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Analysis of The arching phenomenon of bored piles in sand
Alexandria Engineering Journal (2016) xxx, xxx–xxx
H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Analysis of The arching phenomenon of bored piles in sand Zahraa A. Kamal *, Mohamed G. Arab, Adel Dif Department of Structural Engineering, Faculty of Engineering, Mansoura University, Egypt Received 10 November 2015; revised 26 January 2016; accepted 4 June 2016
KEYWORDS Numerical modeling; Bored pile; Pile bearing capacity; Limit shaft resistance; Arching phenomenon
Abstract Several bored pile field-testing observations showed the arching phenomena and its effect on side shear resistance. Finite element numerical model is developed in this paper to study the arching phenomena of bored pile and the effect on the overall compression capacity of single board piles. The numerical models developed apply a hardening/softening model (multi-surface) constitutive model to account for sandy soil nonlinear behavior. 2D-axisymmetric Finite Elements single pile model has been developed and validated using several field-testings available in the literature. The numerical study has been conducted to investigate the effect of arching close to the single pile shaft on pile bearing capacity considering three major influence factors: pile length, pile diameter and sand relative density. The numerical analyses conducted show the importance of the arching phenomenon on the overall behavior of piles and on the prediction of bored piles bearing capacity. Ó 2016 Production and hosting by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
1. Introduction Pile foundation has gained popularity lately in Egypt especially in high-rise buildings and heavy structures. Side resistance is an important source of pile resistance, especially for long board piles. Several analytical methods have been developed to predict pile shaft resistant based on soil shear properties. In design practice, the unit shaft resistance (qsL) is often calculated as percentage of vertical effective stress as follows: qsL ¼ Kr0vo tan d
ð1Þ
* Corresponding author. E-mail addresses: [email protected] (Z.A. Kamal), [email protected] (M.G. Arab), [email protected] (A. Dif). Peer review under responsibility of Faculty of Engineering, Alexandria University.
where r0vo is initial vertical effective stress, d is the friction angle mobilized along the vertical shaft wall, and K is the lateral earth pressure coefficient at limit shaft resistance conditions. Due to axial loading of the pile, the soil around piles shears and as a result the normal effective stress acting on the shaft evolves from its initial (geostatic) value to an ultimate value. The new values for the effective normal stress will greatly affect the prediction for the shaft resistance of piles. Terzaghi [7] proved experimentally using trapped door experiment that stresses in the soil body changes take place during soil shearing and these changes are due to shearing resistance along the boundaries between the moving and stationary mass of sand. Similarly, upon axial loading of pile and shearing of soil around the shaft while the soil lying further away from the pile shaft is stationary causing changing of the stresses along the pile shaft from initial stresses devel-
http://dx.doi.org/10.1016/j.aej.2016.06.035 1110-0168 Ó 2016 Production and hosting by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: Z.A. Kamal et al., Analysis of The arching phenomenon of bored piles in sand, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/ j.aej.2016.06.035
2
Z.A. Kamal et al.
oped before shearing. Two distinct zones are developed around the tip of the pile as a result of the downward movement of the pile, these zones are the flow zone and the arching zone as illustrated in Fig. 1 [3]. This paper studies the arching effect in bored piles in sandy soils and possible effect on pile bearing capacity using numerical modeling and advanced constitutive model. 2. Experimental data from single pile loading The Center for Highway Research (CFHR) has conducted a research program to investigate the behavior of drilled shafts installed in a variety of soils located in Houston. One site named (G1) was chosen in this research to calibrate the numerical model to investigate the suitability of the constitutive model used for soil elements to reproduce pile behavior. Soil profile and soil properties in this site are shown in Fig. 2. The properties of the pile based on Touma and Reese [3] installed in this site are as follows: 18 m length, 0.95 m average diameter, the Young’s modulus of the pile shaft is 33 GPa, the Poisson’s ratio is 0.2 and the specific weight of the pile shaft is 23 kN/m3. Touma and Reese [3] showed that the soil profile in the site is a 9.5-m thick clay stratum with an average undrained shear strength of about 86 kPa overlaying sand layer of medium density of an average standard penetration number (Nblows/ft) = 22. 3. Numerical analysis
Figure 2
For the work described herein, in order to capture the behavior of single bored piles in sandy soils a finite element model is developed using the commercial software ABAQUS 6.10 [6]. The proposed model is able to realistically capture the most important aspects of pile loading.
Figure 1
Standard penetration test of selected Site-Gl [3].
3.1. Constitutive model The constitutive model used in this paper to predict sand nonlinear behavior is Drucker-Prager model (DP) available in ABAQUS 6.10. The DP is noncircular yield surface in the devi-
Schematic of the stresses around the pile in the case of a pile loaded axially in compression [3].
Please cite this article in press as: Z.A. Kamal et al., Analysis of The arching phenomenon of bored piles in sand, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/ j.aej.2016.06.035
Analysis of The arching phenomenon of bored piles in sand
3
atoric plane to match different yield values in triaxial tension and compression. Input data parameters define the shape of the yield and flow surfaces in the meridional and deviatoric planes. The Drucker-Prager criterion is used which can be represented by equation: F ¼ t p tan b d
ð2Þ
where P is the equivalent pressure stress, t is the Mises equivalent stress, b is the slope of the linear yield surface in the p–t stress plane and is commonly referred to the friction angle of the material, d is the cohesion of the material and K is the ratio of the yield stress in triaxial tension to the yield stress in triaxial compression, where b and d could be expressed in terms of Mohr-Column parameters c and u as follows: tan b ¼ d¼
6 sin / 3 sin /
ð3Þ
18c cos / 3 sin /
The model is referred to as an isotropic ‘‘hardening” and the evolution of the yield surface with plastic deformation is described in terms of the equivalent stress (rc) and plastic strain (ePL). 3.2. Calibration of constitutive model Analyses were performed to simulate laboratory triaxial tests conducted on Toyoura and Ottawa sand in the literature. The backbone curve for the sandy soil was used to develop model parameters for hardening yield surface. The input model parameters are listed in Table 1. Analyses were performed using ABAQUS 6.10 to simulate triaxial behavior of Toyoura and Ottawa sand. The single element illustrated in Fig. 3 was used to simulate the laboratory tests. Confining pressure equal to r3 is applied to the sides of the element and a vertical displacement d is applied to upper boundary of the single element. The results of the numerical analyses are shown in Fig. 4 along with the triaxial results from drained triaxial compression tests on Toyoura sand [4] and clean Ottawa sand [1] measured in the laboratory.
Table 1
Figure 3
ð4Þ
Single element used for simulation.
4. Finite element model Analyses were performed to simulate single pile test presented earlier in the Center for Highway Research (CFHR) at the University of Texas at Houston, site named G1. A finite element model is developed to simulate single bored pile loaded axially. The finite element program ABAQUS 6.10 is used in the simulation of pile behavior. Fig. 5 presents the finite element (FE) mesh and boundary conditions of base model in this analysis. The pile and soil are modeled using 8-noded axisymmetric elements; the radius of the soil domain is 15.0 m, and the depth is 30.0 m. An elastic model is used for the 18 m long pile rested in sand. Soil is divided into two layers, the upper layer represents clay layer with thickness 9.5 m modeled as Mohr-Coloumb model and the lower layer of the soil is a sand layer modeled by Drucker-Prager model illustrated earlier. Fine mesh is used near the pile–soil interface, and it becomes coarser further from the pile. The interface between the pile and the soil is defined using an interface element available in ABAQUS as ‘‘penalty” behavior. Tangentially, the properties
Soil data using presented Drucker-Prager model.
Material
Relative density (%)
Void ratio (e)
Elastic properties
Inelastic properties
Hardening behavior rc (MPa)
ePL
Toyoura sand
90
0.671
E = 132 MPa m = 0.15
b = 56.1° K = 0.778 w = 25°
0.104 0.21 0.42 0.53 0.46
0.0 0.004 0.02 0.06 0.126
Ottawa sand
78
0.545
E = 114 MPa m = 0.15
b = 50.2° K = 0.778 w = 20°
27
0.699
E = 85 MPa m = 0.15
b = 42° K = 0.778 w = 5°
0.130 0.20 0.207 0.164 0.123 0.02 0.092 0.117 0.116 0.100
0.0 0.01 0.032 0.098 0.258 0.0 0.042 0.0954 0.1605 0.252
Please cite this article in press as: Z.A. Kamal et al., Analysis of The arching phenomenon of bored piles in sand, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/ j.aej.2016.06.035
4
Z.A. Kamal et al. 4.1. Comparison with experimental field data The calculated load-settlement curve of the numerical model of the test loading, together with the measured response of the tested pile using 2D nonlinear analysis is shown in Fig. 6. The results presented in the figure are the following: the pile total resistance (Q), pile shaft resistance (Qs) and pile tip Resistance (Qt) due to 20 mm settlement. Results presented in Fig. 6 show that the numerical models calculate accurately the frictional behavior of the single pile testing in this case while a slight difference exists between the calculated tip resistant and the measured tip resistant especially at high settlement values (near failure).
Figure 4 Fitting drained triaxial compression tests of Toyoura sand and clean Ottawa sand.
4.2. Critical depth of sand mass Vesic [8] was among the first theoreticians to present the concept of limiting average unit shaft resistance. Vesic reported that shaft resistance does not increase infinitely with depth, but reaches a constant value at some critical depth (Dc). The calculated shear stress along pile shaft from numerical model presented earlier shows a reduction in shear stress at specific depth (critical depth) (3 m) beneath sand layer surface in a good agreement with field result as presented in Fig. 7. 4.3. Comparison with the Egyptian code for soil and foundation design [2] The ultimate bearing capacity of bored piles according to Egyptian code (EG-Code) using field test results can be calculated by the equation: " # H¼D X Qult ¼ Ca L þ KHC Po tan dDH 2pR þ Pb Nq pR2 ð5Þ H¼0
where Ca is the adhesion of pile in clay soil taken equal to 0.35Cun, as Cun is the average undrained cohesion of clay (1st layer), L is the length of pile in clay layer, KHC is the coefficient of earth pressure, Po is the effective stress, d is the friction angle between pile shaft and sand layer taken here according to Egyptian code as 0.75 soil friction angle, Pb is the effective earth pressure at pile toe, Nq is the bearing capacity factor related to the internal angle of friction of sand particles, R is the radius of the pile.
Figure 5 Typical finite element mesh and boundary conditions in full pile simulation.
of the interface are specified by an interface friction coefficient, l = tan d = 0.6, d = 0.98uc as uc is the true friction angle at critical state [5] and tangential stiffness Ks where Ks = G/ts, where G is the shear modulus and ts is the thickness of interface layer taken 2 mm. Analysis is divided into two steps; first the overburden pressure is defined in geostatic options as unit weight of soil part = 20 kN/m3 and initial coefficient of earth pressure Ko = 0.5. In the second step a vertical displacement is applied on the surface of the pile.
Figure 6 Comparison between field test data and numerical simulations of the load–settlement curve (Site –G1) [3].
Please cite this article in press as: Z.A. Kamal et al., Analysis of The arching phenomenon of bored piles in sand, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/ j.aej.2016.06.035
Analysis of The arching phenomenon of bored piles in sand
5 Note: Effective pressure according to EG-Code calculated assuming a critical depth (Dc) at which arching will occur at 20R in Loose sand and 40R in dense sand. A parametric study is conducted to compare the pile capacity results from the base numerical model developed earlier with the calculated values from the EG-Code predictions. In the parametric study, only one parameter in the base model is the pile length; L is varied while keeping the other variables constant. The results of the comparison are shown in Fig. 8. The results show that EGCode predicted values for ultimate bearing capacity are overall conservative especially in loose sand. 4.4. Critical depth (Dc) in multi-layer soil profile
Figure 7 Field test result of shear stress along pile’s shaft compared with numerical result.
Figure 8
Parametric study was conducted to examine the effect of changing soil profile on the critical depth calculated. Three typical soil profiles from three different cities in Egypt’s Delta were used in this study. For each soil profile a numerical model was developed. To illustrate the influence of clay layers on the development of the critical depth for sand, parametric study was comparing numerical results from the multi-layer soil pro-
Values of ultimate bearing capacity in (MN) of single modeled pile in different cases compared with Egyptian Code.
Figure 9
Shear stress along pile’s shaft of analyzed Mansoura (Site 1 & 2) vs a sand soil profile.
Please cite this article in press as: Z.A. Kamal et al., Analysis of The arching phenomenon of bored piles in sand, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/ j.aej.2016.06.035
6
Z.A. Kamal et al. Table 3
Soil data used in numerical model (Mansoura).
Soil type
Used model
Elastic prop.
Medium hard clay
MohrColoumb DruckerPrager MohrColoumb
E = 50 MPa Cun = 50 kPa m = 0.2 Ottawa Loose Sand (Table 1)
Coarse sand Medium clay
Table 4
E = 30 MPa m = 0.2
Inelastic prop.
Cun = 25 kPa
Properties of soil profile in Damietta.
Depth
Soil type
qun
b
0–12 12–32 32–End of boring
Fine sand Soft clay Coarse sand
– 30 kPa
50.2° – 42°
Figure 10 Shear stress along pile’s shaft of analyzed New Damietta vs a sand soil profile. Table 5
file with a numerical analyses for a pile in a sand soil only. The results are calculated and drawn next to each soil profile (Figs. 9 and 10), as shown each soil profile result is compared with a sand soil profile. Typical soil profile in Mansoura is shown in Fig. 9, with properties summarized in Table 2. The numerical model developed for the soil profile typically encountered in Mansoura has the properties shown in Table 3. Typical New Damietta soil profile with soft clay underlying a medium dense sand layer is shown in Fig. 10, with properties summarized in Table 4. Also a numerical model was developed with properties illustrated in Table 5. Fig. 9a shows results of the first numerical model of the typical soil profile in Site 1 in Mansoura. The shear stress calculated along pile’s shaft is constant along clay layer and then at the beginning of sand layer it increases gradually up to a maximum value close to pile tip. In the same figure the shear stress of a sand soil profile is drawn showing a gradual increase in shear stress up to the end of pile also, knowing that the length of the pile is only 15 m in both cases. The critical depth was not developed in this case due to the length of the pile is not long enough. Fig. 9b shows results of a numerical model calculated for typical soil profile encountered in Mansoura city. The shear stress calculated along pile’s shaft in clay is constant and then increases in sand, until reaches the second clay layer the shear stress continues constantly again and finally it increases again in the final sand layer reaching a constant value at the end of pile. Another model was developed with the same Table 2
Properties of typical soil profile in Mansoura. Depth
Soil type
qun
b
Site-1
0–13 13–End of boring
Medium hard clay Coarse sand
100 kPa 30 kPa
– 42°
Site-1
0–7 7–12 12–20 12–End of boring
Medium clay Coarse sand Medium clay Coarse sand
50 kPa – 50 kPa –
– 42° – 42°
Soil data used in numerical model (Damietta).
Soil type
Used model
Elastic prop.
Inelastic prop.
Fine sand Soft clay
Drucker-Prager Mohr-Coloumb
Coarse sand
Drucker-Prager
Ottawa Dense Sand (Table 1) E = 50 MPa Cun = 15 KPa m = 0.2 Ottawa Loose Sand (Table 1)
pile properties but in dense sand. Shear stress calculated in this case shows development of a critical depth of about 15 m at which shear stress along pile shaft is constant. Also comparing shear stress calculated along pile shaft in multi-layer profile to the only sand soil is equal at depth of 22 m. Similarly, Fig. 10 shows numerical analysis conducted for the typical soil profile encountered in New Damietta City. The shear stress calculated increases with depth in the first sand layer until it reaches the soft clay layer. Calculated Shear stress decreases and becomes constant through the whole clay layer. Comparing with the results of a sand soil profile, Dc can be noticed and its value is higher in case of dense sand than loose sand. 5. Summary and conclusions (1) The field testing for a single augured pile in deep sand deposits was reproduced numerically. (2) The sand relative density was modeled numerically by changing hardening behavior in Drucker-Prager constitutive model. (3) The arching phenomenon around pile shaft was calculated successfully using numerical modeling. (4) There is evidence from the field and from numerical modeling that the shear stress along pile shaft does not increase linearly for infinity rather reaches a constant value at a critical depth. (5) The Egyptian code equation for predicting single pile capacity in sandy soils is overall conservative and gives a comparable results with the numerical simulations presented in this paper.
Please cite this article in press as: Z.A. Kamal et al., Analysis of The arching phenomenon of bored piles in sand, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/ j.aej.2016.06.035
Analysis of The arching phenomenon of bored piles in sand (6) Critical depth, at which shear stress along pile shaft is constant, develops from the first sand soil pile penetrates regardless of soil layering.
References [1] J.A.H. Carraro, Mechanical Behavior of Silty and Clayey Sands PhD Dissertation, Purdue University, 2004. [2] Egyptian Code for Soil Mechanics and Design and Execution of Foundations, ECP (202), 2007.
7 [3] Fadlo T. Touma, Lymon C. Reese, The Behavior of Drilled Shaft, Report No. CFHR 3-5-72-1761, 1972. [4] S. Fukushima, F. Tatsuoka, Strength and deformation characteristics of saturated sand at extremely low pressures, Soils Found. 24 (4) (1984) 30–48. [5] D. Loukidis, R. Salgado, Analysis of the shaft resistance of nondisplacement piles in sand, Ge´otechnique 58 (4) (2008) 283–296. [6] Simulia, Abaqus version 6.10 documentation, USA, 2010. [7] K. Terzaghi, Theoretical Soil Mechanics, Wiley, New York, 1943. [8] A.S. Vesic, A Study of Bearing Capacity of Deep Foundations, Final Report B-189, Georgia Institute of Technology, Atlanta, 1967, p. 279.
Please cite this article in press as: Z.A. Kamal et al., Analysis of The arching phenomenon of bored piles in sand, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/ j.aej.2016.06.035
H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Analysis of The arching phenomenon of bored piles in sand Zahraa A. Kamal *, Mohamed G. Arab, Adel Dif Department of Structural Engineering, Faculty of Engineering, Mansoura University, Egypt Received 10 November 2015; revised 26 January 2016; accepted 4 June 2016
KEYWORDS Numerical modeling; Bored pile; Pile bearing capacity; Limit shaft resistance; Arching phenomenon
Abstract Several bored pile field-testing observations showed the arching phenomena and its effect on side shear resistance. Finite element numerical model is developed in this paper to study the arching phenomena of bored pile and the effect on the overall compression capacity of single board piles. The numerical models developed apply a hardening/softening model (multi-surface) constitutive model to account for sandy soil nonlinear behavior. 2D-axisymmetric Finite Elements single pile model has been developed and validated using several field-testings available in the literature. The numerical study has been conducted to investigate the effect of arching close to the single pile shaft on pile bearing capacity considering three major influence factors: pile length, pile diameter and sand relative density. The numerical analyses conducted show the importance of the arching phenomenon on the overall behavior of piles and on the prediction of bored piles bearing capacity. Ó 2016 Production and hosting by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
1. Introduction Pile foundation has gained popularity lately in Egypt especially in high-rise buildings and heavy structures. Side resistance is an important source of pile resistance, especially for long board piles. Several analytical methods have been developed to predict pile shaft resistant based on soil shear properties. In design practice, the unit shaft resistance (qsL) is often calculated as percentage of vertical effective stress as follows: qsL ¼ Kr0vo tan d
ð1Þ
* Corresponding author. E-mail addresses: [email protected] (Z.A. Kamal), [email protected] (M.G. Arab), [email protected] (A. Dif). Peer review under responsibility of Faculty of Engineering, Alexandria University.
where r0vo is initial vertical effective stress, d is the friction angle mobilized along the vertical shaft wall, and K is the lateral earth pressure coefficient at limit shaft resistance conditions. Due to axial loading of the pile, the soil around piles shears and as a result the normal effective stress acting on the shaft evolves from its initial (geostatic) value to an ultimate value. The new values for the effective normal stress will greatly affect the prediction for the shaft resistance of piles. Terzaghi [7] proved experimentally using trapped door experiment that stresses in the soil body changes take place during soil shearing and these changes are due to shearing resistance along the boundaries between the moving and stationary mass of sand. Similarly, upon axial loading of pile and shearing of soil around the shaft while the soil lying further away from the pile shaft is stationary causing changing of the stresses along the pile shaft from initial stresses devel-
http://dx.doi.org/10.1016/j.aej.2016.06.035 1110-0168 Ó 2016 Production and hosting by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: Z.A. Kamal et al., Analysis of The arching phenomenon of bored piles in sand, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/ j.aej.2016.06.035
2
Z.A. Kamal et al.
oped before shearing. Two distinct zones are developed around the tip of the pile as a result of the downward movement of the pile, these zones are the flow zone and the arching zone as illustrated in Fig. 1 [3]. This paper studies the arching effect in bored piles in sandy soils and possible effect on pile bearing capacity using numerical modeling and advanced constitutive model. 2. Experimental data from single pile loading The Center for Highway Research (CFHR) has conducted a research program to investigate the behavior of drilled shafts installed in a variety of soils located in Houston. One site named (G1) was chosen in this research to calibrate the numerical model to investigate the suitability of the constitutive model used for soil elements to reproduce pile behavior. Soil profile and soil properties in this site are shown in Fig. 2. The properties of the pile based on Touma and Reese [3] installed in this site are as follows: 18 m length, 0.95 m average diameter, the Young’s modulus of the pile shaft is 33 GPa, the Poisson’s ratio is 0.2 and the specific weight of the pile shaft is 23 kN/m3. Touma and Reese [3] showed that the soil profile in the site is a 9.5-m thick clay stratum with an average undrained shear strength of about 86 kPa overlaying sand layer of medium density of an average standard penetration number (Nblows/ft) = 22. 3. Numerical analysis
Figure 2
For the work described herein, in order to capture the behavior of single bored piles in sandy soils a finite element model is developed using the commercial software ABAQUS 6.10 [6]. The proposed model is able to realistically capture the most important aspects of pile loading.
Figure 1
Standard penetration test of selected Site-Gl [3].
3.1. Constitutive model The constitutive model used in this paper to predict sand nonlinear behavior is Drucker-Prager model (DP) available in ABAQUS 6.10. The DP is noncircular yield surface in the devi-
Schematic of the stresses around the pile in the case of a pile loaded axially in compression [3].
Please cite this article in press as: Z.A. Kamal et al., Analysis of The arching phenomenon of bored piles in sand, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/ j.aej.2016.06.035
Analysis of The arching phenomenon of bored piles in sand
3
atoric plane to match different yield values in triaxial tension and compression. Input data parameters define the shape of the yield and flow surfaces in the meridional and deviatoric planes. The Drucker-Prager criterion is used which can be represented by equation: F ¼ t p tan b d
ð2Þ
where P is the equivalent pressure stress, t is the Mises equivalent stress, b is the slope of the linear yield surface in the p–t stress plane and is commonly referred to the friction angle of the material, d is the cohesion of the material and K is the ratio of the yield stress in triaxial tension to the yield stress in triaxial compression, where b and d could be expressed in terms of Mohr-Column parameters c and u as follows: tan b ¼ d¼
6 sin / 3 sin /
ð3Þ
18c cos / 3 sin /
The model is referred to as an isotropic ‘‘hardening” and the evolution of the yield surface with plastic deformation is described in terms of the equivalent stress (rc) and plastic strain (ePL). 3.2. Calibration of constitutive model Analyses were performed to simulate laboratory triaxial tests conducted on Toyoura and Ottawa sand in the literature. The backbone curve for the sandy soil was used to develop model parameters for hardening yield surface. The input model parameters are listed in Table 1. Analyses were performed using ABAQUS 6.10 to simulate triaxial behavior of Toyoura and Ottawa sand. The single element illustrated in Fig. 3 was used to simulate the laboratory tests. Confining pressure equal to r3 is applied to the sides of the element and a vertical displacement d is applied to upper boundary of the single element. The results of the numerical analyses are shown in Fig. 4 along with the triaxial results from drained triaxial compression tests on Toyoura sand [4] and clean Ottawa sand [1] measured in the laboratory.
Table 1
Figure 3
ð4Þ
Single element used for simulation.
4. Finite element model Analyses were performed to simulate single pile test presented earlier in the Center for Highway Research (CFHR) at the University of Texas at Houston, site named G1. A finite element model is developed to simulate single bored pile loaded axially. The finite element program ABAQUS 6.10 is used in the simulation of pile behavior. Fig. 5 presents the finite element (FE) mesh and boundary conditions of base model in this analysis. The pile and soil are modeled using 8-noded axisymmetric elements; the radius of the soil domain is 15.0 m, and the depth is 30.0 m. An elastic model is used for the 18 m long pile rested in sand. Soil is divided into two layers, the upper layer represents clay layer with thickness 9.5 m modeled as Mohr-Coloumb model and the lower layer of the soil is a sand layer modeled by Drucker-Prager model illustrated earlier. Fine mesh is used near the pile–soil interface, and it becomes coarser further from the pile. The interface between the pile and the soil is defined using an interface element available in ABAQUS as ‘‘penalty” behavior. Tangentially, the properties
Soil data using presented Drucker-Prager model.
Material
Relative density (%)
Void ratio (e)
Elastic properties
Inelastic properties
Hardening behavior rc (MPa)
ePL
Toyoura sand
90
0.671
E = 132 MPa m = 0.15
b = 56.1° K = 0.778 w = 25°
0.104 0.21 0.42 0.53 0.46
0.0 0.004 0.02 0.06 0.126
Ottawa sand
78
0.545
E = 114 MPa m = 0.15
b = 50.2° K = 0.778 w = 20°
27
0.699
E = 85 MPa m = 0.15
b = 42° K = 0.778 w = 5°
0.130 0.20 0.207 0.164 0.123 0.02 0.092 0.117 0.116 0.100
0.0 0.01 0.032 0.098 0.258 0.0 0.042 0.0954 0.1605 0.252
Please cite this article in press as: Z.A. Kamal et al., Analysis of The arching phenomenon of bored piles in sand, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/ j.aej.2016.06.035
4
Z.A. Kamal et al. 4.1. Comparison with experimental field data The calculated load-settlement curve of the numerical model of the test loading, together with the measured response of the tested pile using 2D nonlinear analysis is shown in Fig. 6. The results presented in the figure are the following: the pile total resistance (Q), pile shaft resistance (Qs) and pile tip Resistance (Qt) due to 20 mm settlement. Results presented in Fig. 6 show that the numerical models calculate accurately the frictional behavior of the single pile testing in this case while a slight difference exists between the calculated tip resistant and the measured tip resistant especially at high settlement values (near failure).
Figure 4 Fitting drained triaxial compression tests of Toyoura sand and clean Ottawa sand.
4.2. Critical depth of sand mass Vesic [8] was among the first theoreticians to present the concept of limiting average unit shaft resistance. Vesic reported that shaft resistance does not increase infinitely with depth, but reaches a constant value at some critical depth (Dc). The calculated shear stress along pile shaft from numerical model presented earlier shows a reduction in shear stress at specific depth (critical depth) (3 m) beneath sand layer surface in a good agreement with field result as presented in Fig. 7. 4.3. Comparison with the Egyptian code for soil and foundation design [2] The ultimate bearing capacity of bored piles according to Egyptian code (EG-Code) using field test results can be calculated by the equation: " # H¼D X Qult ¼ Ca L þ KHC Po tan dDH 2pR þ Pb Nq pR2 ð5Þ H¼0
where Ca is the adhesion of pile in clay soil taken equal to 0.35Cun, as Cun is the average undrained cohesion of clay (1st layer), L is the length of pile in clay layer, KHC is the coefficient of earth pressure, Po is the effective stress, d is the friction angle between pile shaft and sand layer taken here according to Egyptian code as 0.75 soil friction angle, Pb is the effective earth pressure at pile toe, Nq is the bearing capacity factor related to the internal angle of friction of sand particles, R is the radius of the pile.
Figure 5 Typical finite element mesh and boundary conditions in full pile simulation.
of the interface are specified by an interface friction coefficient, l = tan d = 0.6, d = 0.98uc as uc is the true friction angle at critical state [5] and tangential stiffness Ks where Ks = G/ts, where G is the shear modulus and ts is the thickness of interface layer taken 2 mm. Analysis is divided into two steps; first the overburden pressure is defined in geostatic options as unit weight of soil part = 20 kN/m3 and initial coefficient of earth pressure Ko = 0.5. In the second step a vertical displacement is applied on the surface of the pile.
Figure 6 Comparison between field test data and numerical simulations of the load–settlement curve (Site –G1) [3].
Please cite this article in press as: Z.A. Kamal et al., Analysis of The arching phenomenon of bored piles in sand, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/ j.aej.2016.06.035
Analysis of The arching phenomenon of bored piles in sand
5 Note: Effective pressure according to EG-Code calculated assuming a critical depth (Dc) at which arching will occur at 20R in Loose sand and 40R in dense sand. A parametric study is conducted to compare the pile capacity results from the base numerical model developed earlier with the calculated values from the EG-Code predictions. In the parametric study, only one parameter in the base model is the pile length; L is varied while keeping the other variables constant. The results of the comparison are shown in Fig. 8. The results show that EGCode predicted values for ultimate bearing capacity are overall conservative especially in loose sand. 4.4. Critical depth (Dc) in multi-layer soil profile
Figure 7 Field test result of shear stress along pile’s shaft compared with numerical result.
Figure 8
Parametric study was conducted to examine the effect of changing soil profile on the critical depth calculated. Three typical soil profiles from three different cities in Egypt’s Delta were used in this study. For each soil profile a numerical model was developed. To illustrate the influence of clay layers on the development of the critical depth for sand, parametric study was comparing numerical results from the multi-layer soil pro-
Values of ultimate bearing capacity in (MN) of single modeled pile in different cases compared with Egyptian Code.
Figure 9
Shear stress along pile’s shaft of analyzed Mansoura (Site 1 & 2) vs a sand soil profile.
Please cite this article in press as: Z.A. Kamal et al., Analysis of The arching phenomenon of bored piles in sand, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/ j.aej.2016.06.035
6
Z.A. Kamal et al. Table 3
Soil data used in numerical model (Mansoura).
Soil type
Used model
Elastic prop.
Medium hard clay
MohrColoumb DruckerPrager MohrColoumb
E = 50 MPa Cun = 50 kPa m = 0.2 Ottawa Loose Sand (Table 1)
Coarse sand Medium clay
Table 4
E = 30 MPa m = 0.2
Inelastic prop.
Cun = 25 kPa
Properties of soil profile in Damietta.
Depth
Soil type
qun
b
0–12 12–32 32–End of boring
Fine sand Soft clay Coarse sand
– 30 kPa
50.2° – 42°
Figure 10 Shear stress along pile’s shaft of analyzed New Damietta vs a sand soil profile. Table 5
file with a numerical analyses for a pile in a sand soil only. The results are calculated and drawn next to each soil profile (Figs. 9 and 10), as shown each soil profile result is compared with a sand soil profile. Typical soil profile in Mansoura is shown in Fig. 9, with properties summarized in Table 2. The numerical model developed for the soil profile typically encountered in Mansoura has the properties shown in Table 3. Typical New Damietta soil profile with soft clay underlying a medium dense sand layer is shown in Fig. 10, with properties summarized in Table 4. Also a numerical model was developed with properties illustrated in Table 5. Fig. 9a shows results of the first numerical model of the typical soil profile in Site 1 in Mansoura. The shear stress calculated along pile’s shaft is constant along clay layer and then at the beginning of sand layer it increases gradually up to a maximum value close to pile tip. In the same figure the shear stress of a sand soil profile is drawn showing a gradual increase in shear stress up to the end of pile also, knowing that the length of the pile is only 15 m in both cases. The critical depth was not developed in this case due to the length of the pile is not long enough. Fig. 9b shows results of a numerical model calculated for typical soil profile encountered in Mansoura city. The shear stress calculated along pile’s shaft in clay is constant and then increases in sand, until reaches the second clay layer the shear stress continues constantly again and finally it increases again in the final sand layer reaching a constant value at the end of pile. Another model was developed with the same Table 2
Properties of typical soil profile in Mansoura. Depth
Soil type
qun
b
Site-1
0–13 13–End of boring
Medium hard clay Coarse sand
100 kPa 30 kPa
– 42°
Site-1
0–7 7–12 12–20 12–End of boring
Medium clay Coarse sand Medium clay Coarse sand
50 kPa – 50 kPa –
– 42° – 42°
Soil data used in numerical model (Damietta).
Soil type
Used model
Elastic prop.
Inelastic prop.
Fine sand Soft clay
Drucker-Prager Mohr-Coloumb
Coarse sand
Drucker-Prager
Ottawa Dense Sand (Table 1) E = 50 MPa Cun = 15 KPa m = 0.2 Ottawa Loose Sand (Table 1)
pile properties but in dense sand. Shear stress calculated in this case shows development of a critical depth of about 15 m at which shear stress along pile shaft is constant. Also comparing shear stress calculated along pile shaft in multi-layer profile to the only sand soil is equal at depth of 22 m. Similarly, Fig. 10 shows numerical analysis conducted for the typical soil profile encountered in New Damietta City. The shear stress calculated increases with depth in the first sand layer until it reaches the soft clay layer. Calculated Shear stress decreases and becomes constant through the whole clay layer. Comparing with the results of a sand soil profile, Dc can be noticed and its value is higher in case of dense sand than loose sand. 5. Summary and conclusions (1) The field testing for a single augured pile in deep sand deposits was reproduced numerically. (2) The sand relative density was modeled numerically by changing hardening behavior in Drucker-Prager constitutive model. (3) The arching phenomenon around pile shaft was calculated successfully using numerical modeling. (4) There is evidence from the field and from numerical modeling that the shear stress along pile shaft does not increase linearly for infinity rather reaches a constant value at a critical depth. (5) The Egyptian code equation for predicting single pile capacity in sandy soils is overall conservative and gives a comparable results with the numerical simulations presented in this paper.
Please cite this article in press as: Z.A. Kamal et al., Analysis of The arching phenomenon of bored piles in sand, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/ j.aej.2016.06.035
Analysis of The arching phenomenon of bored piles in sand (6) Critical depth, at which shear stress along pile shaft is constant, develops from the first sand soil pile penetrates regardless of soil layering.
References [1] J.A.H. Carraro, Mechanical Behavior of Silty and Clayey Sands PhD Dissertation, Purdue University, 2004. [2] Egyptian Code for Soil Mechanics and Design and Execution of Foundations, ECP (202), 2007.
7 [3] Fadlo T. Touma, Lymon C. Reese, The Behavior of Drilled Shaft, Report No. CFHR 3-5-72-1761, 1972. [4] S. Fukushima, F. Tatsuoka, Strength and deformation characteristics of saturated sand at extremely low pressures, Soils Found. 24 (4) (1984) 30–48. [5] D. Loukidis, R. Salgado, Analysis of the shaft resistance of nondisplacement piles in sand, Ge´otechnique 58 (4) (2008) 283–296. [6] Simulia, Abaqus version 6.10 documentation, USA, 2010. [7] K. Terzaghi, Theoretical Soil Mechanics, Wiley, New York, 1943. [8] A.S. Vesic, A Study of Bearing Capacity of Deep Foundations, Final Report B-189, Georgia Institute of Technology, Atlanta, 1967, p. 279.
Please cite this article in press as: Z.A. Kamal et al., Analysis of The arching phenomenon of bored piles in sand, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/ j.aej.2016.06.035