Deterministic And Probabilistic Study On Three-Dimensional Active Earth Pressures Based On Limit Analysis

Retaining walls play a vital role in various engineering projects,and the key to their design is to determine the active earth pressure induced by backfills on the walls.Most of traditional approaches for calculating active earth pressures are based on the assumption of plane-strain conditions.However,the failures of soil masses behind walls usually show three-dimensional(3D)characteristics,especially when the wall height is close to its longitude width.In the framework of limit analysis,the deterministic computational models of 3D active earth pressures under the influence of different factors are obtained according to the work-energy balance equation.On this basis,the input parameters are further regarded as random variables.Then,probabilistic assessments of 3D active earth pressures and reliability analyses of retaining walls are carried out.Finally,three active learning-based algorithms for reliability analysis are proposed,which can efficiently realize the prediction on failure probabilities.The contributions of this dissertation can provide a theoretical reference for the stability analysis and design of retaining structures.The main contents of this dissertation are summarized as follows:(1)Based on the upper-bound theorem of limit analysis,a 3D curvilinear cone failure mechanism associated with the Mohr-Coulomb yield criterion is constructed.The formula for 3D active earth pressures is deduced from the work-energy balance equation.Considering that the soil has relatively low tensile strength,the tensile strength cut-off and vertical cracks are further introduced to modify the failure mechanism,and the corresponding computational models are then obtained.By using the multitangent method and its corresponding multi-cone failure mechanism,the calculation of 3D active earth pressure under the condition of nonlinear strength is carried out,and the influence of soil strength nonlinearity is explored.(2)The seismic action will significantly increase driving forces on the soil masses behind walls,thus increasing the active earth pressures.Reasonable description of earthquake input is necessary for the calculation of seismic active earth pressures.The pseudo-static and pseudo-dynamic approaches are successively used to capture the earthquake acceleration.The external work rate due to earthquake forces is calculated and introduced into the work-energy balance equation.Then,the pseudo-static and pseudo-dynamic solutions under the linear Mohr-Coulomb strength criterion are obtained.The modified pseudo-dynamic approach is further used to investigate the problem of seismic active earth pressures with considering the nonlinearity of soil strength.(3)In geotechnical practice,most of soils are unsaturated.Considering this fact,the suction stress-based effective stress principle is introduced to capture the stress state of unsaturated soil.The distributions of matric suction and suction stress under steady and transient unsaturated seepage conditions are derived,and the corresponding internal energy dissipation rate caused by unsaturated effects is computed.Then,the models for the calculation of 3D active earth pressures under steady and transient seepage are obtained.On such a basis,the impact of hydraulic hysteresis on 3D active earth pressures is investigated.(4)Considering the fact that the original calculation models of 3D active earth pressure are computationally expensive,sparse polynomial chaos expansions(SPCEs)are used as the surrogate model.Based on this,the input parameters are considered as random variables,and the probabilistic distributions of 3D active earth pressure coefficients are obtained using the Monte Carlo simulation.Then,the global sensitivity analysis is undertaken to assess the contributions of random input parameters to the uncertainty of model outputs.Finally,the reliability of retaining walls under 3D conditions is analyzed to verify the applicability of SPCEs in reliability analysis of retaining walls.(5)Based on the probability theory and active learning,three algorithms for reliability analysis are proposed.The proposed algorithms all first train the machine learning model through a small number of initial training data,and use the active learning functions to select new training samples one by one.Then,the machine learning models are updated accordingly.The above process continues until the specified stopping criteria are met.Finally,two mathematical examples are used to verify the calculation accuracy and efficiency of the proposed algorithms.At the same time,the proposed algorithms are employed to the reliability analysis of retaining walls considering 3D effects to verify their potentials in solving engineering reliability problems.(6)Based on a gravity retaining wall of a shed renovation project in Luohu District,Shenzhen,the calculation models proposed in this dissertation are applied in engineering practice to calculate the active earth pressures under static and seismic conditions.The obtained results verify the effectiveness and engineering applicability of the approaches proposed in this dissertation.The conclusions of this dissertation can provide theoretical references for the stability analysis and design of similar projects.There are 123 figures,29 tables and 303 references.