A Study On Numerical Methods For Analyses Of Bearing Capacity Behaviour Of Offshore Foundation Under Combined Loading

In coastal and offshore engineering, major structures and foundations are usually subjected to simultaneous application of three loading components including horizontal load (H), vertical load (V) and moment (M). Such a loading pattern is defined as combined loading mode. Furthermore, these loading components are varied in magnitude and alternating in direction with time periodically or irregularly. Under such circumstances, the loading pattern is called varied combined loading mode. The bearing capacity behavior of foundation under combined loading mode even under varied combined loading mode has been not well solved in offshore geotechnical engineering and still keeps challenge. There are lacks of rational analysis method and effective computational model for evaluating the ultimate bearing capacity of offshore foundations under monotonic combined loading and shakedown under varied loading. Therefore the studies are emphasized in this thesis on the numerical method for analyzing stability of offshore foundations under both monotonic and varied loadings. The main investigations consist of the following parts.1. The possibilities and performance of several types of finite elements with lower-order interpolation function applied to limit-equilibrium problems of geotechnical engineering are examined. Through numerical computations, it is shown that 4-node quadrilateral element is able to achieve numerical results which are more convergent than other types of elements. In analyses of slope stability by using elasto-plastic finite element method based on shear strength reduction technique, a new criterion is presented on the basis of the computed curve relating dimensionless maximum vertical displacement (δ_max|ˉ) of the top of the slope to the shear strength reduction factor F_s. The point on the curve where the dimensionless maximum vertical displacement (δ_max|ˉ) is abruptly increased isregard as the limit-equilibrium state which tends to give the critical safety factor of the slope against overall shear instability. The criterion for evaluating the limit-equilibrium state proposed here can avoid a certain man-made uncertainties as occurred in the conventional procedures.2. The soil foundations in engineering practice usually display strong nonhomogeneity along depth. For example, undrained shear strength of soil strata commonly increases with depth proportionally or in a certain pattern. On the other hand, the fast Lagrangian analysis for continua with the solver FLAC by using Lagrangian explicit finite difference method can reproduce the large-displacement behavior of geo-structures near the limit-equilibrium state which cannot be simulated by common FEM softwares. Therefore the FLAC is employed to investigate bearing capacity behavior and failure mechanism of footing on such nonhomogeneous clays foundations with a increasing shear strength with depth. It is demonstrated that failure zone is more centralized around footing as nonhomogeneity degree of foundation strength increases andthe empirical formulae respectively given by Skempton, Peck and et al tend to obviously overestimate bearing capacity factor N for nonhomogeneous soils.3. The extended criterion of spatial mobilization plane (SMP) proposed by Matusoka and et al can take account the effect of intermediate principal stress on the shear strength of soils. Based on this strength criterion, the strength parameters of soils under plane-strain condition or other general three-dimensional stress condition can be determined by the strength parameters of soils under common axisymetrical stress condition achieved by triaxial shear tests. Then the soil strength parameters defined in this manner are directly used in the analytical solutions of bearing capacity obtained by slip-line method for both strip foundation and circular foundation. Through comparison, the effect of the intermediate principal stress and three-dimensional stress state on the bearing capacity of foundation are examined and the correlation factor of footing shape in the formulae of bearing capacity are identified. It is noted that the empirical values of shape factor proposed by Terzaghi are rather reasonably in most cases while the correlation factor of bearing capacity coefficient, Cp, resulting from contribution of soil weight on bearing capacity may be overestimated for the condition of smooth base. In this case, it is proposed that Crs=0.4 instead of Cys=0.6 as given by Terzaghi.4. Swipe test procedure is widely used to define the overall failure envelopes of foundations under combined loading in experiments and numerical analyses. However sometime it cannot give an accurate envelope. In order to effectively improve the accuracy of this procedure which is easily implemented, a modified on this procedure is made. Then the improved Swipe procedure is incorporated into FEM analysis software ABAQUS. It is shown that the precision and path-dependence is improved effectively by the modified procedure. Furthermore the method for controlling loading and displacement is presented for accurately determining bearing capacity of foundations under combined loading and then is combined with the improved Swipe procedure. The failure envelope in three-dimensional load space (H, V, M) of three components can be established based on numerical results. It is displayed that such an envelope is obviously asymmetrical with respect to the plane of H=0 which is dependent on the magnitude of vertical load component of V. Various failure behavior and collapse mechanism of foundations under different loading patterns can be numerically simulated by the FEM-based computations. It is shown that failure mechanisms and collapse patterns of foundations are closely related to the combination of three load components. For example, under the condition of combined loading without vertical component V=0, the failure pattern of foundation varies from the symmetrical scoop mechanism to the scoop-double-wedges mechanism and the double-wedge mechanism as the horizontal load component increases. However, under the condition of combined loading with a certain vertical load (e.g., F=0.5Fuit), the soil failure pattern of foundation varies from the asymmetrical scoop mechanism to thescoop-fan-triangle mechanism, the scoop-Hansen-type mechanism and the Hansen-type mechanism as the horizontal load increases.5. In order to construct the compatible velocity field of geo-structures, the velocity-type finite elements are presented. Based on the upper-bound theorem of limit analysis, a linear mathematical program issue is presented by using the proposed velocity elements and linearized Mohr-Coulomb's yield condition. The linear programming is solved by primal-dual interior-point method which is polynomial time algorithm. In order to reproduce the nature of velocity field of footing-foundation systems, triangle element and rigid-plate element are respectively presented to simulate the velocity distribution of deformable foundation and movement of rigid footing. At the same time, two different types of contact conditions of footing-foundation interface are used according to tensile strength behavior of the interface. In the contact mode I, a definite tensile strength is imposed on the interface while the tensile strength is completely overlooked in the contact mode II. Two types of velocity elements and two types of contact modes of the interface are combined together and velocity discontinuity of the footing-foundation system can be reproduced by imposing kinematical compatibility conditions. The upper-bound theorem is numerically implemented by using these techniques to work out a best upper-bound approximation of ultimate loads of foundations under combined loading condition. As an example, the vertical bearing capacity factor Ny of uniform foundation is analyzed and itis found the computed ultimate load is almost lower than all other upper-bound solutions available at present. Bearing capacity and failure mechanism of foundation under combined loading can be examined by the computed failure envelope in the three-dimensional load space (H, V, M). It is shown that the bearing capacity and failure behavior of foundation are highly dependent on the contact condition of footing-subsoil interface.6. Based on the lower-bound theorem of limit analysis, a linear program problem is presented by using stress-type elements and linearized Mohr-Coulomb's yield condition. The resulting linear program is solved by primal-dual interior-point method. Based on the computational results of FEM, foundation failure patterns of foundation under combined load can be visualized respectively by the slip-line field and stress-level distribution corresponding to limit-equilibrium state. Two types of constraint conditions on the contact forces are imposed on the footing-foundation interface to reproduce the contact behavior of interface according to the tensile strength and the stress discontinuity of the footing-foundation system under combined loading can be displayed. By incorporating these stress-type elements and contact conditions into lower-bound theorem of limit analysis, numerical implementation based on FEM is made to analyze the vertical bearing capacity factor Nr of foundation. The lower-bound solution obtained by the proposedmethod is between other two lower-bound solutions available. Furthermore, bearingcapacity and failure behavior of foundation under combined loading is investigated by the proposed method and the failure envelope in the three-dimensional load space (H, V, M) is obtained. It is shown that the bearing capacity and failure behavior of foundation are highly dependent on the contact condition of footing-subsoil interface. The lower-bound solutions can agree well with the upper-bound solutions by finite element method proposed as above.7. Based on Melan's static theorem of shakedown, a linear program problem is established and then solved by the primal-dual interior-point method. A statically-admissible residual stress field is constructed by finite element method based on the proposed method as given in lower-bound numerical analysis and then are added to elastic stress fields induced restively by three unit loads. Shakedown envelopes for different combination types of three components are defined. As the bearing capacity envelope of foundations under combined loads can be used for evaluating the stability of foundations subjected to monotonic loading, it is practically significant that the shakedown envelope obtained under combined loads can be utilized to evaluate the dynamic stability of foundations subjected to varying loads. Therefore shakedown analysis is as important as limit analysis for offshore foundations.