CN111666620A - Quantitative description method for lateral pressure distribution characteristics of granular material - Google Patents

Quantitative description method for lateral pressure distribution characteristics of granular material Download PDF

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CN111666620A
CN111666620A CN202010466314.6A CN202010466314A CN111666620A CN 111666620 A CN111666620 A CN 111666620A CN 202010466314 A CN202010466314 A CN 202010466314A CN 111666620 A CN111666620 A CN 111666620A
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CN111666620B (en
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来志强
江恩慧
王仲梅
赵连军
徐梓曜
徐阳
梅锐锋
任棐
武彩萍
吴国英
高梓轩
樊科伟
王嘉仪
潘丽
张文皎
王远见
李军华
张向萍
许琳娟
张敏
来嘉豪
来亮
张清清
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Abstract

The invention relates to a parameter determination method in hydraulic design, in particular to a parameter determination method for quantitatively describing the lateral pressure distribution characteristics of a granular material, belonging to a general method in the field of hydraulic engineering, wherein the IPC classification number of the method is E02B 1/00. The method of the invention definitely aims at the measuring size value range for describing the lateral pressure characteristics of the granular material, accurately determines the numerical values of two parameters of the lateral pressure action position concentration and the distribution intensity fluctuation, quantitatively describes the lateral pressure distribution characteristics, can truly reflect the discrete characteristics of the lateral pressure distribution of the granular material, can guide engineering designers to more accurately determine the pressure distribution during the engineering design of retaining walls, foundation pits, deep-buried tunnels and the like, and ensures the engineering safety.

Description

Quantitative description method for lateral pressure distribution characteristics of granular material
Technical Field
The invention relates to a parameter determination method in hydraulic design, in particular to a parameter determination method for quantitatively describing the lateral pressure distribution characteristics of a granular material, belonging to a general method in the field of hydraulic engineering, wherein the IPC classification number is E02B 1/00.
Background
Common granular materials in reservoir dam engineering include rockfill, soil, silt and the like which are dam building materials. These particulate materials generate lateral pressure due to their own weight or external load, and must be considered in the construction of high rockfill dams, retaining walls, deep-buried tunnels and the like. In particular, the research on the lateral pressure problem of the earth and the stone has been over 200 years, and the lateral pressure calculation theory commonly used in the engineering at present is the Rankine and Coulomb earth pressure theory. Both classical theories assume that the lateral pressure is linearly distributed along the depth of accumulation of particulate materials such as earth and stone bodies. The assumption that the lateral pressure is linearly distributed is widely applied to the engineering fields of retaining wall design specifications, foundation pit structure stability analysis, deep-buried tunnels and the like at home and abroad.
However, engineering materials such as earth and stone are very complex particle materials, and the traditional macroscopic continuous medium theory often neglects consideration of discrete characteristics of the engineering materials. In recent years, the development of Discrete Element Method (DEM) and the rapid improvement of computer performance have made it possible to study the mechanical behavior characteristics of granular materials such as earth and stone by a microscopic numerical Method. At present, the existing numerical simulation of discrete elements [1-3] researches show that the accumulation of granular materials such as earth and stone leads to the existence of an arch structure effect, so that the lateral pressure of the granular materials presents nonlinear distribution (broken line type distribution), and the design value of partial lateral pressure value compared with linear distribution is suddenly increased, which is very unfavorable for engineering safety.
When the lateral pressure of the granular material on certain parts of the retaining wall is too much and the pressure intensity changes violently, the retaining wall is easy to collapse unstably under the stress concentration effect. Therefore, the research on the concentration and the distribution intensity fluctuation of the lateral pressure action position has very important significance on the engineering design safety. However, no relevant documents and reports exist for quantitative description of the position concentration and distribution intensity fluctuation of the lateral pressure distribution of the granular material.
Relevant documents retrieved are given below:
[1] bengewei et al, simulation study of particle discrete element mesomechanics of gabion retaining walls [ J ] geomechanics, 2010, 31 (8): 2677-2681.
[2] Liu winter, etc. Limited width fill active soil pressure based on DEM analysis [ J ] road engineering, 2019, 44 (02): 36-40.
[3] Active destruction of non-viscous limited soil body and soil pressure discrete element analysis [ J ]. civil and environmental engineering newspaper (Chinese and English), 2019, 41 (03): 22-29.
[4] Fringed-fractal geometry and fluid [ M ]. shanghai: shanghai society of sciences publisher, 2014: 3-14.
Disclosure of Invention
The present invention is made to solve the above problems, and an object of the present invention is to provide a method for quantitatively describing a lateral pressure distribution characteristic of a particulate material. The method is simple and effective, has clear physical meaning of parameters, and can objectively and accurately quantify the concentration of the lateral pressure distribution position of the granular material and the fluctuation of the distribution strength.
The invention discloses a quantitative description method for the lateral pressure distribution characteristics of a granular material, which comprises the following steps:
step 1, selecting a particle material lateral pressure distribution position concentration measurement scale: measuring the height H after the particulate material has been settled0(m) selecting a series of measurement scale parameters ri(i ═ 1, 2, … n), where r1Satisfy the requirement of
Figure BSA0000210039260000021
The conditions of (1).
Step 2, obtaining the measurement number of the lateral pressure distribution position concentration under different measurement scales: measurement scale roDividing the retaining wall into equal number
Figure BSA0000210039260000022
A pitch length of riThe statistical subgroup contains the subgroup number n of lateral pressure action pointsi。
Step 3, solving a parameter d for describing the lateral pressure distribution position concentration: a series of r obtained in step 2iAnd corresponding niDrawing in a log-log coordinate system, and fitting logriAnd logniLinear relation between them, and obtaining its coefficient of determination R2When R is2And when the absolute value of the slope of the fitting straight line is more than 0.8, the absolute value of the slope of the fitting straight line is the lateral pressure distribution position concentration parameter d.
The lateral pressure distribution position concentration parameter d of the granular material is a numerical value between 0 and 1, wherein 0 represents that the action position distribution is almost concentrated at a certain point, and 1 represents that the action position distribution is linearly and continuously distributed. A larger d indicates a more dispersed location of the pressure distribution laterally of the particulate material.
Step 4, selecting a particle material lateral pressure distribution intensity fluctuation measurement scale: drawing a lateral pressure distribution diagram of the granular material, and defining the upper end point and the lower end point of a lateral pressure broken line as P respectivelyupAnd PdownSelecting a series of scale parameters Ri(i ═ 1, 2, … n), where R isiSatisfy the requirement of
Figure BSA0000210039260000031
The conditions of (1).
Step 5, obtaining the measurement number of the lateral pressure distribution intensity fluctuation under different measurement scales: the upper end point P of the broken line is distributed by the lateral pressure of the granular materialupAs a circle center, with RiDrawing a circle for the radius, said circle intersecting the lateral pressure distribution polyline at a point P1(ii) a However, the device is not suitable for use in a kitchenThen, the point P is used1As a circle center, with RiIs a circle drawn by the radius and intersects the side pressure distribution broken line at a point P2(ii) a By analogy, when the intersection point PnAnd PdownThe distance l on the lateral pressure distribution broken line is less than or equal to RiWhen the measurement is finished, the final result is RiMeasuring the number N of lateral pressure distribution polylines for a scalei＝n+l/Ri。
And 6, solving the fluctuation parameters for describing the lateral pressure distribution strength. Subjecting step 5 to obtain a series of RiAnd corresponding NiDrawing in a dual logarithmic coordinate system, and fitting logRiAnd logNiLinear function relationship between them to obtain its coefficient of determinability R2(ii) a When fitting the coefficient of the function2And when the absolute value of the slope of the fitting straight line is more than 0.8, the absolute value of the slope of the fitting straight line is the lateral pressure distribution intensity fluctuation parameter D.
The value of the fluctuation parameter D of the lateral pressure distribution intensity of the particle material is between 1 and 2, wherein 1 represents that the lateral pressure intensity distribution is in a straight line distribution, and 2 represents that the lateral pressure intensity distribution is in a plane distribution. The larger D indicates the larger fluctuation of the lateral pressure distribution intensity, the more obvious arch structure effect is, and the more lateral pressure sudden increase points are.
Compared with the prior art, the invention has the advantages that:
the traditional soil pressure theory is based on continuous medium assumption, which is contrary to the nature of discrete characteristics of particle materials such as earth and stone, and the lateral pressure distribution characteristics of the particle materials are not accurately described. The method improves the fractal theory thought, selects the measurement scale value range of the lateral pressure distribution characteristics of the granular material, accurately determines the numerical values of two parameters of lateral pressure action position concentration and distribution strength fluctuation, quantitatively describes the lateral pressure distribution characteristics, can truly reflect the discrete characteristics of the lateral pressure distribution of the granular material, can guide engineering designers to more accurately determine the pressure distribution during engineering design of retaining walls, foundation pits, deep-buried tunnels and the like, and ensures the engineering safety.
Drawings
FIG. 1 is a schematic diagram of a method for quantitatively describing the positional concentration of a lateral pressure distribution of a particulate material;
FIG. 2 is a schematic diagram of a quantitative description of the intensity fluctuation of the lateral pressure distribution of a particulate material;
FIG. 3 is a diagram of a particle material after stacking stabilization using DEM numerical simulation;
FIG. 4 is a graph (a) showing a lateral pressure distribution and a distribution intensity fluctuation analysis under the conditions that the particle diameter s is 0.01m and the particle friction coefficient μ is 0.30;
FIG. 5 is a graph showing the quantitative concentration of lateral pressure distribution under different particle sizes and friction coefficientsiAnd niFitting a functional relation;
FIG. 6 is a graph showing the quantitative relationship of R in the quantitative description of the fluctuation of the lateral pressure distribution strength under different particle diameters and particle friction coefficientsiAnd NiFitting a functional relation;
FIGS. 7 to 11 are side pressure distribution diagrams under different particle diameters and particle friction coefficients.
Detailed Description
The technical solution of the present invention is further specifically described below with reference to the accompanying drawings and examples. According to the embodiment, the DEM is adopted to simulate the natural deposition process of the granular materials, and the simulation parameters are selected according to the DEM simulation stone, soil and other granular material related documents[1，2]To ensure the correctness of the simulation results, the simulation parameters are shown in table 1. The DEM numerically simulates the particulate material after the stabilization of the packing as shown in fig. 3, and then extracts the lateral pressure of the particulate material acting on the left wall as shown in fig. 4(a) (the particle diameter s is 0.01m, and the friction coefficient of the particles is 0.30). The lateral pressures in the graphs (b) to (e) in fig. 4 are quantitatively described by using the quantitative description method for the lateral pressure distribution characteristics of the granular material provided by the invention. When the lateral pressure applied to some parts of the retaining wall is intensive (stress concentration) and the lateral pressure intensity is suddenly increased, the retaining wall is easy to be unstable under the condition of the abrupt mechanical boundary. Therefore, the invention selects two parameters of the lateral pressure action position concentration and the distribution intensity fluctuation to quantitatively describe the lateral pressure distribution characteristics. The invention specifically comprises the following steps:
step 1, defining the particle materialAnd (3) measuring the concentration of the material lateral pressure distribution position. Measuring to determine the height H of the particulate material after stable packing0(in m) because the particulate material must rely on the retaining wall to stabilize the packing, it is also commonly referred to in the art as the retaining wall height H0As shown in fig. 1. Where line 1 (longitudinal straight line) represents the wall, line 2 (transverse solid line) represents the lateral pressure application location, and line 3 (transverse dotted line) represents the dividing line of the equally spaced intervals. According to the theory of fractal[4]For a certain object with specific geometric characteristics, different scales r are adoptediMeasuring the geometric characteristics to obtain corresponding measurement number ni(ii) a When r isiAnd niBetween have
Figure BSA0000210039260000051
When the correlation is good, n can be obtained by function fittingi＝c1ri -d+c2In the formula, the position concentration measurement scale r is distributediIn m, the number of measurements niIn units of dimensionless, c1And c2All the constants are constants obtained by fitting, the units are dimensionless, the parameter d is a constant reflecting geometric characteristics, and the units are dimensionless.
In the present embodiment, the height H of the particulate material after stable deposition0Is 1.95 m. In satisfying
Figure BSA0000210039260000052
Under the condition, a series of scale parameters r are selected1＝0.025m、 r2＝0.030m、r3＝0.035m、r4＝0.040m。
And 2, acquiring the measurement number of the lateral pressure distribution position concentration under different measurement scales. Measurement scale riDividing the retaining wall into equal number
Figure BSA0000210039260000061
(if
Figure BSA0000210039260000062
Is a fraction, then rounded to an integer)A pitch length of riBetween adjacent lines 3. The number n of subgroups containing lateral pressure application points (line 2) in the subgroup is countedi(niIs an integer).
In the present embodiment, r is1Dividing the retaining wall into 78 subgroups with interval length of 0.025m, and counting the number n of subgroups including lateral pressure acting points1Is 63; for r20.030m, evenly dividing the retaining wall into subgroups with the number of 65 and the spacing length of 0.030m, counting the number n of subgroups containing lateral pressure action points in the subgroups2Is 54; for r3Dividing the retaining wall into subgroups with the number of 56 and the interval length of 0.035m on average, and counting the number n of subgroups containing the lateral pressure action points in the subgroups3Is 49; for r4Dividing the retaining wall into sub-groups with the number of 49 and the interval length of 0.040m on average at 0.040m, and counting the number n of the sub-groups containing the lateral pressure acting points4Is 46.
And 3, solving a parameter d for describing the lateral pressure distribution position concentration. Subjecting step 2 to a series of (at least 4) riAnd corresponding niDrawing in a log-log coordinate system, and fitting logriAnd logniLinear relation between them, and obtaining its coefficient of determination R2(R2Being dimensionless, the closer it is to 1, indicating
Figure BSA0000210039260000063
The stronger the correlation). When R is2Above 0.8, it is considered that
Figure BSA0000210039260000064
There is a strong correlation when the absolute value of the slope of the fitted line is the lateral pressure distribution position concentration parameter d.
The lateral pressure distribution position concentration parameter d of the granular material is a numerical value between 0 and 1, wherein 0 represents that the action position distribution is almost concentrated at a certain point, and 1 represents that the action position distribution is linearly and continuously distributed. A larger d indicates a more dispersed location of the pressure distribution laterally of the particulate material.
In this embodiment, r is obtained in step 21＝0.025m、r2＝0.030m、r3＝0.035m、 r40.040m and corresponding n1＝63、n2＝54、n3＝49、n4Plotted in a log-log coordinate system (shown in fig. 5), fitted logr 46i(i ═ 1, 2, 3, 4) and logni(i is 1, 2, 3, 4) to obtain R20.98, indicates
Figure BSA0000210039260000071
The correlation is strong, and the absolute value of the slope of the fitting straight line is the parameter d equal to 0.67.
And 4, selecting a measurement scale of the lateral pressure distribution intensity fluctuation of the granular material. And according to the DEM numerical simulation calculation result, drawing a granular material lateral pressure distribution diagram by taking the retaining wall height as a vertical axis and the lateral pressure of the granular material as a horizontal axis. As shown in FIG. 2, the distribution line of the lateral pressure of the granular material along the height of the retaining wall is a polygonal line, and the upper and lower end points of the polygonal line defining the distribution of the lateral pressure are PupAnd PdownAs shown in fig. 2. Selecting a series of scale parameters Ri(i ═ 1, 2, … n), where R isiSatisfy the requirement of
Figure BSA0000210039260000072
The conditions of (1).
In the present embodiment, the following conditions are satisfied
Figure BSA0000210039260000073
Under the condition, a series of scale parameters R are selected1＝0.1m、 R2＝0.2m、R3＝0.3m、R40.4 m. Defining the upper and lower end points of the side pressure broken line distribution as PupAnd PdownAs shown in fig. 4.
And 5, acquiring the measurement number of the lateral pressure distribution intensity fluctuation under different measurement scales. For R10.1m, with the upper end point P of the broken line of the lateral pressure distribution of the granular material in FIG. 4upAs a circle center, with R1Circle is drawn with radius of 0.1mIntersects the lateral pressure distribution polyline at a point P1(ii) a Then, at point P1As a circle center, with R1Circle is drawn with radius of 0.1m and intersects with the side pressure distribution broken line at point P2(ii) a By analogy, when the intersection point P139And PdownThe distance l of the folding line under the lateral pressure is less than R when the distance l is 0.0111When the average particle size is 0.1m, the measurement is finished to obtain the final product of R1Measuring the number N of the lateral pressure distribution broken lines with the scale of 0.1m1＝n+l/R1139+ 0.011/0.1-139.11, as shown in fig. 4 (b). N can be obtained by the same method as described above2＝60.12、N3＝30.05、N4＝26.78。
And 6, solving the fluctuation parameters for describing the lateral pressure distribution strength. Obtaining R in the step 51＝0.1m、 R2＝0.2m、R3＝0.3m、R40.4m and the corresponding N1＝139.11、N2＝60.12、N3＝30.05、N426.78 are plotted in a log-log coordinate system (shown in fig. 6). Fitting logRi(i ═ 1, 2, 3, 4) and logNi(i is 1, 2, 3, 4) to obtain R20.95 indicates that
Figure BSA0000210039260000081
Strong correlation (R)2The closer to 1, the more
Figure BSA0000210039260000082
The stronger the correlation), the absolute value of the slope of the fitted line is the lateral pressure distribution intensity fluctuation parameter D equal to 1.23.
The value of the fluctuation parameter D of the lateral pressure distribution intensity of the particle material is between 1 and 2, wherein 1 represents that the lateral pressure intensity distribution is in a straight line distribution, and 2 represents that the lateral pressure intensity distribution is in a plane distribution. The larger D indicates the larger fluctuation of the lateral pressure distribution intensity, the more obvious arch structure effect is, and the more lateral pressure sudden increase points are.
In addition, under the condition of ensuring that other numerical calculation parameters are not changed, the particle size s (0.01 m for soil and 0.40m for stone) and the particle friction coefficient mu (0.30, 0.60 and 0.90) are changed to obtain the lateral pressure distribution of the particle material under different conditions, as shown in FIGS. 7-11; the technical scheme of the invention is utilized to respectively carry out quantitative description on the distribution position concentration and the distribution intensity fluctuation so as to verify the applicability of the technical scheme of the invention.
Table 2 shows the dimension parameter r of the lateral pressure distribution position of the particle material under the conditions of different particle diameters and particle friction coefficients obtained by calculation according to the technical scheme of the inventioniA corresponding number niA quantitative density description parameter d and a lateral pressure distribution intensity scale parameter RiA corresponding number NiAnd a quantitative description parameter D of the fluctuation of the distribution intensity. R under the conditions of different particle diameters and particle friction coefficientsiAnd ni、RiAnd NiThe fitting functions are shown in fig. 5 and 6, respectively.
It can be seen that n is different under different conditionsiAnd
Figure BSA0000210039260000083
Niand
Figure BSA0000210039260000084
all have strong correlation. Therefore, the invention can objectively and effectively describe the lateral pressure distribution characteristics of the granular material quantitatively. The description parameter d of the lateral pressure distribution position concentration of the particle material is greatly influenced by the particle size and the friction coefficient of the particles; the larger the particle size and the particle friction coefficient, the smaller d is, which indicates that the lateral pressure distribution position is denser, and the safety and stability of the rigid retaining wall are more unfavorable. The description parameter D of the lateral pressure distribution strength fluctuation of the particle material is not greatly influenced by the particle size and the particle friction coefficient, and the distribution range is 1.17-1.29.
At present, engineering practice and physical tests are difficult to comprehensively obtain the lateral pressure distribution of the particle materials after stable accumulation, and the discrete unit method DEM numerical simulation can finely obtain the lateral pressure distribution information of the particle materials. The method is mainly applied to quantitatively describing the lateral pressure distribution position density and distribution intensity fluctuation of the granular material obtained by numerical simulation of a discrete unit method DEM, and is helpful for guiding engineering designs such as retaining walls, foundation pits and the like on a microscopical level. The method provided by the invention is based on the theory of fractal theory, further defines the measurement size value range for describing the lateral pressure characteristics of the granular material, has the advantages of simple and effective description parameters, clear physical significance and strong applicability, and can truly reflect the discrete characteristics of the lateral pressure distribution of the granular material.
TABLE 1 DEM numerical simulation calculation parameters
Figure BSA0000210039260000091
TABLE 2 quantitative description of the position intensity of lateral pressure distribution under different particle sizes s and friction coefficients mu of the particles
Figure BSA0000210039260000101
TABLE 3 quantitative description of the lateral pressure distribution intensity fluctuations under different particle sizes s and particle friction coefficients μ
Figure BSA0000210039260000102

Claims (1)

1. A quantitative description method for the lateral pressure distribution characteristics of a granular material is characterized by comprising the following steps:
step 1, selecting a particle material lateral pressure distribution position concentration measurement scale: measuring the height H after the particulate material has been settled0(also referred to as wall height in m) by selecting a series of measurement scale parameters ri(i ═ 1, 2, … n), where riSatisfy the requirement of
Figure FSA0000210039250000011
The conditions of (1).
Step 2, obtaining the measurement number of the lateral pressure distribution position concentration under different measurement scales: measurement scale riDividing the retaining wall into equal number
Figure FSA0000210039250000012
A pitch length of riThe statistical subgroup contains the subgroup number n of lateral pressure action pointsi。
Step 3, solving a parameter d for describing the lateral pressure distribution position concentration: a series of r obtained in step 2iAnd corresponding niDrawing in a log-log coordinate system, and fitting log riAnd log niLinear relation between them, and obtaining its coefficient of determination R2When R is2And when the absolute value of the slope of the fitting straight line is more than 0.8, the absolute value of the slope of the fitting straight line is the lateral pressure distribution position concentration parameter d.
The lateral pressure distribution position concentration parameter d of the granular material is a numerical value between 0 and 1, wherein 0 represents that the action position distribution is almost concentrated at a certain point, and 1 represents that the action position distribution is linearly and continuously distributed. A larger d indicates a more dispersed location of the pressure distribution laterally of the particulate material.
Step 4, selecting a particle material lateral pressure distribution intensity fluctuation measurement scale: drawing a lateral pressure distribution diagram of the granular material, and defining the upper end point and the lower end point of a lateral pressure broken line as P respectivelyupAnd PdownSelecting a series of scale parameters Ri(i ═ 1, 2, … n), where R isiSatisfy the requirement of
Figure FSA0000210039250000013
The conditions of (1).
Step 5, obtaining the measurement number of the lateral pressure distribution intensity fluctuation under different measurement scales: the upper end point P of the broken line is distributed by the lateral pressure of the granular materialupAs a circle center, with RiDrawing a circle for the radius, said circle intersecting the lateral pressure distribution polyline at a point P1(ii) a Then, again at point P1As a circle center, with RiIs a circle drawn by the radius and intersects the side pressure distribution broken line at a point P2(ii) a By analogy, when the intersection point PnAnd PdownThe distance l on the lateral pressure distribution broken line is less than or equal to RiWhen the measurement is finished, the final result is RiMeasuring the number N of lateral pressure distribution polylines for a scalei＝n+l/Ri。
And 6, solving the fluctuation parameters for describing the lateral pressure distribution strength. Subjecting step 5 to obtain a series of RiAnd corresponding NiDrawing in a log-log coordinate system, and fitting log RiAnd log NiLinear function relationship between them to obtain its coefficient of determinability R2(ii) a When fitting the coefficient of the function2And when the absolute value of the slope of the fitting straight line is more than 0.8, the absolute value of the slope of the fitting straight line is the lateral pressure distribution intensity fluctuation parameter D.
The value of the fluctuation parameter D of the lateral pressure distribution intensity of the particle material is between 1 and 2, wherein 1 represents that the lateral pressure intensity distribution is in a straight line distribution, and 2 represents that the lateral pressure intensity distribution is in a plane distribution. The larger D indicates the larger fluctuation of the lateral pressure distribution intensity, the more obvious arch structure effect is, and the more lateral pressure sudden increase points are.
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