Theoretical Study And Numerical Analysis On Ultimate Bearing Capacity And Shakedown Of Foundations Subjected To Combined Loading

At present, in civil engineering, hydraulic engineering, coastal and offshore engineering, the, clay foundations are usually subjected to vertical loading with a long-period acting and simultaneous or cyclic loading components including horizontal loading and moment loading. Such a loading pattern is defined as combined loading mode. Furthermore, when these loading components are varying in magnitude and alternating in direction with time periodically or irregularly, the loading pattern is called varied combined loading mode. According to the ultimate bearing capacity of foundation under combined loading mode and the shakedown characteristic under varied combined loading mode, the failure pattern and the ultimate bearing capacity of clay foundation are analyzed and investigated in this paper by adopting the limit equlibrium method, the limit analysis method and the finite element method, which are based on theoretical analysis and numerical calculation. The main investigations of this study are as follows:1. On the basis of the limit equlibrium theorem, the variational method is applied in this paper to solve the ultimate bearing capacity of the two- and three- dimensional foundations under combined loading mode, then to get theoretically the ultimate bearing capacity, the failure envelope and the sliding surface equation of clay foundation under combined loading mode. And the influencing factors of the friction angle of soilφ, the cohesive force, the footing ratio of LIB, the shear strength ratio c_i/c_i+1 and the fluctuation of groundwater level et al on the failure envelope are analyzed theoretically.2. Based on the limit analysis principle, and on the assumption of Mohr failure theory and soil rigid-plasticity model, the statical allowing variable stress field and the kinematic allowing variable velocity field are given in this paper, and then the lower bound solution and upper bound solution of ultimate bearing capacity of two- and three- dimensional foundations are given. The results show that the friction angle of soil can affect the limit analysis results greatly. For the undrained saturated foundation, the upper- and lower-bound solutions are identical and equal to the genuine solution. On the other hand, For the clay foundation, the upper- and lower-bound solutions are different, but there must exist a genuine solution between the lower- and upper-bound solution.3. In order to investigate the influence factors on the failure envelope under combined loading in detail, the failure patterns of foundation are analyzed in this paper using numerical calculation method by virtue of the general finite element analysis software ABAQUS. The results are as follows: 1) the failure patterns of surface creep failure, superficial sliding failure and deep sliding failure are controlled by vertical loading V. 2) the horizontal loading H acted on the footings makes the failure pattern of foundation asymmetry. 3) the moment loading M changes the effective width of footing, then causes the elastic kernel beneath the footing to appear and makes different failure patterns in M-H-V loading space.In a conclusion, the failure patterns of foundation include surface creep failure, superficial and deep sliding failure in V-H loading space; the failure patterns incude tilted scoop failure and deep sliding failure in V-M loading space. The failure patterns in M-H-V loading space are more complex compared to that in V-H or V-M loading space, firstly the failure patterns can be defined as forward-tilted scoop and backward-tilted scoop failure according to the direction of horizontal loading H and moment loading M; then based on the terminal condition of the appearance of the elastic body beneath the footing, the failure patterns can be sorted further into surface creep failure, forward-tilted-scoop failure, backward-tilted-scoop failure, scoop-dual-wedge failure, wedge failure, scoop-fan-wedge failure, fan-wedge failure, Green failure, and Hansen failure et al.4. The effect of the elastic-plastic matrix of friction soil with nonrelevant flow rule on the numerical convergence of finite element method is analyzed in this paper; and the effect of elastic modular, poisson ratio and earth pressure coefficient on numerical results are studied in this paper. At the same time, the hybrid element with a mixture of displacement and stress variables and the conventional element with solely displacement variable are compared when used in geomaterials. The results of numerical analysis show that the elastic modular and the poisson ratio have no effect on two-dimensional bearing capacity, but can affect the ultimate bearing capacity of three-dimensional foundations and control the convergence and precision of finite element calculation; the earth pressure coefficient controls the geostatic stress of foundation, sequentially affects the ultimate bearing capacity of foundations and the convergence of numerical calculation. When calculating the ultimate bearing capacity of undrained saturated foundation, the complete formulation exists shear locking, and reduce formulation exists hourglassing, so the hybrid formulation is suitable to imitate the geomaterial. When the soil obeys nonrelevent flow rule, the yielding function is different from potential function, and the elastic-plastic matrix of soil is asymmetric, so the unsymmetry numerical solver and appropriate finite element mesh is required.5. By the numerical analysis of the ultimate bearing capacity of two- and three-dimensional footing under combined loading mode, the results show that the effect of alteration of underground water lever on bearing capacity of three-dimensional foundation is more than on that of two-dimensional foundation, the effect of soil gravity on bearing capacity of three-dimensional foundation is more than that of two-dimensional foundation. At the same time, the numerical calculation process of ABAQUS indicates that whether the geostatic stress is balanced or not has great effect on the numerical convergence. In view of the effect extent of dilation angle of soil on the ultimate bearing capacity and the failure pattern of foundation, the condition of two-dimensional plane strain is higher than that of the three-dimensional foundation.6. In M-H-V loading space, the chang rate of asymmetry of failure envelope of foundation under three-dimensional rectangular footings is higher than that of two-dimensional footings for the effect of end-effect, when the vertical loading V is less than the vertical critical loading, the result shows that the end-effect can weaken the forward-tilted scoop failure pattern and backward-tilted scoop failure pattern. On the other hand, when the vertical loading V'\s higher than the vertical critical loading, the symmetry of failure envelope of three-dimensional foundation in H-M loading space is more optimal than that of the two-dimensional foundation.7. Based on the Melan lower bound shakedown theory, the paper adopts elastic-plastic finite element analysis software ABAQUS to construct residual stress field which does not need the linearization of the yielding criterion, then analyzes the shakedown of foundation under varied combined loading mode. The investigation shows that the shakedown loading is lower than the limit loading significantly. The varied loading patterns can affect the shakedown loadings. The friction angle of soil can affect the shakedown of foundation significately. Under the condition of undrained saturated foundation, the vertical shakedown loading is equal to the vertical limit loading; the horizontal shakedown loading and the moment shakedown loading are lower than the horizontal limit loading and the moment limit loading individually. Under the condition of clay foundation, the vertical shakedown loading is lower than the vertical limit loading obviously; the horizontal and moment shakedown loading are reduced compared to the limit loading. On the results of the numerical calculation, the conclusion can be drawn that the shakedown of three-dimensional rectangular footings is better than that of the two-dimensional strip footings; and when the vertical loading is larger to induce deep sliding failure of foundation, the shakedown failure pattern of foundation is different from the limit failure pattern in M-H-V loading space.