Research On Displacement-dependent Earth Pressure Of Rigid Retaining Walls Via Mathematical Fitting In Unsaturated Soils

Accurate estimation of earth pressure is the basis for ensuring the safety and economy of retaining walls.The reason why it's difficult for the soil to reach the limit state is that the displacement of the retaining wall is generally within the design allowable range,especially the passive limit state.The Rankine and Coulomb earth pressure theories can't fully reflect the influence of the displacement of the retaining wall.The mathematical fitting method to characterize the displacement-dependent earth pressure of the retaining wall has been widely used,although they were limited to saturated or dry soil,which ignore the unsaturated state of the filled soil behind the wall.Based on the shear strength theory of unsaturated soil and the concept of total cohesion,considering the the influence of matrix suction and the state of rainfall infiltration and water evaporation reasonably,this paper obtained the expansion mathematical fitting formula of the displacement-dependent earth pressure for the unsaturated soil.In addition,it proposes an expansion hyperbolic fitting formula,displacement-dependent earth pressure for the unsaturated soil,based on Duncan-Chang model.Finally,relevant verification and parameter impact analysis are carried out.The main research contents and conclusions are as follows:(1)According to different functional forms,the representative displacement-dependent earth pressure formulations are divided into six categories.These six categories are:trigonometric function,exponential function,hyperbolic function,power function,sigmoid function and other ones.There are a large number of function forms and different parameter values,the fitting formulas are diversified,which also causes the current mathematical fitting research is extensive and unsystematic.But there is a lack of comparative research and the impact of the unsaturated characteristics of the soil isn't considered.(2)Based on the two state stress variables,the extension mathematical fitting formulas of displacement-dependent earth pressure for unsaturated soil considering the influences of matric suction is established.It is rationalized and feasible as well as fitting difference to expansion formulas by analyzing the influence of unsaturated soil characteristics and comparing with model test,which also show that displacement-dependent earth pressure for unsaturated soil under high matric suction changes more than the saturated state,and the influence of suction angle has a similar effort.The effect under linear suction isn't as significant as when uniform suction is applied.(3)Based on suction stress,the extension mathematical fitting formulas of displacement-dependent earth pressure for unsaturated soil considering rainfall infiltration and water evaporation is established.The vertical discharge and saturated hydraulic conductivity in sand,silt and clay are discussed.The results show that the vertical discharge and saturated hydraulic conductivity have significant effects on clay,followed by silt,and have no obvious effect on sand.The extension formulas are affected by the two factors in different degrees.(4)Using the hyperbolic stress-strain relationship of the Duncan-Chang model and unifying the non-lateral strain point and the active/passive state distinction point,the hyperbolic formula of displacement-dependent earth pressure for unsaturated soil is established.The formula has been verified by model test of unsaturated soil and degradation case of saturated soil.It is concluded that it better reflects the unsaturated characteristics of soil and can provide reference for engineering practice.