Research On Foundation Bearing Capacity Based On Limit Analysis Method

The foundation bearing capacity involves almost all of the current infrastructure construction,including high-rise buildings,highways,railways,water conservancy construction,etc.The study of foundation bearing capacity provides a reliable theoretical basis for human engineering construction.At present,the research methods of foundation bearing capacity mainly include the classic limit equilibrium method,slip line method,and limit analysis method.With the development of computers,numerical simulation has achieved remarkable results in modern research on foundation bearing capacity.Based on the limit analysis method,this paper uses theoretical derivation and numerical calculation methods to carry out upper limit analysis and lower limit analysis on the ultimate bearing capacity of foundations.Finally,simulations prove the rationality of the results.The upper limit analysis of ultimate bearing capacity derives the calculation formula of the upper limit of ultimate bearing capacity according to the upper limit theorem.The influence law of the active zone bottom angleα,internal friction angleφ,correction coefficientλand other parameters on the bearing capacity coefficient is analyzed,and the optimal solution of the upper limit is solved.The lower limit analysis of the ultimate bearing capacity calculates the lower limit of the ultimate bearing capacity through the lower limit theorem.Using the finite element method to discretize the soil into finite triangular elements,according to the lower limit theorem,the static allowable stress field is constituted to determine the constraint conditions,combined with the MATLAB linear programming toolbox,the lower limit of the ultimate bearing capacity is calculated by programming.The influence of parameters such as the number of inscribed polygon sides P and the number of meshing units on the calculation accuracy is also analyzed.The paper introduces the correction factorλ,derives the expression of the upper limit bearing capacity coefficient,and analyzes the change of the bearing capacity coefficient when the foundation is smooth and completely rough.When the internal friction angleφis constant,the range of the base angleαis:φ≤α≤π/4+φ/2,then the bearing capacity coefficients N_q and N_c will gradually decrease with the increase ofαand the rate of change will gradually decrease,N_γAsαincreases,it first decreases and then increases.When the internal friction angleφis constant,andφ≤α≤π/4+φ/2,the upper limit of the ultimate bearing capacity first decreases and then increases with the increase ofα,and the upper limit has a minimum value and this minimum The value is the optimal solution for the upper limit.The upper limit of the ultimate bearing capacity has an approximate exponential growth relationship with the internal friction angle,and an approximate linear growth relationship with the correction coefficientλ.According to the idea of element discrete,the model mesh is divided into triangular elements through ANSYS and the node information and element information are exported and stored in the notebook,according to the lower bound theorem and finite element method,the MATLAB program is compiled by myself to calculate the lower limit of the ultimate bearing capacity of the foundation.The study found that the greater the number of inscribed polygonal sides P and the denser the mesh of the finite element method yield condition,the closer the calculation accuracy is to the theoretical accuracy.However,considering that the larger the value of P and the greater the number of grid cells,the longer the calculation time.According to calculations,when P=24,the calculation accuracy requirements can be met.Compare and analyze the upper limit and lower limit of the calculated ultimate bearing capacity,according to the limit analysis method,the precise value of the ultimate bearing capacity forms an interval between the upper limit and the lower limit.The size of the interval can be adjusted by the correction coefficient,so that a more accurate ultimate bearing capacity can be obtained.