Internal Variable Gradient Model For Quasi-periodical Distribution Of Earth Pressure Acting On Retaining Wall

In-situ observations and laboratory experiments show that the distribution of earth pressure along the retaining wall is nonlinear periodic,apparently contradicting the hypothesis of liner distribution in the classic earth pressure theory.The nonlinear periodic phenomenon has been accepted by most geotechnical worker and many theories are suggested to explain it among which the method of horizontal layer analysis based on the horizontal soil element is most representative.The method of horizontal layer analysis gives parabolic distribution of earth pressure and it cannot explain the intermediate state and how the earth broke.Above all,the existing earth pressure theory cannot explain this phenomenon of “R”-shaped distribution or periodical distribution well.In this article,we take the significant advantage of internal variable gradient model in interpreting strain localization,size effect and the spatial distribution of the stress and strain and try to provide new ideas for the further studies on the earth pressure.As a typical granular material,the soil is different from the general continuous medium which always shows nonlocal characteristics in mechanical behavior.The classical earth pressure theories are based on the traditional elastic and plastic mechanics and take the soil as a continuous medium which has certain limitations.That's the exact reason why the classical theories cannot explain periodical distribution of earth pressure.(1)In order to consider the localization of deformation and stress,we introduce a gradient term of the first invariant function of stress tensor as internal variable into the Mohr-Coulomb failure criterion.The distribution of horizontal earth pressure along the retaining wall under plane strain condition is obtained.This internal variable gradient model can well describe the periodical distribution of horizontal earth pressure along the retaining wall.(2)We do further study on t he influence of intrinsic length to the distribution of the active earth pressure.The intrinsic length representing material's internal characteristic is introduced to ensure the balance of the dimension,take soil's self-organization and dissipation and the long-range interactions of material particles into consideration.With the increasing of depth,soil's density becomes larger resulting in the growing of intrinsic length.Its periodicity and fluctuation increase too.(3)Basic on the obtained internal variable gradient model,when considering the softening branch of stress-strain relation of soil,we obtain the solution of earth pressure changing with the displacement of the retaining wall by expressing the strain in terms of the displacement;(4)After studying the relationship between the displacement of retaining wall and the stress and strain of the soil under translational mode,two basic rotation modes,rotating around the bottom(RB mode)and rotating around the top(RT mode)are further considered.The rotational parameter which quantitatively describes the rotation state of the retaining wall is introduced into the internal variable gradient model to describe the earth pressure distribution under different rotational state.The solution contacts the equivalent internal friction angle of interlayer and different rotation mode and describe distribution of earth pressure throughout the whole process from the static state to limit state then to post-limit state.In this essay,the calculation model is improved by introducing the concept of elastic-plastic partition.The failure surface and the shape of elastic-plastic of the soil are further clarified.The height of the boundary between elastic and plastic zones can be determined.The determination of control coefficients in the internal variable gradient model refer to the above research results of continuous and smooth boundary between elastic and plastic zones.Moreover,by absorbing the former scholars' concepts and theories on elastic-plastic partition of the soil,the softening branch of stress-strain relationship of soil and the equivalent internal friction angle of interlayer,the internal variable gradient model is the inheritance and development of traditional earth pressure.