- Email: [email protected]
Discussion on “An analytical approach for the prediction of single pile and pile group behaviour in clay”
Computers and Geotechnics xxx (2017) xxx–xxx
Contents lists available at ScienceDirect
Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo
Discussion on ‘‘An analytical approach for the prediction of single pile and pile group behaviour in clay” Zhi-qiang Li School of Civil Engineering and Architecture, Weifang University, Weifang, China
a r t i c l e
i n f o
Article history: Received 14 December 2016 Accepted 13 January 2017 Available online xxxx Keywords: Load transfer function Skin friction End resistance
a b s t r a c t In the paper of Sheil and McCabe (2016), the ‘t–z method’ was used to capture the nonlinear response of single pile and pile group. However, some key questions on the skin friction and end resistance were not clearly addressed in their paper. In the present paper, analyses of the load transfer functions of the skin friction and end resistance are discussed in detail. Ó 2017 Elsevier Ltd. All rights reserved.
In the paper of Sheil and McCabe [1], a hyperbolic model proposed by Guo and Randolph [2] was employed to describe the base load-displacement relationship. For the analysis of the pile-soil interface behaviour, the partial slip was considered in their paper. However, some key questions, e.g., the load transfer function of the end resistance and the pile-soil interface behaviour were not described clearly. There is a need to clarify these questions on the load transfer functions of the skin friction and end resistance.
1. Analysis of the skin friction load transfer function To analyse the soil nonlinearity, the hyperbolic model [3–6] or the exponential function model [7], can be used in practice. However, a softening behaviour of the skin friction has been observed in field tests [8,9]. As suggested by Zhang and Zhang [10], the following equation can be used to describe the softening behaviour of the skin friction:
ssoil ¼
ws ða þ cws Þ ða þ bws Þ
2
ðD1Þ
where ssoil is the shaft shear stress at the pile-soil interface; ws is the displacement along the pile-soil interface; and a, b and c are empirical coefficients. In Case III, a softening response of a single pile was observed when the skin friction was fully mobilized, as shown in Figs. 15 and 16. However, in the paper of Sheil and McCabe [1], the softening behaviour of the skin friction was not considered. This may be E-mail address: [email protected]
the reason that the softening response of a single pile cannot be predicted using the method of Sheil and McCabe [1]. Furthermore, in the method of Sheil and McCabe [1], the limiting pile-soil relative shear displacement, ccrit, was a key parameter and used to describe the residual state of the skin friction. However, the methodology to determine the magnitude of ccrit was not explicitly given. It is well known that the magnitude of ccrit is affected by soil depth (effective stress), soil type, roughness of the pile-soil interface, and shear rate. It may be unreasonable that the value of ccrit was adopted as 5 mm in their paper. The determination of the magnitude of ccrit should have been discussed in detail. 2. Analysis of the end resistance load transfer function In their paper, a hyperbolic model (see Eq. (6)), named hyperbolic model I in the present paper, was employed to describe the relationship between the base load and the displacement mobilized at the pile base. However, the hyperbolic model used in the paper of Sheil and McCabe [1] is different from the hyperbolic model commonly used in practice [3–5]. The hyperbolic model commonly used in practice, named hyperbolic model II in the present paper, is introduced to describe the base load-displacement relationship and can be expressed in the following form [6]:
wb ¼
Pb A P b ð1 t s Þ 1 ¼ 1 BPb 4RGib 1R
Pb bf P bu
ðD2Þ
where A is the reciprocal of the spring stiffness of the soil below the pile base [11], whose value can be computed as A = (1 vs)/(4RGib);
http://dx.doi.org/10.1016/j.compgeo.2017.01.008 0266-352X/Ó 2017 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Li Z-q. Discussion on ‘‘An analytical approach for the prediction of single pile and pile group behaviour in clay”. Comput Geotech (2017), http://dx.doi.org/10.1016/j.compgeo.2017.01.008
2
Z.-q. Li / Computers and Geotechnics xxx (2017) xxx–xxx
Pile base load (kN) 0
0
100
200
300
400
500
600
Pile base settlement (mm)
20 40 60 80 100
References
120 140
was taken as 30 MPa. The value of Rfb used was 0.90. The base load-displacement relationship estimated using the hyperbolic models is shown in Fig. D1. It can be seen from Fig. D1 that the base load-displacement relationship estimated using Eq. (6) is different from that predicated using Eq. (D2), especially at a high level of loading. Note that the reliability of the hyperbolic model expressed as Eq. (D2) had been demonstrated in practice. The reliability of the hyperbolic model used in the paper of Sheil and McCabe (see Eq. (6)) should be further discussed.
Hyperbolic model I (see Eq.(6) [1]) Hyperbolic model II (see Eq.(D2) [6])
160 Fig. D1. Relationship between the pile base load and the pile base settlement estimated using hyperbolic models.
B is the reciprocal of the pile toe stress corresponding to an infinite pile end displacement, whose value can be estimated by B = Rbf/Pbu; wb is the pile end displacement; Pb is the pile base load; Gib is the shear modulus of the soil below the pile base; ts is the Poisson’s ratio of the soil below the pile base; Rbf is an empirical coefficient; and Pbu is the limiting base load. The following case is carried out to evaluate the differences between the calculated values derived from hyperbolic model I and the predicted results estimated from hyperbolic model II. The pile radius, R, was assumed to be 0.50 m. Following the suggestion of Randolph and Wroth [11], the pile base shape and depth factor, x, was adopted as 1.0. The limiting base load, Pbu, was assumed to be 600 kN, the Poisson’s ratio of the soil at the pile base was adopted as 0.30, and the shear modulus at the pile base, GiB,
[1] Sheil BB, McCabe BA. An analytical approach for the prediction of single pile and pile group behaviour in clay. Comput Geotech 2016;75:145–58. [2] Guo WD, Randolph MF. Vertically loaded piles in non-homogeneous media. Int J Numer Anal Meth Geomech 1997;21(8):507–32. [3] Lee KM, Xiao ZR. A simplified nonlinear approach for pile group settlement analysis in multilayered soils. Can Geotech J 2001;38(5):1063–80. [4] Castelli F, Maugeri M. Simplified nonlinear analysis for settlement prediction of pile groups. J Geotech Geoenviron Eng 2002;128(1):76–84. [5] Zhang QQ, Zhang ZM, He JY. A simplified approach for settlement analysis of single pile and pile groups considering interaction between identical piles in multilayered soils. Comput Geotech 2010;37(7–8):969–76. [6] Zhang QQ, Li SC, Liang FY, Yang M, Zhang Q. Simplified method for settlement prediction of single pile and pile group using a hyperbolic model. Int J Civ Eng 2014;12(2B):179–92. [7] Wang ZJ, Xie XY, Wang JC. A new nonlinear method for vertical settlement prediction of a single pile and pile groups in layered soils. Comput Geotech 2012;45:118–26. [8] Zhang ZM, Zhang QQ, Yu F. A destructive field study on the behaviour of piles under tension and compression. J Zhejiang Univ-SC A 2011;12(4) [291-00]. [9] Zhao CF, Lu J, Sun QC, Zhu T, Li SF. Experimental study of load transmission property of large-diameter bored cast-in-situ deep and long pile in different soil layers. Chin J Rock Mech Eng 2009;28(5):1020–6 (in Chinese). [10] Zhang QQ, Zhang ZM. A simplified nonlinear approach for single pile settlement analysis. Can Geotech J 2012;49(11):1256–66. [11] Randolph MF, Wroth CP. Analysis of deformation of vertically loaded piles. J Geotech Eng Div, ASCE 1978;104(GT12):1465–88.
Please cite this article in press as: Li Z-q. Discussion on ‘‘An analytical approach for the prediction of single pile and pile group behaviour in clay”. Comput Geotech (2017), http://dx.doi.org/10.1016/j.compgeo.2017.01.008
Contents lists available at ScienceDirect
Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo
Discussion on ‘‘An analytical approach for the prediction of single pile and pile group behaviour in clay” Zhi-qiang Li School of Civil Engineering and Architecture, Weifang University, Weifang, China
a r t i c l e
i n f o
Article history: Received 14 December 2016 Accepted 13 January 2017 Available online xxxx Keywords: Load transfer function Skin friction End resistance
a b s t r a c t In the paper of Sheil and McCabe (2016), the ‘t–z method’ was used to capture the nonlinear response of single pile and pile group. However, some key questions on the skin friction and end resistance were not clearly addressed in their paper. In the present paper, analyses of the load transfer functions of the skin friction and end resistance are discussed in detail. Ó 2017 Elsevier Ltd. All rights reserved.
In the paper of Sheil and McCabe [1], a hyperbolic model proposed by Guo and Randolph [2] was employed to describe the base load-displacement relationship. For the analysis of the pile-soil interface behaviour, the partial slip was considered in their paper. However, some key questions, e.g., the load transfer function of the end resistance and the pile-soil interface behaviour were not described clearly. There is a need to clarify these questions on the load transfer functions of the skin friction and end resistance.
1. Analysis of the skin friction load transfer function To analyse the soil nonlinearity, the hyperbolic model [3–6] or the exponential function model [7], can be used in practice. However, a softening behaviour of the skin friction has been observed in field tests [8,9]. As suggested by Zhang and Zhang [10], the following equation can be used to describe the softening behaviour of the skin friction:
ssoil ¼
ws ða þ cws Þ ða þ bws Þ
2
ðD1Þ
where ssoil is the shaft shear stress at the pile-soil interface; ws is the displacement along the pile-soil interface; and a, b and c are empirical coefficients. In Case III, a softening response of a single pile was observed when the skin friction was fully mobilized, as shown in Figs. 15 and 16. However, in the paper of Sheil and McCabe [1], the softening behaviour of the skin friction was not considered. This may be E-mail address: [email protected]
the reason that the softening response of a single pile cannot be predicted using the method of Sheil and McCabe [1]. Furthermore, in the method of Sheil and McCabe [1], the limiting pile-soil relative shear displacement, ccrit, was a key parameter and used to describe the residual state of the skin friction. However, the methodology to determine the magnitude of ccrit was not explicitly given. It is well known that the magnitude of ccrit is affected by soil depth (effective stress), soil type, roughness of the pile-soil interface, and shear rate. It may be unreasonable that the value of ccrit was adopted as 5 mm in their paper. The determination of the magnitude of ccrit should have been discussed in detail. 2. Analysis of the end resistance load transfer function In their paper, a hyperbolic model (see Eq. (6)), named hyperbolic model I in the present paper, was employed to describe the relationship between the base load and the displacement mobilized at the pile base. However, the hyperbolic model used in the paper of Sheil and McCabe [1] is different from the hyperbolic model commonly used in practice [3–5]. The hyperbolic model commonly used in practice, named hyperbolic model II in the present paper, is introduced to describe the base load-displacement relationship and can be expressed in the following form [6]:
wb ¼
Pb A P b ð1 t s Þ 1 ¼ 1 BPb 4RGib 1R
Pb bf P bu
ðD2Þ
where A is the reciprocal of the spring stiffness of the soil below the pile base [11], whose value can be computed as A = (1 vs)/(4RGib);
http://dx.doi.org/10.1016/j.compgeo.2017.01.008 0266-352X/Ó 2017 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Li Z-q. Discussion on ‘‘An analytical approach for the prediction of single pile and pile group behaviour in clay”. Comput Geotech (2017), http://dx.doi.org/10.1016/j.compgeo.2017.01.008
2
Z.-q. Li / Computers and Geotechnics xxx (2017) xxx–xxx
Pile base load (kN) 0
0
100
200
300
400
500
600
Pile base settlement (mm)
20 40 60 80 100
References
120 140
was taken as 30 MPa. The value of Rfb used was 0.90. The base load-displacement relationship estimated using the hyperbolic models is shown in Fig. D1. It can be seen from Fig. D1 that the base load-displacement relationship estimated using Eq. (6) is different from that predicated using Eq. (D2), especially at a high level of loading. Note that the reliability of the hyperbolic model expressed as Eq. (D2) had been demonstrated in practice. The reliability of the hyperbolic model used in the paper of Sheil and McCabe (see Eq. (6)) should be further discussed.
Hyperbolic model I (see Eq.(6) [1]) Hyperbolic model II (see Eq.(D2) [6])
160 Fig. D1. Relationship between the pile base load and the pile base settlement estimated using hyperbolic models.
B is the reciprocal of the pile toe stress corresponding to an infinite pile end displacement, whose value can be estimated by B = Rbf/Pbu; wb is the pile end displacement; Pb is the pile base load; Gib is the shear modulus of the soil below the pile base; ts is the Poisson’s ratio of the soil below the pile base; Rbf is an empirical coefficient; and Pbu is the limiting base load. The following case is carried out to evaluate the differences between the calculated values derived from hyperbolic model I and the predicted results estimated from hyperbolic model II. The pile radius, R, was assumed to be 0.50 m. Following the suggestion of Randolph and Wroth [11], the pile base shape and depth factor, x, was adopted as 1.0. The limiting base load, Pbu, was assumed to be 600 kN, the Poisson’s ratio of the soil at the pile base was adopted as 0.30, and the shear modulus at the pile base, GiB,
[1] Sheil BB, McCabe BA. An analytical approach for the prediction of single pile and pile group behaviour in clay. Comput Geotech 2016;75:145–58. [2] Guo WD, Randolph MF. Vertically loaded piles in non-homogeneous media. Int J Numer Anal Meth Geomech 1997;21(8):507–32. [3] Lee KM, Xiao ZR. A simplified nonlinear approach for pile group settlement analysis in multilayered soils. Can Geotech J 2001;38(5):1063–80. [4] Castelli F, Maugeri M. Simplified nonlinear analysis for settlement prediction of pile groups. J Geotech Geoenviron Eng 2002;128(1):76–84. [5] Zhang QQ, Zhang ZM, He JY. A simplified approach for settlement analysis of single pile and pile groups considering interaction between identical piles in multilayered soils. Comput Geotech 2010;37(7–8):969–76. [6] Zhang QQ, Li SC, Liang FY, Yang M, Zhang Q. Simplified method for settlement prediction of single pile and pile group using a hyperbolic model. Int J Civ Eng 2014;12(2B):179–92. [7] Wang ZJ, Xie XY, Wang JC. A new nonlinear method for vertical settlement prediction of a single pile and pile groups in layered soils. Comput Geotech 2012;45:118–26. [8] Zhang ZM, Zhang QQ, Yu F. A destructive field study on the behaviour of piles under tension and compression. J Zhejiang Univ-SC A 2011;12(4) [291-00]. [9] Zhao CF, Lu J, Sun QC, Zhu T, Li SF. Experimental study of load transmission property of large-diameter bored cast-in-situ deep and long pile in different soil layers. Chin J Rock Mech Eng 2009;28(5):1020–6 (in Chinese). [10] Zhang QQ, Zhang ZM. A simplified nonlinear approach for single pile settlement analysis. Can Geotech J 2012;49(11):1256–66. [11] Randolph MF, Wroth CP. Analysis of deformation of vertically loaded piles. J Geotech Eng Div, ASCE 1978;104(GT12):1465–88.
Please cite this article in press as: Li Z-q. Discussion on ‘‘An analytical approach for the prediction of single pile and pile group behaviour in clay”. Comput Geotech (2017), http://dx.doi.org/10.1016/j.compgeo.2017.01.008