| The inherent properties of natural rock and soil determine that geotechnical engineering is closely related to uncertainty in the process of investigation,design and construction,which makes it difficult to obtain accurate results by deterministic analysis.In recent decades,many scholars have studied the uncertainty of geotechnical parameters,and put forward some analysis methods including random variable model,random field model and so on.In this paper,random field model combined with Monte Carlo analysis method is used to analyze several common problems in geotechnical engineering,such as convergence deformation of underground cavern,foundation settlement and minimum support force of tunnel excavation.(1)A random field discretization program is developed,which can be combined with the finite difference software to realize the modeling of autocorrelation random field.The Monte Carlo stochastic finite difference model of underground circular cavern is established.The deformation of cavern considering the spatial variability of elastic modulus is analyzed.The influence of Monte Carlo simulation times and the number of elements on the results of stochastic finite difference calculation is studied.The results show that the number of Monte Carlo simulation should be more than 500 times for the stochastic finite difference analysis of conventional structures.For the same structure,the number of cells has little effect on the mean value of the simulation results,but has great effect on the standard deviation of the simulation results.The less the number of cells,the greater the standard deviation of the simulation results.(2)The Monte Carlo stochastic finite difference model of foundation settlement is established.The foundation settlement under isotropic and transversely isotropic elastic modulus distribution is analyzed,and the influence of fluctuation range on foundation settlement is studied.The results show that the "effective elastic modulus" of soil considering the spatial variability of elastic modulus is smaller than that of homogeneous soil.The convergence value of foundation settlement will increase with the increase of elastic modulus fluctuation range,and larger fluctuation range will increase the difference of foundation settlement results.The fluctuation range in the vertical direction has a great influence on the foundation settlement,and the influence of the fluctuation range in the horizontal direction on the foundation settlement is mainly reflected in the probability of changing the extreme distribution form of elastic modulus.(3)Based on Monte Carlo stochastic finite difference method,the critical support force model of tunnel excavation considering the spatial variability of cohesion and friction angle is established.According to the clustering characteristics of random field and its numerical simulation results,a set of Monte Carlo stochastic finite difference fast calculation method based on spatial interpolation algorithm is established.This method can greatly reduce the calculation amount of Monte Carlo analysis,and through the preset selection and discrimination mechanism,it can ensure the fast calculation result will not reduce the safety reserve of the structure.The results show that: compared with the full Monte Carlo analysis,the fast calculation method proposed in this paper can obtain quite accurate convergence results on the premise of greatly reducing the amount of calculation,and the simulation error is biased to the safer side. |
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