Technical Paper by A. Fakher and C.J.F.P. Jones WHEN THE ...

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FAKHER & JONES • When Bending Stiffness of Geosynthetic Reinforcement is Important G E = ------------------- ( = 1.2 × 10 21 ( + ν) 7 Pa) (1) E K = ---------------------- ( = 4.1 × 10 (2) 31 ( – 2ν) 7 Pa) The elastic properties of super soft clays are difficult to measure; however, experimental studies have shown that the elastic modulus of the super soft clay is not significant in the problem (Fakher 1997). Based upon experimental findings the shear modulus and bulk modulus of the super soft clay were assumed equal to 42 and 20 MPa, respectively. The shear strength of the super soft clay was assumed to be 50 Pa for the majority of the analysis, but was increased up to a value of 1,000 Pa to illustrate the influence of stronger and stiffer soil. An elastic-perfectly plastic behaviour was assumed for the soils in order to simplify the analyses. 2.3 Geosynthetic Reinforcement The reinforcements were modelled in two ways in order to investigate the effects of reinforcement bending stiffness on the bearing capacity of the super soft clay: 1. As cable elements, with no bending stiffness. This method is frequently used to model geosynthetic reinforcements when bending is considered unimportant. The cable elements used in the analyses were one-dimensional axial elements described in terms of cross-sectional area, elastic modulus, and yield strength of the cable. 2. As beam elements with elastic bending stiffness. The beam elements used in the analyses were two-dimensional elements with three degrees of freedom at each node providing displacement in two perpendicular directions and rotation. The beam elements were described in terms of cross-sectional area, elastic modulus, second moment of area (moment of inertia), and plastic moment. The moment capacity was assumed to be infinite. The reinforcements were fixed to the line of symmetry (Figure 1). However, they were not fixed to any other vertical boundary so as not to cause an unrealistic pull-out resistance. The length of the geosynthetic reinforcement was 2 × 7B, where B is the width of the footing. In view of the low value of the shear strength of super soft clay, it was assumed that perfect adherence existed between the clay and the reinforcement. The elastic modulus and cross-sectional area of the reinforcement were assumed to be equal to 1 × 10 5 Pa and 0.0033 m 2 , respectively. The second moment of area, I, of the beam elements was assumed to be equal to 7.64 × 10 -7 m 4 . However, this value was varied from 1 × 10 - 8 to 2.15 × 10 - 6 m 4 in order to study the effect of bending stiffness, EI. The bond stiffness and the bond strength of the element-soil interface and the yield strength of the cable elements were assumed to be 3 × 10 7 N/m/m, 4.5 × 10 4 N/m, and 6.8 × 10 3 N, respectively for all the analyses. Details of the material properties used in the different analyses are shown in Table 1. 448 GEOSYNTHETICS INTERNATIONAL • 2001, VOL. 8, NO. 5
FAKHER & JONES • When Bending Stiffness of Geosynthetic Reinforcement is Important Table 1. Variables used in the analyses. Analysis no. Second moment of area beam elements I (m 4 ) Ratio of sand thickness, D, and footing width, B D/B Shear strength of super soft clay C (Pa) Footing width B (mm) Displacement increment (mm) Grid aperture (mm) f-20 7.64E-07 0.51 50 50.4 30 × 33 f-21 7.64E-07 0.51 500 50.4 1 30 × 33 f-22 7.64E-07 0.51 100 50.4 1 30 × 33 f-23 7.64E-07 0.51 250 50.4 1 30 × 33 f-24 7.64E-07 0.51 1000 50.4 1 30 × 33 f-26 2.00E-07 0.51 50 50.4 1 30 × 33 f-27 8.50E-08 0.51 50 50.4 1 30 × 33 f-28 1.00E-08 0.51 50 50.4 1 30 × 33 f-29 2.15E-06 0.51 50 50.4 1 30 × 33 f-30 7.64E-07 0.51 50 108 2 30 × 33 f-31 7.64E-07 0.51 50 252 5 30 × 33 f-32 7.64E-07 0.51 50 504 10 30 × 33 f-33 7.64E-07 0.51 50 1008 20 30 × 33 f-40 7.64E-07 0.17 50 50.4 1 30 × 31 f-42 7.64E-07 0.51 50 50.4 1 30 × 33 f-44 7.64E-07 1.54 50 50.4 1 30 × 39 f-45 7.64E-07 2.06 50 50.4 1 30 × 42 2.4 Applied Loading At the start of the analysis, the model was switched to gravity to produce the initial stress state. Following this, a surface load was simulated by exerting successive displacement increments. The program was run for each displacement increment and an out-put file for each increment was stored; following this, the next displacement increment was exerted using the data in the stored file as the starting criteria. The displacement increment used in the analyses was found to be critical. An increment of 0.02B was found to be satisfactory for the analyses. A discussion on the effects of different displacement increments and different methods of applying load using FLAC is given by Fakher (1997). 3 RESULTS AND DISCUSSION A plot of the vertical loading on the footing versus vertical displacement for each analysis is shown in Figure 3. The results show no peak bearing capacity and the selection of the point of ultimate bearing capacity is a subjective matter, which depends on engi- GEOSYNTHETICS INTERNATIONAL • 2001, VOL. 8, NO. 5 449
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