Study And Application On The Spatial Correlation Of Soil Parameters And Random Field Simulation

Due to the forming process of soil deposits and other reasons,geotechnical material is randomness and spatial correlation.In the early study,the geotechnical parameters were treated as random variables.However,it is found that geotechnical parameters can't fully reflect their probabilistic characteristics with random variable.The randomness of geotechnical parameters is related to its spatial location,and is also has the characteristics of autocorrelation.Random field theory is adopted to describe the spatial correlation characteristics of soil by correlation function,which can reflect the randomness and correlation of soil.In this paper,two parameters,tip resistance_cq and sleeve frictionf_s,based on the Cone Penetration Test(CPT)collected from a particular site in Shandong Province is adopted here.The autocorrelation function of two CPT parameters is studied in silt,clay,silty sand and silty clay soil,and the spatial structure correlation of two parameters is discussed.The results show that the correlation structure of two CPT parameters is relatively close in the same site deposits,which shows that the spatial correlation of the soil in the same site is unified,so the different parameters can be described with the same correlation function.It will help to push the random field theory into reality.In this context,the spatial correlation of the different parameters can be represented by the same correlation structure.It further means that the spatial structure of the soil is related to the physical composition of the soil,the age of deposition and the conditions of origin.The soil autocorrelation data are fitted by the least square method using the most commonly used correlation functions,such as exponential function(SNX),the exponential cosine function(CSX)and the linear exponential correlation function(LNX),and the corresponding correlation distance of each model is obtained.From the correlation function curve,it can be seen that the curve of the correlation function first descends quickly to zero,to negative,and then back to the zero point again with the increase of the relative distance.Based on this property and considering the differentiable of the correlation function at zero point,an improved correlation function which combines the LNX function and the CSX function,is proposed.It is entitled as linear-exponential-cosine model(LNCS),as it combines the linear exponential term and the cosine term.The autocorrelation data of soil parameters is simulated using this model,which can reflect the related characteristics of soil better.Further,the Karhunen-Loeve(K-L)decomposition method is applied to simulate the random field.The eigenvalue and eigenfunction of the covariance matrix composed of correlation function are obtained by numerical method,and compared with the analytical solution,the accuracy is higher and the applicability is better.At the same time,the converged rate of the LNCS correlation function is studied.It is found that the LNCS function model converges faster than the SNX,CSX and LNX models under the same conditions.Thus,fewer terms suffice to meet the accuracy in the K-L decomposition.The random field on elastic modulus of soil parameters is adopted here.Using the finite element method,the settlement analysis is done,and the probability characteristic is also analyzed.It is found that the distribution of the settlement obeys the logarithmic normal distribution,which is the same as the reference,and the mean value is close to the reference value,with relative error of 23.6%.However,maximum likelihood estimation shows that the maximum likelihood estimation of the settlement is consistent with the mean value in the reference.Finally,the non-uniform settlement of an engineering project is analyzed.The calculated settlement of the north side is close to the actual observation value,and the settlement of the south side is about 5.3%smaller than the actual observation.The settlement is fitted to normal distribution,and the actual observed values on both sides of north and south are in the interval(?-3?,?(10)3?)of the calculated settlement.