1 Introduction
2 Skin friction distribution
2.1 Pile–soil interface model
2.2 Mobilization of skin friction
3 Stress concentration ratio
3.1 Element selection from a piled embankment system
3.2 Stress and deformation of pile and soil
3.3 Boundary and compatibility conditions
3.4 Solution for stress concentration ratio
4 Case study
Material | Physical and mechanical properties | N.G. | ||
---|---|---|---|---|
Values | Method | |||
Case 1 | Embankment | hf =11.5 m (G1), 12.2 m (G3); | p = 230 kPa (G1), | \(p = {\gamma_{\text{f}}} \cdot {h_{\text{f}}}\) |
γf =20 kN/m3 | 244 kPa (G3) | |||
Cushion | hc =0.5 m; γc =20 kN/m3; | Cc = 1.67×10-5 m/kPa | Eq. (28) | |
Ec=30 MPa | ||||
Pile | l=8 m (G1), 12 m (G3); | b=0.945 m (G1), | Eq. (9) | |
S=1.8 m (G1), 2.0 m (G3); | 1.05 m (G3) | |||
d=0.5 m; dcap=1.0 m; | ||||
Ep=20 GPa | ||||
Adjacent soil | hs=8 m (G1), 12 m (G3); | ca=21 kPa | Eq. (4a) | |
γs=19.0 kN/m3; cs=30 kPa; | φa=24.5° | Eq. (4b) | ||
φs=35°; Es=30 MPa; vs=0.35 | \(U_{1}^{^{\prime}} = U_{2}^{^{\prime}}\) =2.5‰ | Interface shear test | ||
K0=0.70 | [45] | |||
Substratum | H=12 m; γsb =19.0 kN/m3; | Cr =1.61×10-5 m/kPa | Eq. (29) | |
csb =30 kPa; φsb=25°; | ||||
Esb=30 MPa; vsb=0.35 | ||||
Case 2 | Embankment | hf =4 m; γf =20 kN/m3 | p = 80 kPa | |
Cushion | hc =0.5 m; γc =20 kN/m3; | Cc = 1.67×10-5 m/kPa | Eq. (28) | |
Ec=30 MPa | ||||
Pile | l=20 m; d=0.4 m; S=2.5 m; | b = 1.41 m | Eq. (9) | |
dcap=1.13 m; Ep=35 GPa | ||||
Adjacent soil | hs=20 m; γs=17.5 kN/m3; | ca = 10.5 kPa | Eq. (4a) | |
cs=15 kPa; φs=9°; Es=2.2 MPa; | φa = 6.3° | Eq. (4b) | ||
vs=0.35 | \(U_{1}^{^{\prime}}=U_{2}^{^{\prime}}\)=1.4‰ | Interface shear test | ||
K0=0.65 | [45] | |||
Substratum | H=5 m; γsb =17.5 kN/m3; | \(C_{\rm{r}} =\) 1.27×10-4 m/kPa | Eq. (29) | |
csb =15 kPa; φsb=9°; | ||||
Esb =2.2 MPa; vsb=0.35 |
4.1 Case 1
4.2 Case 2
Method | Load share ratio \(R_{{\text{p}}}\) (%) | Depth of neutral plane l0 (m) |
---|---|---|
FEM | 66.7 | 7.79 |
Chen’s method | 74.0 | 8.05 |
Present method | 64.2 | 8.35 |