Boundary Pressure Experiment And Theoretical Study Of Grain Like Material In Silo

Grain like materials have complex mechanical properties.Because it can withstand static shear stress,the static"solid-liquid"boundary of zero shear force can not be taken as fluid pressure in the calculation of space static stress.Instead,we need to consider the"solid-solid"boundary with shear force.At the same time,it is necessary to determine the constitutive relationship of samples.At present,there is no suitable constitutive model for grain materials such as wheat in the theoretical analysis of grain storage pressure in silos.The boundary conditions of the storage pressure problem are simply defined at the wall boundary and the free surface of the grain stack,which limits the accuracy and applicability of the solution of the storage pressure problem.Therefore,it is difficult to deduce a generally applicable method for calculating grain spatial pressure only under current conditions.The experimental research is also troubled by filling mode,warehouse deformation,displacement of built-in sensors during filling,difficulty in observing internal stress and wall friction of grain stack,etc.Effective and repeatable test schemes are rare.In this paper,model silo tests and theoretical studies of storage pressure are carried out for bulk grain stacks in silos.The values of lateral pressure coefficient（constitutive problem）and external friction coefficient（boundary problem）are discussed in detail.The main contents are as follows:（1）This paper proposes that the variation of friction（wall friction and vertical shear stress）along the radial direction and depth of the silo is the main factor causing the non-uniform distribution of vertical pressure in the same depth of the silo.Based on the results of numerical simulation and experimental data,the distribution of effective friction coefficient at the wall and inside of the silo is discussed under the influence of silo diameter,grain loading height,external friction coefficient,grain stack depth and depth ratio,and a piecewise mathematical expression of effective friction coefficient of the silo is proposed.（2）According to the distribution law of effective friction coefficient of silos,the grain like materials are divided into concentric rings along the radial direction.Assuming that the vertical pressure on each concentric ring is uniformly distributed,the calculation method of vertical pressure at any point in the grain stack space is deduced according to the equilibrium equation.Based on some assumptions,the simplified algorithm proposed in this paper is in good agreement with the numerical simulation results.The simplified calculation method is relatively simple and can provide theoretical support for the determination of storage pressure load and the unsolved problem of storage direction in the design of grain storage structure.（3）In this paper,the lateral pressure coefficient and the external friction coefficient are coupled as a quantifiable index parameter.Through the model silo test,it is found that the change of characteristic height is relatively stable when the filling height H is larger than the diameter D of the silo,and only slightly decreases with the increase of filling height.For this large-scale model,the effect of this weak change on boundry pressure is negligible.According to the micro-slit separation design of the silo floor in this paper,the silo is separated into four solid cylinder isolators.It is found that each cylinder can maintain a constant value ofλ_i.The size ofλ_i is related to the radius of the cylinder.Because this test method avoids the measurement ofμ₀ and K in the granary,and the research results have certain regularity,it should be a feasible way to observe the internal state of the granular system.（4）For flexible silos,neglecting the influence of wall deformation will lead to errors in calculating wall lateral pressure.In this paper,a method for calculating the lateral pressure of flexible silo wall is presented.The results show that when the grain depths are small,the calculation results of this method are almost identical with those of Janssen’s formula,which proves that the elastic deformation of the silo wall is small and the influence of lateral pressure calculation is weak,and can be treated as a rigid silo.When the grain depths are greater than 0.6 m,the calculation results of Janssen’s formula are gradually larger than those of this method,and the error is up to 8.70%.It shows that for flexible silos,Janssen’s formula is used.The lateral pressure of the silo wall obtained by the formula will be larger than the actual value,and the error will increase with the increase of the depth of the grain pile.This is because the influence of the axial and radial stresses in the silo wall is gradually significant.It is suggested that the generalized Hooke’s law be used for analysis.