Probabilistic Back-analysis Of Spatial Variability Of Hydraulic Parameters For Unsaturated Soil Slopes

It is widely recognized that soil properties exhibit spatial variability due to mineralogical composition,stress history,and deposition processes.When the unsaturated soil slopes subject to rainfall infiltration or water level changes,the spatial variability of hydraulic properties has a significant impact on the slope stability and response.Therefore,proper characterization of spatial variability for hydraulic properties is of great significance in landslide prevention and control.At present,the estimation of soil spatial variability is mainly based on field investigated data.It is difficult to grasp the overall spatial variability of the slope based on the limited number of investigated samplings.The monitoring data is a comprehensive response of the slope with characteristics of instantaneity and continuity.Therefore,spatial variability estimation by monitoring data can provide an alternative way and provide new insights for site characterization.The principal objective of this research is to develop inverse methods for soil spatial variability estimation.Concerning the soil hydraulic properties,the spatial variability of unsaturated soil slopes under rainfall infiltration is systematically studied.The main content and conclusions are as follows:(1)Considering soil spatial variability,the unsaturated soil slope models under rainfall infiltration are established.Two-dimensional steady-state and transient-state unsaturated flows are modeled.The sensitivity and stochastic analysis are studied based on these models.The saturated permeability coefficient k_s is viewed as spatially varied soil properties and generated by random field theory.The uncertainty and statistics of pore pressure head of the slopes are investigated based on Monte Carlo simulation.The spatial variability of k_s has a significant impact on the distribution of pore water pressure.The pore pressure at the crest of the slope is more sensitive to k_s,while the sensitivity at the toe of the slope is low.As the rainfall progresses,the uncertainty of the pore pressure increases with time.The statistical characteristics of the pore pressure near the groundwater level reach steady faster.(2)Based on the Bayesian theory and surrogate model,a high-efficiency inverse method for the estimation of two-dimensional random field theory is proposed.The estimation of soil spatial variability is achieved based on the steady-state model of unsaturated infiltration.To reduce the dimensionality,the spatially varied soil hydraulic property is simulated using the Karhunen-Loève expansion method.The polynomial chaos expansion(PCE)is used as a surrogate model to approximate the deterministic numerical model to reduce the computational load.Markov Chain Monte Carlo(MCMC)simulation is adopted to acquire the posterior distributions.The effects of different monitoring schemes on spatial variability estimation are discussed.The proposed method is accurate and reliable for spatial variability estimation for steady-state models.Denser monitoring points along with section and depth can improve the effectiveness of the estimation.The effects of spatial variability estimation are closely related to the distribution of soil heterogeneity.When larger k_s is distributed in the unsaturated zone at the crest of the slope,the estimation will be close to reality.(3)The transient-state model of unsaturated infiltration suffers from high nonlinearity.To solve this problem,the adaptive sparse polynomial chaos expansion(AS-PCE)is constructed based on norm truncation and stepwise regression to improve the efficiency and accuracy of the PCE surrogate models for inverse estimation.The performance of AS-PCE as surrogate models of the transient-state model is evaluated.The influence of monitoring frequency and monitoring period are explored.AS-PCE works well for transient-state model.It can at least accurately fit the pore pressure to the second moments.As the monitoring frequency decreases,the convergence rate becomes slow,and the error and uncertainty increase.The estimation of spatial variability is more accurate using a later stage of monitoring data under rainfall.(4)A case of a monitoring project of natural terrain in Tung Chung,Hong Kong is selected to study the spatial variability at the site based on the field monitoring data.First,to illustrate the necessity of considering spatial variability,the effects of single-layer and double-layer soil models are compared.Second,the recursive Bayesian method is constructed to for estimation and updating of soil parameters of time-varying monitoring data.Finally,two-dimensional random field theory is adopted to describe the spatial variability of hydraulic parameters around the piezometers.The spatially varied k_s estimated by monitoring data soundly reflect the field spatial variability of the study area by the comparisons of borehole and dynamic cone penetration test(DPT)data.The double-layer model can more effectively reduce the uncertainty of parameters than the single-layer soil model,and the predictions agree well with the measurement data.Time-varying monitoring data can improve the estimation of soil spatial variability and reduce the predicted errors.