考虑各向异性空间变异性抗滑桩加固边坡可靠度上限分析OA

Objective Accurately assessing the probability of slope failure induced by the anisotropic spatial variability of soil is crucial for slope reinforce-ment and risk evaluation.A current limitation in existing research is the insufficient discussion of the reinforcement effects of anti-slide piles and limit analysis under anisotropic random fields.This study introduces the discrete mechanism of limit analysis into general rotational anisotropic random fields and employs the upper-bound analysis method to evaluate slope reliability. Methods Firstly,the random field was generated using the Cholesky decomposition method.The autocorrelation function was transformed through a coordinate system conversion before the decomposition of the autocorrelation coefficient matrix to ensure that the random field demon-strated general rotational anisotropy.This procedure generated representative random fields for the soil strength parameters c and φ,which exhib-ited transverse isotropy and general rotational anisotropy,respectively.Then,the discrete mechanism upper-bound analysis theory was employed to generate velocity discontinuity surfaces in spatially variable soils,which rigorously satisfied the associated flow rule in plasticity mechanics.Specifically,at any spatial location,the angle between the tangential velocity along the velocity discontinuity surface and the actual velocity equaled the soil's internal friction angle.Next,to evaluate the reinforcement effect of anti-slide piles,the elastic-plastic analysis theory was ap-plied to determine the ultimate lateral soil pressure acting on the piles.Assuming a linear distribution of lateral soil pressure along the piles,an en-ergy balance equation was established for the slope reinforced with anti-slide piles.Finally,the strength reduction method was employed to calcu-late the safety factor at the critical state of slope failure.The influences of fluctuation scales,coefficients of variation,and correlation coefficients on the reliability of slopes reinforced with anti-slide piles were compared for the two types of anisotropic spatial variability random fields. Results and Discussions The verification of the calculation for the homogeneous pile-reinforced slope was conducted by setting all unit grid pa-rameters of the random field to equal values,simulating a homogeneous condition.The safety factors for Examples 1 and 2 were calculated as 1.63 and 1.46,respectively,with an average error of 1.8%in the verification results.For the anisotropic spatially variable slope,the error in the failure probability was on the order of 10-3.In addition,the variation trends of the failure probability for the anisotropic random field based on co-ordinate transformation remained consistent regardless of the differences between the minimum and maximum fluctuation angles.When analyz-ing the influence of fluctuation scales,the probability density function(PDF)curves of the safety factor became higher and narrower as the mini-mum fluctuation scale decreased.The influence of the minimum fluctuation scale on the PDF curve was more significant than that of the maxi-mum fluctuation scale.As the minimum and maximum fluctuation scales increased,the PDF curves for general rotational anisotropy exhibited a greater tendency to become shorter and wider compared to those for transverse anisotropy.Regarding the influence of the coefficient of variation,as Vc and Vφ increased,the corresponding PDF curves became shorter and wider while shifting to the left,resulting in a significant increase in fail-ure probability.As the coefficient of variation of the internal friction angle(Vφ)increased,the distribution of the critical sliding surface of the slope became more dispersed.This result indicated that when the soil's Vφ value was high,ensuring slope stability could require increasing the burial depth of the anti-slide piles.Regarding the influence of the cross-correlation coefficient,the failure probability(Pf)increased as ρc,φ in-creased.Under identical cross-correlation coefficients,transverse anisotropic slopes exhibited greater reliability than general rotational anisotro-pic slopes.Regarding the installation position of the anti-slide piles,for transverse anisotropic random fields,Pf initially decreased as the height of the pile arrangement increased,before slightly increasing.For general rotational anisotropic random fields,Pf generally decreased as the height of the pile arrangement increased.The failure probability of the general rotational anisotropic spatially variable pile-reinforced slope was higher than that of the transverse anisotropic pile-reinforced slope.The optimal pile position Xf/Lx(the ratio of the distance from the pile installation posi-tion to the toe of the slope to the distance from the top of the slope to the toe of the slope)for the general rotational anisotropic spatially variable pile-reinforced slope approached 0.8.In contrast,for the transverse anisotropic pile-reinforced slope,it ranged between 0.6 and 0.7.When design-ing spatially variable pile-reinforced slopes,neglecting the influence of anisotropy on design parameters can lead to risks in determining the anti-slide pile installation position. Conclusions The results demonstrate that the optimal pile position is relatively insensitive to spatial variability parameters.However,a signifi-cant difference in the optimal pile position is observed between the two typical anisotropic random fields.In particular,under general rotational anisotropy conditions,the use of the Xf/Lx=0.6 pile position in practical engineering can pose potential risks.In addition,the internal friction angle of soil shows more significant fluctuations in spatial distribution.When the slope becomes unstable,the slip surface distribution tends to be-come more discrete and deeper.Therefore,increasing the embedding depth of anti-slide piles in engineering projects is essential to improve the re-liability of slope stability.