| Building Foundation Design Code only defines the calculation formula for the bending moment of the foundation plate when "the aspect ratio of steps is less than 2.5",but has no regard for any calculation formula when the aspect ratio is greater than 2.5.At present,the aspect ratio of the foundation plate is also controlled as per 2.5 for the foundation design in flexible soil for transmission line,which makes the thickness of the foundation plate bigger and also increases the ferroconcrete consumption of the foundation plate.The reliability of the calculation method of the bending moment of the foundation plate lies in truly determining the contact stress distribution between the foundation plate and the ground soil.In the traditional calculation methods and Code for Design of Building Foundation,the contact stress is assumed to be linear distribution.In fact,under the load effect,the contact stress between the foundation plate and the ground often takes on a nolinear distribution of power and exponential functions,the coefficient of which is decided by the foundation soil types,the width-to-thickness ratio of the foundation plate and the magnitude of load.Therefore,the research work of analyzing the true contact stress distribution between the foundation plate and the ground and obtaining the calculation method of the bending moment of the foundation plate under the effect of contact stress distribution of power and exponential functions is of great theoretical and application values.For circular foundation plates,this paper adopts the analytic method to deduce the displacement field,radial stress field and ring stress field when the upper part of the foundation plate is imposed with a concentrated force and the lower part is imposed with power function distributed load.The first step is to assume the power function distribution of the contact stress between the foundation plate and the ground under the load effect when the foundation plate is between clay and sand,and the next step is to substitute it into the differential governing equation of the foundation plate,so as to solve the displacement field of the foundation plate through the boundary conditions of force and displacement,and finally solve the internal force field and stress field of the circular foundation plate.For free square foundation plates,this paper introduces the structural symmetry conditions into double cosine displacement deflection function with supplementary remainder proposed by Yan Zongda,et al,represents the internal force of the foundation plate with the displacement function,expands the force boundary conditions expressed in displacement function and the power and exponential functions of contact stress distribution of the upper and lower parts of the foundation plate into a cosine series function,solves the displacement field of the foundation plate through the differential control equation and the force boundary conditions of the foundation plate,and then solves the internal forces of the foundation plate according to the displacement field and the internal force relations of the foundation plate.In order to verify the capacity of the nonlinear power and exponential functions in describing true contact stress distribution,this paper carries out massive research work from two aspects of numerical simulation and test measurement.In the aspect of numerical simulation,the finite element model was established by use of ANSYS,the interaction between the foundation plate and the ground under the effect of axial load and eccentric load was analyzed,the contact stress distribution between the foundation plate and the ground was obtained under different aspect ratios and different soil types through numerical simulation.The finite element calculation results were fitted against the proposed power and exponential functions of nonlinear contact stress distribution and the fitting result was good,which verified the applicability of the power and exponential functions of contact stress distribution proposed in this paper.In the aspect of test measurement,the indoor pressure film basic model test,the indoor real model test and the field real model test were carried out.It was expected to find out whether the proposed power and exponential functions of contact stress distribution can well fit the true contact stress distribution between the foundation plate with great flexibility and soil or sand through the tests.In this paper,a series of foundation plates of different aspect ratios were designed and experimental measurement work was carried out at three different places.1.In the mechanics experiment center of the school,the model test of foundation plates of different aspect ratios was carried out by use of the pressure membrane system;and the model foundation plates are small in size.The contact stress distribution between the model foundation plate and soil or sand was measured.2.In the deep foundation pit of the soil mechanics laboratory of the school,the stress distribution of the foundation plate was measured by use of earth pressure cell and the contact stress distribution between the foundation plates of different aspect ratios and soil or sand was also measured.3.The true contact stress distribution of the flexible foundation plate was measured by use of earth pressure cell in the wild.By means of test measurement,the test measurement methods of the nonlinear contact stress distribution between the foundation plate and the ground and the fitting methods of power and exponential functions of contact stress distribution for corresponding test data have been obtained;and the understanding in the following aspects has also been achieved:the contact stress distribution between the foundation plate with great flexibility and the ground;the effects of soil types on the contact stress distribution of the foundation plate with great flexibility;the contact stress distribution of the foundation plate with great flexibility in various load cases,such as off-centre up-pulling and off-centre down-pushing.The proposed power and exponential functions of contact stress distribution and the test determination methods of the corresponding undetermined coefficients were confirmed through the tests.The measured results were fitted against the proposed power and exponential functions of contact stress distribution,and the fitting result was good,which further verified the rationality of the power and exponential functions of contact stress distribution proposed in this paper.Compared with the conventional foundation plates whose aspect ratio is less than 2.5,the foundation plates with great flexibility whose aspect ratio is greater than 2.5 have smaller contact stress around the four peripheries at the bottom,while the contact stress near the center at the bottom is larger.The contact stress distribution of the foundation with great flexibility makes the bending moment imposed on it smaller;From the test results,it can be seen that:the current calculation methods based on the hypothesis of linear distribution of bending moment and shearing force of flexible foundation fail to give the true bending moment and shearing force the value is bigger imposed on the flexible foundation in a good way;But the current calculation methods of bending moment and shearing force of the flexible foundation are widely used in engineering,and their safe reliability has been verified by numerous tests and engineering examples.For this purpose,with the existing strength design methods of the flexible foundation as reference standard,this paper puts forwards the concept of reduction coefficient of the foundation with great flexibility,the results of which are of great theoretical value and can provide reference for engineering design. |
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