur throughout most portions of the pile within the active zone with the maximum stress developing near the mid height of the pile. # 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction Expansive soils cover more than one third of the Sudan area. This area contains the most important metropolitan areas and development projects. Annual damage induced by expansive soils was more than 6 million US dollars in 1983 [1]. To reduce the eect of heave, in the past, engineers in Sudan preferred to use a combination of shallow foundations (such as strips and pads) and soil modi®cation techniques (e.g. replacement and compaction). Structures (specially light structures) constructed using these techniques did not perform well in most cases. This is because expansive soils in Sudan extend to greater depths and also because of the semi-arid climate * Corresponding author. 0266-352X/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0266-352X(99)00008-7
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that results in a relatively deep active zone. Recently short piles were introduced as an alternative to shallow foundations to support light structures. Because of limited local case histories, design and construction of these piles follow normal international practices without due consideration to local soil conditions. Thus, analytical methods supplemented by experimental ®eld results are needed to establish acceptable local design and construction techniques. The objective of this study is to provide a ®nite element model for analysis of piles in expansive soils in Sudan. 2. Literature review The ®nite element method is a powerful analytical technique that can be used eectively to analyze the soil±pile system in expansive soils. Ellison et al. [2] used the ®nite element method to study the load deformation mechanism for bored piles in London clay. The axisymmetric stress condition was assumed. The pile was assumed linear elastic and a trilinear elastic stress±strain relationship was assumed for the soil. Amir and Sokolov [3] used the ®nite element method to study the behavior of piles in expansive soils. The conditions of axisymmetric stress for a single pile was assumed and the soil was modeled as linear elastic. Lytton [4] suggested a ®nite element model for calculating the stresses and displacements in a pile founded in expansive soil. This method assumed the soil to behave elastically. Justo et al. [5] presented a three-dimensional ®nite element method to ®nd the stresses and strains in piles in expansive soils. In their method the stress-path followed by the soil elements during the loading and wetting processes were taken into account. From the above review it can be concluded that most of the above methods assumed the soil is linear elastic. In this study the soil is modeled as non-linear elastic by using the Duncan±Chang model or modi®ed Duncan±Chang model [6]. The pile material is assumed linear elastic. 3. Finite element formulation of expansive media The ®nite element formulation is described in detail elsewhere [7,8]. Only the formulation relevant to piles in expansive soils is presented in this section. The swellinginduced forces can be obtained following the formulation presented by Lytton [4]. The equilibrium equations for a soil element undergoing volume change are: BT C"dv 1 F vol
Where F B C "
=nodal forces induced by expansion of the soil; =strain±displacement matrix; =stress±strain matrix; =swelling-induced strains.
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233
Also C"
2
where =stress vector. Lytton [4] suggested the swelling-induced strains to be related to the change in moisture content. However, heave can be better evaluated in terms of soil suction because soil suction is a fundamental factor in controlling mechanical properties of partially saturated soils. Unlike the change in moisture content which is an environmental factor, the soil suction is related to both the intrinsic and extrinsic properties of an expansive soil. Several methods have been proposed for prediction of swell potential and magnitude of heave based on soil suction measurements [9±11]. In these methods, swell is related to change in soil suction through a volume change parameter which is an intrinsic property of the soil. Mckeen's method [10] is one of the methods in which the total heave is related to soil suction change by a parameter called suction compression index. In one-dimensional form, Mckeen's equation can be written as: H hf S log H h0
3
where H H s h f , h0
=swelling-induced strains="; =suction compression index; =®nal and initial suctions, respectively.
The swelling-induced strain vector " in three dimensions can be obtained from the following equation: 2 3 s1 hf 4 " 4 s2 5log h0 s3 where s1 , s2 and s3 are the suction compression indices in the x, y and z directions for the three dimensions stress condition. Eqs. (3) and (4) show that the heave strain can be related to soil suction. The suction compression indices s can also be related to the change in moisture content since the change in moisture content has a well de®ned relation to the change in soil suction. In this study Eq. (4) is implemented in the computer program developed to compute the soil heave. The suction compression indices in the three dimensions are assumed to be equal to the suction compression index obtained from one-dimensional
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consolidation ( i.e. s1 s2 s3 s , where ( s ) can be obtained from the results of one-dimensional swelling tests by measuring the amount of swelling, and change in suction i.e. s
%swell log hf =h0
5
where % swell can be measured in a one-dimensional consolidation swelling test. The change in soil suction can be measured by dierent methods [12]. The assumption of equal s in all directions (i.e. isotropic soil) is a simplifying assumption and is consistent with the isotropic stress±strain relationship used in this study . The values of s from a 1-dimensional consolidation test are greater than the actual values of s for 3-dimensional conditions; thus, the above assumption will give conservative results (i.e. overestimates swelling under 3-dimensional conditions). Further s is considered to be constant over a given change in suction from h0 and hf . This is believed to be a reasonable assumption as long as h0 ÿ hf is kept as small as possible. 4. The computer program The displacement based ®nite element formulation for soil±structure interaction was implemented in a computer program developed by Mohamedzein [13]. In this study, subroutines and modi®cations were added to simulate the soil±pile systems in expansive soil. Major changes to the existing code were the addition of new subroutines for calculation of the displacements in the soil and pile due to an increase or change in soil suction following the procedure outlined in the previous section. A subroutine for generation of an automated mesh was developed. The program can be executed on any personal computer and it runs very well on a 486 PC. Fig. 1 shows a typical ®nite element mesh for a single pile. The dimensions of the mesh are given in terms of pile length, pile diameter and the thickness of expansive layer from the ground surface. The lateral extent of the mesh is solely controlled by the pile diameter. The mesh extends 5.5D (where D is the diameter). The vertical extent of the mesh is controlled by the pile length and the thickness of the expansive layer. This representation is found reasonable for layer thickness up to 12 m and pile length up to 6 m. These limits are considered to cover the usual lengths of short piles in practice. The pile is divided into ten 8-noded isoparametric elements. The soil media is represented by 95 8-noded isoparametric elements. The boundary conditions are shown in Fig. 1. The rollers on the left vertical face of the mesh are intended to simulate the condition of symmetry. Complete contact between the soil and the pile is assumed at the soil±pile interface. The condition of a complete contact is considered appropriate for small movements (<40 mm) [14]. Previous studies also have shown that complete contact conditions overestimate pile movement and stresses [15].
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235
Fig. 1. The ®nite element mesh.
5. Results and comparisons The ®eld and laboratory testing experiments were carried out by El Sharief [16] at two sites in Sudan. Site (1) is located near Wad Medani city the capital of El Gezira State, while Site (2) is located in El Fao town the headquarters of the Rahad Irrigation Scheme. Tables 1 and 2 show generalized soil pro®les at Sites (1) and (2), respectively. The soils are classi®ed as inorganic clays of high plasticity (liquid limit varied between 63 and 71). Numerous calcareous concretions were observed in soil samples from both sites. The amount of calcareous deposits were noted to increase
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with depth specially at Site 2 . The percentage clay fraction (<2 mm) was found to range from 47 to 65% for Site 1 and from 46 to 58% for Site 2. Measured swelling pressure varied from 156 to 337 kPa in Site (1) and from 382 to 701 kPa in Site (2). Wide shrinkage cracks were observed at Site (1), while at Site (2) the surface cracks were less prominent. The ®eld experiments were intended to allow observation of the movement of free (unloaded) piles installed at dierent depths. These observations were carried out following an arti®cial irrigation of the two sites. Figs. 2 and 3 show the moisturecontent pro®le for the two sites, respectively. Fig. 4 shows the relation between moisture content and total suction for the two sites. Table 3 gives the change of soil swelling (heave strain) with depth. The swelling values shown are obtained from the one-dimensional swelling under load tests for undisturbed soil samples collected from the respective depths in the ®eld. The load applied to the samples is equal to the total overburden load in the ®eld. The swelling values below depths of 3±4 m are not consistent with the moisture pro®les in Figs. 2 and 3. This inconsistency is because the moisture content of the tested samples was increased far beyond the actual increase in moisture content in the ®eld. In the present study no swelling is allowed below a depth of 4 m for Site (2). For Site (1) no swelling is allowed below a depth of 3 m. The ®nite element computer program is used to predict the vertical movement of dierent free piles installed in the two sites. The soil parameters required for the Table 1 General description of soil pro®le at site (1) Depth
0±6 m
Soil description
Brown to dark brown highly plastic clay with calcareous concretion (CH) 63±70 29±35 16.7±19.4 kN/m3 156±337 kN/m2 47±65%
Liquid limit Plasticity index Unit weight Swelling pressure Percentage of particles <2 mm
Table 2 General description of soil pro®le at site (2) Depth
0±6 m
Soil description
Dark grey to dark brown highly plastic clay with calcareous concretions (CH) 64±71 33±37 19.5±20.2 kN/m3 382±701 kN/m2 46±58%
Liquid limit Plasticity index Unit weight Swelling pressure Percentage of particles <2 mm
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Fig. 2. Moisture content pro®les before and after ¯ooding (Site 1).
Fig. 3. Moisture content pro®le before and after ¯ooding (Site 2).
analysis are listed in the Tables 4 and 5. Table 4 lists the values of s (suction compression index) with depth. The values in Table 4 were obtained from Figs. 2, 3 and 4 and Table 3. It should be noted that values of s below a depth of 3 m for Site (1) and a depth of 4 m for Site (2) are not used in the present study. Table 5 contains the parameters for the Modi®ed Duncan±Chang nonlinear elastic model. The parameters were obtained from the data base provided by Duncan et al. [6].
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Fig. 4. Suction±moisture content relationship. Table 3 Laboratory-measured percentage swell values for soil samples from sites (1) and (2) Depth (m) 1 2 3 4 5 6
Percentage swell % Site (1) 5.65 6.05a 5.05a 6.50a
Percentage swell % Site (2) 10.3 6.10 5.05 4.10a 4.90a 4.10a
a
In this study no swelling is allowed for these depths (since the active depth is 3 m at Site (1) and 4 m at Site (2)).
The predicted vertical movement of piles at Sites (1) and (2), are shown in Figs. 5 and 6, respectively. The dierence between the measured and predicted values is generally small. These results are considered reasonable since there are a number of features in the ®eld that can not be modeled in the program such as surface cracks. The program does not account for this initial gap between the soil and pile. The interaction mechanism itself is time dependent and that was not modeled by the program. The condition of complete contact at the interface assumed in the ®nite element analysis also increases the vertical heave this is specially true for pile lengths of 3 and 4 m. 6. Parametric study Many examples were analyzed to illustrate the use of the ®nite element program and to gain some insight into the eect of important factors on the pile±soil response in an expansive soil. The results were obtained using soil parameters relevant to the two sites.
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Table 4 Coecient of expansion s for the two sites Site (1) s
Depth (m) 1 2 3
%swell hf log h0
0.045 0.0334
Site (2) s
%swell hf log h0
0.0453 0.022 0.058
Table 5 Soil parameters for modi®ed Duncan nonlinear elastic model Parameter
Value 2
Cohesion intercept c(kN/m ) Prictional angle parameter ; ( in parantheses) Modulus number K Modulus exponent n Failure ratio Rf Bulk modulus number kb Bulk modulus exponent m Dry unit weight (kN/m3) Earth pressure coecient k0
67.57 1.0(0.0) 65.0 0.14 0.77 25.0 1.05 15.11 0.75
6.1. Eect of pile length The eect of pile length for constant pile diameter is studied using the program. Dierent pile lengths were used to ®nd resultant heave when dierent axial loads are applied to the piles. Heave versus load for dierent pile lengths for Site 2 is shown in Fig. 7. The response for Site (1) is similar in trend but the magnitudes are dierent. Fig. 7 indicates that the upward vertical movement of the pile increases when the applied axial load decreases and the pile length decreases. So by increasing the pile length we minimize the vertical movement of piles in expansive soil. The ®gure shows that increasing pile length is more eective in decreasing heave than increasing the axial load. The eect of axial load in reducing heave is similar for each length of pile. A combination of length of 4 m and an axial load greater than 90 kN is required to reduce heave to a negligible amount in this site. Design charts similar to those of Fig. 7 can be developed for a speci®c site using the program if the necessary soil parameters and pile diameter are known. 6.2. Stress in pile One of the bene®ts of this computer program is that the stresses at any point within the pile±soil system can be determined. The values of these stresses are very useful because they can be used for the determination of the area of steel required to
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resist tensile stresses in the pile. The maximum tensile stresses due to heave versus load for dierent pile lengths are plotted for Site (2) in Fig. 8. As expected the maximum tensile axial stress increases with the pile length since all pile lengths considered are within the zone of soil heave (active zone). The relation between load and maximum tensile stress is approximately linear. The maximum axial tensile stresses decrease when the applied axial load in the pile increases. The maximum axial tensile stresses due to swelling must not exceed the maximum tensile stress of concrete that is usually taken as 1/8 of the cubic strength of concrete (e.g. for fcu 40000 kPa, the maximum tensile strength of concrete=5000 kPa). The
Fig. 5. Comparison of vertical movement of pile between F.E. and ®eld experiment (Site 1).
Fig. 6. Comparison of vertical movement of pile between F.E. and ®eld experiment (Site 2).
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241
Fig. 7. Eect of pile length and axial load on heave.
Fig. 8. Maximum axial tensile stress in pile.
maximum axial tensile stresses predicted by the program was 3400 kPa for pile length=4 m in Site (2), and this value is within the elastic limit i.e. it didn't exceed the maximum tensile strength of concrete. This supports the assumption of linear elastic behavior for the pile material under the assumed conditions. The distributions of axial stress in the pile due to heave under dierent applied axial loads were plotted for pile length=3 m and pile diameter=0.25 m at Site 2 and are shown in Fig. 9. From this ®gure the maximum tensile stress in a pile caused by an expansive soil usually occurs near the mid height of the pile and the tensile stresses are signi®cant in the middle third of the pile. The ®gure also indicates the
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Fig. 9. Distribution of axial stress in pile.
presence of tensile stresses throughout the lower two thirds of the pile length. Thus steel reinforcement to resist tensile stresses in the pile must extend to the total depth of the active zone. 7. Conclusions A two dimensional axisymetric ®nite element model for analysis of short piles in expansive soil is presented. The pile material was modeled as linear elastic and the soil was assumed to be a nonlinear elastic material. Heave-induced strains were computed in terms of change in soil suction. The proposed model gave reasonable values of vertical upward movement of piles in expansive soil when compared to the results obtained from the ®eld experiments. This proposed ®nite element program can be used to ®nd the distribution of tensile stresses in a pile needed for design against tensile failure; and the optimum pile length and diameter needed to resist upward movements due to soil heave. Based on the parametric study presented in this paper the following results were obtained. 1. An increase in pile length decreases the upward vertical movement of the pile due to soil heave. The upward vertical movement also decreases with the increase in axial compressive load. The decrease in heave due to increase in pile length is more signi®cant than that due to increase in axial compressive load. For the El Fao site considered in this study a combination of a pile length of 4 m, a diameter of 0.25 m, and an axial load of greater than 90 kN are required to reduce heave to zero. 2. The maximum axial tensile stress increases when the pile length increases for piles installed completely in the zone of soil heave.
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243
3. The tensile stress decreases as the axial load increases and eventually the pile may be subjected only to compressive stresses. 4. The maximum tensile stress in the axially loaded pile usually occurs near the mid height of the pile. For loaded piles tensile stresses occur throughout the lower two thirds of the pile length within the active zone. 5. For the site considered, maximum tensile stresses are less than the tensile strength of concrete. Although these ®ndings are expected, they were quanti®ed for the site under consideration. The ®nite element program presented in this study requires further modi®cation to account for interface behavior between the soil and pile. The assumption of isotropic swelling behavior of expansive soils must be properly modeled. The time-dependent behavior of expansive soil must be accounted for. These topics are presently under active development. References [1] Osman MA, Charlie W. Expansive soils in Sudan. Building and Road Research Institute current paper No.CP 3/83, University of Khartoum, Khartoum, Sudan, 1983. [2] Ellison RD, D'Appolnia E, Thiers GR. Load deformation mechanism for bored piles. J Soil Mech Fdns, ASCE 1971;97:661±72. [3] Amir JM, Sokolov M. Finite element analysis of piles in expansive soils. J Soil Mech Fdns, ASCE 1976;102:701±20. [4] Lytton RL. Foundations in expansive soils. In: Desai CS, Chritian JT, editors. Numerical methods in geotechnical engineering. New York: McGraw Hill Book Company, 1977. p. 427±57. [5] Justo JL, Rodriguez JE, Delgado A, Jaramillo A. A ®nite element method to design and calculate pier foundations in expansive soils. In: Proceedings of Fifth International Conference on Expansive Soils, Adelaide, Australia, 1984. p. 119±123. [6] Duncan JM, Byrne P, Wong KS, Mabry P. Strength, stress strain and bulk modulus parameters for ®nite element analysis of stress and movements in soil masses. Report No. UCB/GT/78-02, University of California, Berkeley, 1978. [7] Bathe KJ. Finite element procedures in engineering analysis. Englewood Clis, New Jersey, 1982. [8] Mohamed MG. Finite element analysis of short piles in expansive soil. M.Sc. Thesis, Faculty of Engineering and Architecture, University of Khartoum, Khartoum, Sudan, 1995. [9] Snethen DR, Huang G. Evaluation of suction-heave prediction methods. In: Proceedings of 7th International Conference on Expansive Soils, Dallas, Texas, 1992. p. 12±17. [10] Mckeen RG. Field study of airport pavements on expansive clay. Fourth International Conference on Expansive Soils, Denver, Colorado, 1980. p. 242±61. [11] Mitchell PW, Avalle DL. A technique to predict expansive soil movement. In: Proceedings of Fifth International Conference on Expansive Soils, Adelaide, Australia, 1984. p. 124±30. [12] Nelson JD, Miller DJ. Expansive soils: problems and practice in foundation and pavement engineering. New York: John Wiley and Sons Inc, 1992. [13] Mohamedzein YE-A. Non-linear ®nite element analysis of soil culvert interaction. Ph.D. thesis, School of Civil Engineering, Purdue University, West Lafayette, IN. 1989. [14] Poulos HG. Piled rafts in swelling or consolidating soils. J Geotech Engrg, ASCE 1993;119:374±80. [15] Poulos HG. Pile behavior Ð theory and application. Geotechnique 1989;39:366±415. [16] El Sharief AM. Field and laboratory investigation of expansive soil heave and the behavior of short piles in expansive clays. M.Sc. thesis, Building and Road Research Institute, University of Khartoum, Khartoum, Sudan, 1987.
Finite element analysis of short piles in expansive soils Yahia E-A. Mohamedzein*, Muzamil G. Mohamed, Ahmed M. El Sharief Building and Road Research Institute, University of Khartoum, PO Box 321, Khartoum, Sudan Received 10 September 1998; received in revised form 24 March 1999; accepted 26 March 1999
Abstract A two dimensional axisymmetric ®nite element based model for analysis of a soil±pile system in expansive soils is developed. The pile is assumed to behave as linearly elastic while the soil is modelled as nonlinear elastic material. Swelling and shrinkage of the soil are related to change in soil suction. The predictions of the model are compared to the results of ®eld experiments from two expansive soil sites in Sudan, Wad Madani and Elfao. The predictions of the numerical model are in good agreement with ®eld results. Parametric studies are performed using the model. The study shows that increase in pile length decreases the upward vertical movement of the pile. As the axial load increases, both the upward vertical movement and the tensile stress decreases and eventually the pile may be subjected only to downward movement and compressive stresses. Tensile stresses for loaded piles occur throughout most portions of the pile within the active zone with the maximum stress developing near the mid height of the pile. # 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction Expansive soils cover more than one third of the Sudan area. This area contains the most important metropolitan areas and development projects. Annual damage induced by expansive soils was more than 6 million US dollars in 1983 [1]. To reduce the eect of heave, in the past, engineers in Sudan preferred to use a combination of shallow foundations (such as strips and pads) and soil modi®cation techniques (e.g. replacement and compaction). Structures (specially light structures) constructed using these techniques did not perform well in most cases. This is because expansive soils in Sudan extend to greater depths and also because of the semi-arid climate * Corresponding author. 0266-352X/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0266-352X(99)00008-7
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that results in a relatively deep active zone. Recently short piles were introduced as an alternative to shallow foundations to support light structures. Because of limited local case histories, design and construction of these piles follow normal international practices without due consideration to local soil conditions. Thus, analytical methods supplemented by experimental ®eld results are needed to establish acceptable local design and construction techniques. The objective of this study is to provide a ®nite element model for analysis of piles in expansive soils in Sudan. 2. Literature review The ®nite element method is a powerful analytical technique that can be used eectively to analyze the soil±pile system in expansive soils. Ellison et al. [2] used the ®nite element method to study the load deformation mechanism for bored piles in London clay. The axisymmetric stress condition was assumed. The pile was assumed linear elastic and a trilinear elastic stress±strain relationship was assumed for the soil. Amir and Sokolov [3] used the ®nite element method to study the behavior of piles in expansive soils. The conditions of axisymmetric stress for a single pile was assumed and the soil was modeled as linear elastic. Lytton [4] suggested a ®nite element model for calculating the stresses and displacements in a pile founded in expansive soil. This method assumed the soil to behave elastically. Justo et al. [5] presented a three-dimensional ®nite element method to ®nd the stresses and strains in piles in expansive soils. In their method the stress-path followed by the soil elements during the loading and wetting processes were taken into account. From the above review it can be concluded that most of the above methods assumed the soil is linear elastic. In this study the soil is modeled as non-linear elastic by using the Duncan±Chang model or modi®ed Duncan±Chang model [6]. The pile material is assumed linear elastic. 3. Finite element formulation of expansive media The ®nite element formulation is described in detail elsewhere [7,8]. Only the formulation relevant to piles in expansive soils is presented in this section. The swellinginduced forces can be obtained following the formulation presented by Lytton [4]. The equilibrium equations for a soil element undergoing volume change are: BT C"dv 1 F vol
Where F B C "
=nodal forces induced by expansion of the soil; =strain±displacement matrix; =stress±strain matrix; =swelling-induced strains.
Y.E-A. Mohamedzein et al. / Computers and Geotechnics 24 (1999) 231±243
233
Also C"
2
where =stress vector. Lytton [4] suggested the swelling-induced strains to be related to the change in moisture content. However, heave can be better evaluated in terms of soil suction because soil suction is a fundamental factor in controlling mechanical properties of partially saturated soils. Unlike the change in moisture content which is an environmental factor, the soil suction is related to both the intrinsic and extrinsic properties of an expansive soil. Several methods have been proposed for prediction of swell potential and magnitude of heave based on soil suction measurements [9±11]. In these methods, swell is related to change in soil suction through a volume change parameter which is an intrinsic property of the soil. Mckeen's method [10] is one of the methods in which the total heave is related to soil suction change by a parameter called suction compression index. In one-dimensional form, Mckeen's equation can be written as: H hf S log H h0
3
where H H s h f , h0
=swelling-induced strains="; =suction compression index; =®nal and initial suctions, respectively.
The swelling-induced strain vector " in three dimensions can be obtained from the following equation: 2 3 s1 hf 4 " 4 s2 5log h0 s3 where s1 , s2 and s3 are the suction compression indices in the x, y and z directions for the three dimensions stress condition. Eqs. (3) and (4) show that the heave strain can be related to soil suction. The suction compression indices s can also be related to the change in moisture content since the change in moisture content has a well de®ned relation to the change in soil suction. In this study Eq. (4) is implemented in the computer program developed to compute the soil heave. The suction compression indices in the three dimensions are assumed to be equal to the suction compression index obtained from one-dimensional
234
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consolidation ( i.e. s1 s2 s3 s , where ( s ) can be obtained from the results of one-dimensional swelling tests by measuring the amount of swelling, and change in suction i.e. s
%swell log hf =h0
5
where % swell can be measured in a one-dimensional consolidation swelling test. The change in soil suction can be measured by dierent methods [12]. The assumption of equal s in all directions (i.e. isotropic soil) is a simplifying assumption and is consistent with the isotropic stress±strain relationship used in this study . The values of s from a 1-dimensional consolidation test are greater than the actual values of s for 3-dimensional conditions; thus, the above assumption will give conservative results (i.e. overestimates swelling under 3-dimensional conditions). Further s is considered to be constant over a given change in suction from h0 and hf . This is believed to be a reasonable assumption as long as h0 ÿ hf is kept as small as possible. 4. The computer program The displacement based ®nite element formulation for soil±structure interaction was implemented in a computer program developed by Mohamedzein [13]. In this study, subroutines and modi®cations were added to simulate the soil±pile systems in expansive soil. Major changes to the existing code were the addition of new subroutines for calculation of the displacements in the soil and pile due to an increase or change in soil suction following the procedure outlined in the previous section. A subroutine for generation of an automated mesh was developed. The program can be executed on any personal computer and it runs very well on a 486 PC. Fig. 1 shows a typical ®nite element mesh for a single pile. The dimensions of the mesh are given in terms of pile length, pile diameter and the thickness of expansive layer from the ground surface. The lateral extent of the mesh is solely controlled by the pile diameter. The mesh extends 5.5D (where D is the diameter). The vertical extent of the mesh is controlled by the pile length and the thickness of the expansive layer. This representation is found reasonable for layer thickness up to 12 m and pile length up to 6 m. These limits are considered to cover the usual lengths of short piles in practice. The pile is divided into ten 8-noded isoparametric elements. The soil media is represented by 95 8-noded isoparametric elements. The boundary conditions are shown in Fig. 1. The rollers on the left vertical face of the mesh are intended to simulate the condition of symmetry. Complete contact between the soil and the pile is assumed at the soil±pile interface. The condition of a complete contact is considered appropriate for small movements (<40 mm) [14]. Previous studies also have shown that complete contact conditions overestimate pile movement and stresses [15].
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235
Fig. 1. The ®nite element mesh.
5. Results and comparisons The ®eld and laboratory testing experiments were carried out by El Sharief [16] at two sites in Sudan. Site (1) is located near Wad Medani city the capital of El Gezira State, while Site (2) is located in El Fao town the headquarters of the Rahad Irrigation Scheme. Tables 1 and 2 show generalized soil pro®les at Sites (1) and (2), respectively. The soils are classi®ed as inorganic clays of high plasticity (liquid limit varied between 63 and 71). Numerous calcareous concretions were observed in soil samples from both sites. The amount of calcareous deposits were noted to increase
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with depth specially at Site 2 . The percentage clay fraction (<2 mm) was found to range from 47 to 65% for Site 1 and from 46 to 58% for Site 2. Measured swelling pressure varied from 156 to 337 kPa in Site (1) and from 382 to 701 kPa in Site (2). Wide shrinkage cracks were observed at Site (1), while at Site (2) the surface cracks were less prominent. The ®eld experiments were intended to allow observation of the movement of free (unloaded) piles installed at dierent depths. These observations were carried out following an arti®cial irrigation of the two sites. Figs. 2 and 3 show the moisturecontent pro®le for the two sites, respectively. Fig. 4 shows the relation between moisture content and total suction for the two sites. Table 3 gives the change of soil swelling (heave strain) with depth. The swelling values shown are obtained from the one-dimensional swelling under load tests for undisturbed soil samples collected from the respective depths in the ®eld. The load applied to the samples is equal to the total overburden load in the ®eld. The swelling values below depths of 3±4 m are not consistent with the moisture pro®les in Figs. 2 and 3. This inconsistency is because the moisture content of the tested samples was increased far beyond the actual increase in moisture content in the ®eld. In the present study no swelling is allowed below a depth of 4 m for Site (2). For Site (1) no swelling is allowed below a depth of 3 m. The ®nite element computer program is used to predict the vertical movement of dierent free piles installed in the two sites. The soil parameters required for the Table 1 General description of soil pro®le at site (1) Depth
0±6 m
Soil description
Brown to dark brown highly plastic clay with calcareous concretion (CH) 63±70 29±35 16.7±19.4 kN/m3 156±337 kN/m2 47±65%
Liquid limit Plasticity index Unit weight Swelling pressure Percentage of particles <2 mm
Table 2 General description of soil pro®le at site (2) Depth
0±6 m
Soil description
Dark grey to dark brown highly plastic clay with calcareous concretions (CH) 64±71 33±37 19.5±20.2 kN/m3 382±701 kN/m2 46±58%
Liquid limit Plasticity index Unit weight Swelling pressure Percentage of particles <2 mm
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Fig. 2. Moisture content pro®les before and after ¯ooding (Site 1).
Fig. 3. Moisture content pro®le before and after ¯ooding (Site 2).
analysis are listed in the Tables 4 and 5. Table 4 lists the values of s (suction compression index) with depth. The values in Table 4 were obtained from Figs. 2, 3 and 4 and Table 3. It should be noted that values of s below a depth of 3 m for Site (1) and a depth of 4 m for Site (2) are not used in the present study. Table 5 contains the parameters for the Modi®ed Duncan±Chang nonlinear elastic model. The parameters were obtained from the data base provided by Duncan et al. [6].
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Fig. 4. Suction±moisture content relationship. Table 3 Laboratory-measured percentage swell values for soil samples from sites (1) and (2) Depth (m) 1 2 3 4 5 6
Percentage swell % Site (1) 5.65 6.05a 5.05a 6.50a
Percentage swell % Site (2) 10.3 6.10 5.05 4.10a 4.90a 4.10a
a
In this study no swelling is allowed for these depths (since the active depth is 3 m at Site (1) and 4 m at Site (2)).
The predicted vertical movement of piles at Sites (1) and (2), are shown in Figs. 5 and 6, respectively. The dierence between the measured and predicted values is generally small. These results are considered reasonable since there are a number of features in the ®eld that can not be modeled in the program such as surface cracks. The program does not account for this initial gap between the soil and pile. The interaction mechanism itself is time dependent and that was not modeled by the program. The condition of complete contact at the interface assumed in the ®nite element analysis also increases the vertical heave this is specially true for pile lengths of 3 and 4 m. 6. Parametric study Many examples were analyzed to illustrate the use of the ®nite element program and to gain some insight into the eect of important factors on the pile±soil response in an expansive soil. The results were obtained using soil parameters relevant to the two sites.
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Table 4 Coecient of expansion s for the two sites Site (1) s
Depth (m) 1 2 3
%swell hf log h0
0.045 0.0334
Site (2) s
%swell hf log h0
0.0453 0.022 0.058
Table 5 Soil parameters for modi®ed Duncan nonlinear elastic model Parameter
Value 2
Cohesion intercept c(kN/m ) Prictional angle parameter ; ( in parantheses) Modulus number K Modulus exponent n Failure ratio Rf Bulk modulus number kb Bulk modulus exponent m Dry unit weight (kN/m3) Earth pressure coecient k0
67.57 1.0(0.0) 65.0 0.14 0.77 25.0 1.05 15.11 0.75
6.1. Eect of pile length The eect of pile length for constant pile diameter is studied using the program. Dierent pile lengths were used to ®nd resultant heave when dierent axial loads are applied to the piles. Heave versus load for dierent pile lengths for Site 2 is shown in Fig. 7. The response for Site (1) is similar in trend but the magnitudes are dierent. Fig. 7 indicates that the upward vertical movement of the pile increases when the applied axial load decreases and the pile length decreases. So by increasing the pile length we minimize the vertical movement of piles in expansive soil. The ®gure shows that increasing pile length is more eective in decreasing heave than increasing the axial load. The eect of axial load in reducing heave is similar for each length of pile. A combination of length of 4 m and an axial load greater than 90 kN is required to reduce heave to a negligible amount in this site. Design charts similar to those of Fig. 7 can be developed for a speci®c site using the program if the necessary soil parameters and pile diameter are known. 6.2. Stress in pile One of the bene®ts of this computer program is that the stresses at any point within the pile±soil system can be determined. The values of these stresses are very useful because they can be used for the determination of the area of steel required to
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resist tensile stresses in the pile. The maximum tensile stresses due to heave versus load for dierent pile lengths are plotted for Site (2) in Fig. 8. As expected the maximum tensile axial stress increases with the pile length since all pile lengths considered are within the zone of soil heave (active zone). The relation between load and maximum tensile stress is approximately linear. The maximum axial tensile stresses decrease when the applied axial load in the pile increases. The maximum axial tensile stresses due to swelling must not exceed the maximum tensile stress of concrete that is usually taken as 1/8 of the cubic strength of concrete (e.g. for fcu 40000 kPa, the maximum tensile strength of concrete=5000 kPa). The
Fig. 5. Comparison of vertical movement of pile between F.E. and ®eld experiment (Site 1).
Fig. 6. Comparison of vertical movement of pile between F.E. and ®eld experiment (Site 2).
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Fig. 7. Eect of pile length and axial load on heave.
Fig. 8. Maximum axial tensile stress in pile.
maximum axial tensile stresses predicted by the program was 3400 kPa for pile length=4 m in Site (2), and this value is within the elastic limit i.e. it didn't exceed the maximum tensile strength of concrete. This supports the assumption of linear elastic behavior for the pile material under the assumed conditions. The distributions of axial stress in the pile due to heave under dierent applied axial loads were plotted for pile length=3 m and pile diameter=0.25 m at Site 2 and are shown in Fig. 9. From this ®gure the maximum tensile stress in a pile caused by an expansive soil usually occurs near the mid height of the pile and the tensile stresses are signi®cant in the middle third of the pile. The ®gure also indicates the
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Fig. 9. Distribution of axial stress in pile.
presence of tensile stresses throughout the lower two thirds of the pile length. Thus steel reinforcement to resist tensile stresses in the pile must extend to the total depth of the active zone. 7. Conclusions A two dimensional axisymetric ®nite element model for analysis of short piles in expansive soil is presented. The pile material was modeled as linear elastic and the soil was assumed to be a nonlinear elastic material. Heave-induced strains were computed in terms of change in soil suction. The proposed model gave reasonable values of vertical upward movement of piles in expansive soil when compared to the results obtained from the ®eld experiments. This proposed ®nite element program can be used to ®nd the distribution of tensile stresses in a pile needed for design against tensile failure; and the optimum pile length and diameter needed to resist upward movements due to soil heave. Based on the parametric study presented in this paper the following results were obtained. 1. An increase in pile length decreases the upward vertical movement of the pile due to soil heave. The upward vertical movement also decreases with the increase in axial compressive load. The decrease in heave due to increase in pile length is more signi®cant than that due to increase in axial compressive load. For the El Fao site considered in this study a combination of a pile length of 4 m, a diameter of 0.25 m, and an axial load of greater than 90 kN are required to reduce heave to zero. 2. The maximum axial tensile stress increases when the pile length increases for piles installed completely in the zone of soil heave.
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3. The tensile stress decreases as the axial load increases and eventually the pile may be subjected only to compressive stresses. 4. The maximum tensile stress in the axially loaded pile usually occurs near the mid height of the pile. For loaded piles tensile stresses occur throughout the lower two thirds of the pile length within the active zone. 5. For the site considered, maximum tensile stresses are less than the tensile strength of concrete. Although these ®ndings are expected, they were quanti®ed for the site under consideration. The ®nite element program presented in this study requires further modi®cation to account for interface behavior between the soil and pile. The assumption of isotropic swelling behavior of expansive soils must be properly modeled. The time-dependent behavior of expansive soil must be accounted for. These topics are presently under active development. References [1] Osman MA, Charlie W. Expansive soils in Sudan. Building and Road Research Institute current paper No.CP 3/83, University of Khartoum, Khartoum, Sudan, 1983. [2] Ellison RD, D'Appolnia E, Thiers GR. Load deformation mechanism for bored piles. J Soil Mech Fdns, ASCE 1971;97:661±72. [3] Amir JM, Sokolov M. Finite element analysis of piles in expansive soils. J Soil Mech Fdns, ASCE 1976;102:701±20. [4] Lytton RL. Foundations in expansive soils. In: Desai CS, Chritian JT, editors. Numerical methods in geotechnical engineering. New York: McGraw Hill Book Company, 1977. p. 427±57. [5] Justo JL, Rodriguez JE, Delgado A, Jaramillo A. A ®nite element method to design and calculate pier foundations in expansive soils. In: Proceedings of Fifth International Conference on Expansive Soils, Adelaide, Australia, 1984. p. 119±123. [6] Duncan JM, Byrne P, Wong KS, Mabry P. Strength, stress strain and bulk modulus parameters for ®nite element analysis of stress and movements in soil masses. Report No. UCB/GT/78-02, University of California, Berkeley, 1978. [7] Bathe KJ. Finite element procedures in engineering analysis. Englewood Clis, New Jersey, 1982. [8] Mohamed MG. Finite element analysis of short piles in expansive soil. M.Sc. Thesis, Faculty of Engineering and Architecture, University of Khartoum, Khartoum, Sudan, 1995. [9] Snethen DR, Huang G. Evaluation of suction-heave prediction methods. In: Proceedings of 7th International Conference on Expansive Soils, Dallas, Texas, 1992. p. 12±17. [10] Mckeen RG. Field study of airport pavements on expansive clay. Fourth International Conference on Expansive Soils, Denver, Colorado, 1980. p. 242±61. [11] Mitchell PW, Avalle DL. A technique to predict expansive soil movement. In: Proceedings of Fifth International Conference on Expansive Soils, Adelaide, Australia, 1984. p. 124±30. [12] Nelson JD, Miller DJ. Expansive soils: problems and practice in foundation and pavement engineering. New York: John Wiley and Sons Inc, 1992. [13] Mohamedzein YE-A. Non-linear ®nite element analysis of soil culvert interaction. Ph.D. thesis, School of Civil Engineering, Purdue University, West Lafayette, IN. 1989. [14] Poulos HG. Piled rafts in swelling or consolidating soils. J Geotech Engrg, ASCE 1993;119:374±80. [15] Poulos HG. Pile behavior Ð theory and application. Geotechnique 1989;39:366±415. [16] El Sharief AM. Field and laboratory investigation of expansive soil heave and the behavior of short piles in expansive clays. M.Sc. thesis, Building and Road Research Institute, University of Khartoum, Khartoum, Sudan, 1987.