| Because of the merits of small post-construction settlement, high stability, rapid construction and so on, the pile-supported and geosynthetic-reinforced embankment has been widely used at home and abroad. There are corresponding design specifications in some countries. However, the load-deformation behavior of the geosynthetic reinforcement (GR) is a complicated three-dimensional (3-D) mechanical problem but it is usually simplified to the two-dimentional (2-D) problem in the engineering design in order to facilitate the calculation, which may result in over-conservative numeric value. Therefore there are great theoretical significance and application value of engineering to develop the real 3-D analytical method for the pile-supported GR, study the properties of its deformation and tensile force under 3-D condition and compare with those under 2-D condition.The GR with piles in square-type layout under 3-D condition is taken as the research object in this paper. The GR partial differential equilibrium equations are derived by the minimum potential energy principle, then simplified by the analog equation method (AEM) and solved by the boundary element method (BEM) and the simplex method. So the real 3-D analytical method for the pile-supported GR is established. For the situations of uniform distribution load and without subsoil reaction in engineering design, the reliability and rationality of the method are validated by a self-complied example and a project example, and the properties of GR deformation and tensile under 3-D condition are researched detailedly. Finally, the results calculated by the real 3-D analytical method are compared with those calculated by several current 2-D methods, by which analyze the similarities and differences of properties of GR deformation and tensile force under 2-D and 3-D conditions. This paper gets following main achievements:1.Under 3-D condition, the partial differential equilibrium equations of the pile-supported GR are derived by the minimum potential energy principle, which reasonably consider the property of GR large deformation and are highly nonlinear.2. The partial differential equilibrium equations are simplified to poisson equations by AEM, then solved by BEM and the simplex method, by which the real 3-D analytical method for the pile-supported GR is established. The method has the advantages of small discretization error, high computation efficiency and so on, the reliability and rationality of which are validated by the project example primarily.3. Under the conditions of uniform distribution load and without subsoil reaction, the similarities and differences of properties of GR deformation and tensile force under 2-D and 3-D conditions are as follow:(1) In terms of deformation, the GR vertical deformation curves are both parabola under 2-D and 3-D conditions, but the maximum of GR deformation under 3-D condition is about 60%-80% of that under 2-D condition.(2) In terms of tensile force along the length of geosynthetic reinforcement strip (GRS), the maximum both occur at the edge of pile caps under 2-D and 3-D conditions, while the minimum both occur in the central area of GRS. The GR tensile force under 3-D condition is generally about 50%-80% of that under 2-D condition, but it is about 10%-20% larger than that under 2-D condition near the corner of pile caps.(3) The GR deformation and tensile force obtained by 2-D analytical methods are generally conservative.4. Under 3-D condition, characteristics of the GR deformation and tensile force are as follows:(1) The distributions of GR vertical deformations form the concave surface in the space, the maximum of which is at the central point between four piles.(2) The distributions of two horizontal components of GR tensile force all form the hyperbolic paraboloid liked the saddle in the space, while the surface formed by maximum principal tensile force is concave. The larger value of the minimum principal tensile force occur at the edge of pile caps and in the central area of four-piled model, while the smaller ones occur in the central area of GRS. Each kind of GR tensile force mentioned above maximizes at the corner of pile caps, and there is mutation around the corner, which lead to the obvious stress concentration phenomenon.(3) GRS is the main stressed area and the direction of the maximum principal tensile force is along the length of GRS.(4) The GR vertical displacement increase obviously with an increase in the pile centre distance or a reduction in GR stiffness. The GR tensile force also increase obviously with the pile centre distance, but it is insensitive to GR stiffness.5. For the proposed 3-D analytical method for the pile-supported GR, the corresponding Fortran calculation program has been worked out. |
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