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

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

A Quantitative Description Method of Lateral Pressure Distribution Characteristics of Granular Materials

technical field

The invention relates to a method for determining parameters in hydraulic design, in particular to a method for determining parameters quantitatively describing lateral pressure distribution characteristics of granular materials, which belongs to a general method in the field of hydraulic engineering, and whose IPC classification number is E02B1/00.

Background technique

The common granular materials in reservoir dam engineering are rockfill, soil, sediment and so on. These granular materials will generate lateral pressure due to their own weight or external loads, which must be considered in the construction of high rockfill dams, retaining walls, deep tunnels and other projects. In particular, the research on the lateral pressure of soil and rock has a history of more than 200 years. At present, the commonly used lateral pressure calculation theory in engineering is the Rankine and Coulomb soil pressure theory. Both classical theories assume that the lateral pressure is linearly distributed along the accumulation depth of granular materials such as soil and rock. The assumption that lateral pressure is linearly distributed is widely used in engineering fields such as retaining wall design specifications, foundation pit structural stability analysis, and deep tunnels.

However, engineering materials such as earth and rock are very complex granular materials, and the traditional macroscopic continuum theory often ignores the consideration of their discrete properties. 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 soil and rock through mesoscopic numerical methods. At present, the existing discrete element numerical simulation [1-3] studies have shown that the accumulation of granular materials such as soil and stone will lead to the existence of the arch structure effect, which makes the lateral pressure of the granular materials present a nonlinear distribution (polygonal distribution), and some Compared with the design value of linear distribution, the lateral pressure value increases sharply, which will be very detrimental to engineering safety.

When the lateral pressure exerted by the granular material on some parts of the retaining wall is too large and the pressure intensity changes drastically, the retaining wall is more prone to instability and collapse under the action of stress concentration. Therefore, it is of great significance for the safety of engineering design to study the fluctuation of the location density and distribution intensity of lateral pressure. However, there are no relevant literatures and reports on the quantitative description method of the position density and distribution intensity fluctuation of the lateral pressure distribution of granular materials.

The relevant papers retrieved are listed below:

[1] Meng Yunwei et al. Study on particle discrete element meso-mechanical simulation of gabion retaining wall [J]. Geotechnical Mechanics, 2010, 31(8): 2677-2681.

[2] Liu Dong et al. Calculation of active earth pressure for finite-width fill based on DEM analysis [J]. Highway Engineering, 2019, 44(02): 36-40.

[3] Wan Li et al. Active failure of incohesive finite soil and discrete element analysis of earth pressure [J]. Chinese and English Journal of Civil and Environmental Engineering, 2019, 41(03): 22-29.

[4] Qu Bo. Fractal geometry and fluid [M]. Shanghai: Shanghai Academy of Social Sciences Press, 2014: 3-14.

SUMMARY OF THE INVENTION

The present invention is made to solve the above-mentioned problems, and the purpose is to provide a quantitative description method for the lateral pressure distribution characteristics of granular materials. The method of the invention is simple and effective, the physical meaning of the parameters is clear, and the fluctuation of the distribution position density and distribution intensity of the lateral pressure of the granular material can be objectively and accurately quantified.

A method for quantitatively describing the lateral pressure distribution characteristics of granular materials of the present invention includes the following steps:

的条件。Step 1, select the measurement scale of the position density of the lateral pressure distribution of the granular material: measure the height H ₀ (unit is m) after the stable accumulation of the granular material is determined, and select a series of measurement scale parameters r _i (i=1, 2, ... n ), where r ₁ satisfies

conditions of.

间距长度为r_i的子组，统计子组中含有侧向压力作用点的子组数目n_i。Step 2: Obtain the number of measurements of the location density of lateral pressure distribution under different measurement scales: The measurement scale r _o divides the retaining wall equally into the number of

For the subgroups whose spacing length is _{ri, count the number of subgroups ni that} contain the action points of lateral pressure in the subgroups.

Step 3, find the density parameter d describing the lateral pressure distribution: draw a series of ri and corresponding _ni obtained in step 2 in a double logarithmic coordinate system, and fit the linear relationship between _{logr i} and logn _i relationship to obtain its coefficient of determination R ² . When R ² is greater than 0.8, the absolute value of the slope of the fitted straight line is the position density parameter d of the lateral pressure distribution.

The position density parameter d of the lateral pressure distribution of granular materials is a value between 0 and 1. 0 means that the action position distribution is almost concentrated at a certain point, and 1 means that the action position distribution is a linear continuous distribution. The larger the d is, the more dispersed the lateral pressure distribution position of the particulate material is.

的条件。Step 4: Select the measurement scale for the fluctuation of the lateral pressure distribution intensity of the granular material: draw the lateral pressure distribution diagram of the granular material, define the upper and lower endpoints of the lateral pressure polyline as P _up and P _down , and select a series of scale parameters Ri ( _i =1, 2,... _n ), where Ri satisfies

conditions of.

Step 5: Obtain the number of measurements of the intensity fluctuation of the lateral pressure distribution under different measurement scales: take the endpoint P _up on the broken line of the lateral pressure distribution of the granular material as the center of the circle, and draw a circle with R _i as the radius, and the circle is related to the lateral pressure. The distribution polyline intersects at point P ₁ ; then, draw a circle with point P ₁ as the center and R _i as the radius, and intersect the lateral pressure distribution polyline at point P ₂ ; and so on, when the intersection points P _n and P _down are at When the distance l on the lateral pressure distribution broken line is less than or equal to R _i , the measurement ends, and finally the number of lateral pressure distribution broken lines measured with R _i as the scale N _i =n+l/R _i is obtained.

Step 6: Obtain parameters describing the fluctuation of lateral pressure distribution intensity. Draw a series of R _i and corresponding N _i obtained in step 5 in the double logarithmic coordinate system, and fit the linear function relationship between logR _i and logN _i to obtain its coefficient of determination R ² ; When the coefficient of determination R ² is greater than 0.8, the absolute value of the slope of the fitted 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 granular materials is between 1 and 2. 1 means that the lateral pressure intensity distribution is a linear distribution, and 2 means that the lateral pressure intensity distribution is a plane distribution. The larger the D, the greater the fluctuation of the lateral pressure distribution intensity, the more obvious the arch structure effect, and the more the lateral pressure sudden increase points.

Compared with the prior art, the advantages of the present invention are as follows:

The traditional earth pressure theory is based on the assumption of continuum, which is contrary to the nature of discrete characteristics of granular materials such as soil and rock, and the description of the lateral pressure distribution characteristics of granular materials is inaccurate. The invention improves the idea of fractal theory, selects the measurement scale value range of the lateral pressure distribution characteristics of granular materials, accurately determines the values of two parameters, the density of the lateral pressure action position and the fluctuation of the distribution intensity, and quantifies the lateral pressure distribution characteristics. The description can truly reflect the discrete characteristics of the lateral pressure distribution of granular materials, and can guide engineering designers to more accurately determine the pressure distribution in the design of retaining walls, foundation pits, deep tunnels and other projects to ensure project safety.

Description of drawings

Figure 1 is a schematic diagram of a method for quantitatively describing the location density of the lateral pressure distribution of granular materials;

Figure 2 is a schematic diagram of a quantitative description method for the fluctuation of the lateral pressure distribution intensity of granular materials;

Figure 3 is the granular material after DEM numerical simulation is used to stabilize the accumulation;

Figure 4 is the lateral pressure distribution diagram (a) and the distribution intensity fluctuation analysis diagrams (b) to (e) under the condition that the particle size s is 0.01 m and the particle friction coefficient μ is 0.30;

Figure 5 is the fitting function relationship between _ri and _ni in the quantitative description of the positional density of lateral pressure distribution under the conditions of different particle sizes and particle friction coefficients;

Fig. 6 is the _fitting function relationship between _Ri and Ni in the quantitative description of the fluctuation of lateral pressure distribution intensity under the conditions of different particle sizes and particle friction coefficients;

Figures 7 to 11 are the lateral pressure distribution diagrams under the conditions of different particle sizes and particle friction coefficients.

Detailed ways

The technical solutions of the present invention will be further described in detail below through the accompanying drawings and embodiments. In this example, DEM is used to numerically simulate the natural deposition process of granular materials, and the simulation parameters are selected according to the literature related to DEM simulation of granular materials such as stones and soils ^{[1, 2]} to ensure the correctness of the simulation results. The simulation parameters are shown in Table 1. Show. The granular material after DEM numerical simulation is shown in Figure 3, and then the lateral pressure of the granular material acting on the left wall is extracted, as shown in Figure 4(a) (the particle size s is 0.01 m, the particle friction μ The coefficient is 0.30). A quantitative description method for lateral pressure distribution characteristics of granular materials provided by the present invention is used to quantitatively describe the lateral pressures in Figs. 4(b)-(e). When the lateral pressure applied to some parts of the retaining wall is dense (stress concentration) and the lateral pressure intensity increases and decreases suddenly, the retaining wall is more prone to instability under the sudden change of mechanical boundary conditions. Therefore, the present invention selects two parameters, the concentration of the action position of the lateral pressure and the fluctuation of the distribution intensity, to quantitatively describe the distribution characteristics of the lateral pressure. The present invention specifically includes the following steps:

良好相关性时，可通过函数拟合得到n_i＝c₁r_i ^-d+c₂，式中分布位置密集度测量尺度r_i的单位为m，度量数目n_i的单位为无量纲，c₁和c₂均为拟合得到的常数，单位均为无量纲，参数d为反映几何特征的常数，单位为无量纲。Step 1: Define the measurement scale of the location concentration of the lateral pressure distribution of the granular material. The measurement determines the height H ₀ (unit is m) of the granular material after stable accumulation. Because the granular material must rely on the retaining wall to stably accumulate, it is also commonly referred to as the retaining wall height H ₀ in the art, as shown in FIG. 1 . Among them, line 1 (longitudinal straight line) represents the retaining wall, line 2 (horizontal solid line) represents the action position of lateral pressure, and line 3 (horizontal dashed line) represents the dividing line of the equally spaced interval. According to the fractal theory ^[4] , for a thing with specific geometric characteristics, different scales _ri are used to measure its geometric characteristics to obtain the corresponding measurement number _ni ; when there is a difference between _ri and _ni

When the correlation is good, n _i =c ₁ r _i ^-d +c ₂ can be obtained by function fitting, where the unit of measurement scale _{ri of distribution location density is m, the unit of measurement number ni is} dimensionless, c ₁ and c ₂ are constants obtained by fitting, and the unit is dimensionless. The parameter d is a constant reflecting geometrical characteristics, and the unit is dimensionless.

条件下，选取一系列尺度参数r₁＝0.025m、 r₂＝0.030m、r₃＝0.035m、r₄＝0.040m。In this embodiment, the height H ₀ after stable accumulation of the particulate material is 1.95 m. in satisfying

Under the conditions, a series of scale parameters r ₁ =0.025m, r ₂ =0.030m, r ₃ =0.035m, and r ₄ =0.040m were selected.

(若

为分数，则四舍五入为整数)、间距长度为r_i的子组(相邻线条3之间)。统计子组中含有侧向压力作用点(线条2) 的子组数目n_i(n_i为整数)。Step 2: Obtain the measurement number of the density of lateral pressure distribution positions under different measurement scales. The measurement scale _ri divides the retaining wall into a number of

(like

is a fraction, rounded to an integer), with a subgroup of interval length _ri (between adjacent lines 3). Count the number of subgroups n _i (n _i is an integer) in the subgroup containing the lateral pressure application point (line 2).

In this embodiment, for r ₁ =0.025m, the retaining walls are evenly divided into 78 subgroups with a spacing length of 0.025m, and the number of subgroups n ₁ including lateral pressure action points in the statistical subgroups is 63; For r ₂ =0.030m, the retaining walls are divided into 65 subgroups with a spacing length of 0.030m, and the number of subgroups n ₂ including lateral pressure action points in the statistical subgroups is 54; for r ₃ =0.035 m, the retaining wall is divided into 56 subgroups with a spacing length of 0.035m, and the number of subgroups n ₃ including lateral pressure action points in the statistical subgroup is 49; for r ₄ =0.040m, the retaining wall is divided into It is divided into 49 subgroups on average and the spacing length is 0.040m, and the number of subgroups n ₄ including lateral pressure action points in the statistical subgroups is 46.

相关性越强)。当R²大于0.8时，认为

存在较强的相关性，此时拟合直线斜率的绝对值即侧向压力分布位置密集度参数d。Step 3: Obtain a parameter d describing the location density of the lateral pressure distribution. Draw a series (at least 4 groups) ri and corresponding _ni obtained in step ₂ in the double logarithmic coordinate system, fit the linear relationship between _logri and _logni , and obtain the coefficient of determination R ² (R ² is dimensionless, the closer it is to 1, the more

the stronger the correlation). When R2 is greater ^than 0.8, it is considered that

There is a strong correlation. At this time, the absolute value of the slope of the fitting line is the density parameter d of the lateral pressure distribution position.

The position density parameter d of the lateral pressure distribution of granular materials is a value between 0 and 1. 0 means that the action position distribution is almost concentrated at a certain point, and 1 means that the action position distribution is a linear continuous distribution. The larger the d is, the more dispersed the lateral pressure distribution position of the particulate material is.

相关性强，拟合直线的斜率的绝对值即为参数 d＝0.67。In this embodiment, r ₁ =0.025m, r ₂ =0.030m, r ₃ =0.035m, r ₄ =0.040m and corresponding n ₁ =63,n ₂ =54,n ₃ =49, n ₄ =46 is plotted in a double logarithmic coordinate system (shown in Figure 5), fitting between logr _i (i=1, 2, 3, 4) and logn _i (i=1, 2, 3, 4) The linear function relationship of , obtains R ² =0.98, indicating that

The correlation is strong, and the absolute value of the slope of the fitted straight line is the parameter d=0.67.

的条件。Step 4, select the measurement scale of the lateral pressure distribution intensity fluctuation of the granular material. According to the calculation results of DEM numerical simulation, take the height of the retaining wall as the vertical axis, and take the lateral pressure of the granular material as the horizontal axis, draw the lateral pressure distribution map of the granular material. As shown in Figure 2, the distribution line of the lateral pressure of granular materials along the height of the retaining wall is a polyline-like curve, and the upper and lower endpoints of the lateral pressure distribution polyline are defined as P _up and P _down , respectively, as shown in Figure 2. Show. Choose a series of scale parameters R _i (i=1, 2,...n), where R _i satisfies

conditions of.

条件下，选取一系列尺度参数R₁＝0.1m、 R₂＝0.2m、R₃＝0.3m、R₄＝0.4m。定义侧向压力折线分布上、下两个端点分别为P_up和P_down，如图4所示。In this embodiment, satisfying the

Under the conditions, a series of scale parameters R ₁ =0.1m, R ₂ =0.2m, R ₃ =0.3m, R ₄ =0.4m are selected. The upper and lower endpoints of the lateral pressure polyline distribution are defined as P _up and P _down , respectively, as shown in Fig. 4 .

Step 5: Obtain the measurement number of the intensity fluctuation of the lateral pressure distribution under different measurement scales. For R ₁ =0.1m, take the endpoint P _up on the lateral pressure distribution line of the granular material in Fig. 4 as the center of the circle, and draw a circle with R ₁ =0.1m as the radius. The circle intersects the lateral pressure distribution line at point P ₁ ; then , draw a circle with point P ₁ as the center and R ₁ =0.1m as the radius, and intersect with the lateral pressure distribution line at point P ₂ ; and so on, when the intersection point P ₁₃₉ and P _down are at a distance l= When 0.011 is less than R ₁ =0.1m, the measurement ends, and finally the number of broken lines of lateral pressure distribution measured with R ₁ =0.1m as the scale N ₁ =n+l/R ₁ =139+0.011/0.1=139.11 is obtained, such as shown in Figure 4(b). Using the same method as above, N ₂ =60.12, N ₃ =30.05, and N ₄ =26.78 can be obtained.

相关性强(R²越接近1，表明

相关性越强)，拟合直线的斜率的绝对值即为侧向压力分布强度波动性参数D＝1.23。Step 6: Obtain parameters describing the fluctuation of lateral pressure distribution intensity. Plot the steps ₅ for R1 ₌ 0.1m, R2=0.2m, _R3 =0.3m, R4=0.4m and corresponding N1 _{= 139.11} , _N2 =60.12, N3 ₌ 30.05, _N4 =26.78 in a double logarithmic coordinate system (shown in Figure 6). Fitting the linear functional relationship between logR _i (i=1, 2, 3, 4) and logN _i (i=1, 2, 3, 4), R ² =0.95 is obtained, indicating that

Strong correlation (the closer R is to ¹ , the more

The stronger the correlation), the absolute value of the slope of the fitted straight line is the lateral pressure distribution intensity fluctuation parameter D=1.23.

The value of the fluctuation parameter D of the lateral pressure distribution intensity of granular materials is between 1 and 2. 1 means that the lateral pressure intensity distribution is a linear distribution, and 2 means that the lateral pressure intensity distribution is a plane distribution. The larger the D, the greater the fluctuation of the lateral pressure distribution intensity, the more obvious the arch structure effect, and the more the lateral pressure sudden increase points.

In addition, under the condition of keeping other numerical calculation parameters unchanged, by changing the particle size s (0.01m for soil, 0.40m for stone) and particle friction coefficient μ (0.30, 0.60, 0.90) to obtain granular materials under different conditions The lateral pressure distribution is shown in Fig. 7-Fig. 11; using the technical solution of the present invention to quantitatively describe its distribution location density and distribution intensity fluctuation, respectively, to verify the applicability of the technical solution of the present invention.

Table 2 shows the position scale parameter r _i , the corresponding number _ni , the quantitative description parameter d of the density and the lateral pressure of the granular material under the conditions of different particle sizes and particle friction coefficients calculated by the technical solution of the present invention The distribution intensity scale parameter R _i , the corresponding number N _i , the distribution intensity volatility quantitative description parameter D. The fitting functions of _ri and _ni and Ri and _Ni under different particle size and particle friction coefficient are shown in Fig. 5 and Fig. 6 _, respectively.

N_i与

均有很强的相关性。因此本发明能够客观有效地定量描述颗粒材料侧向压力分布特征。颗粒材料侧向压力分布位置密集度描述参数d受颗粒粒径和颗粒摩擦系数影响较大；颗粒粒径和颗粒摩擦系数越大，则d越小，表明侧向压力分布位置越密集，越不利于刚性挡墙的安全稳定。颗粒材料侧向压力分布强度波动性描述参数D受颗粒粒径和颗粒摩擦系数影响不大，分布范围在1.17～1.29之间。It can be seen that under different conditions, n _i and

_Ni and

are strongly correlated. Therefore, the present invention can objectively and effectively quantitatively describe the lateral pressure distribution characteristics of granular materials. The density description parameter d of the lateral pressure distribution of granular materials is greatly affected by the particle size and the particle friction coefficient; the larger the particle size and the particle friction coefficient, the smaller the d, indicating that the lateral pressure distribution is denser and less stable. Conducive to the safety and stability of rigid retaining walls. The description parameter D of the lateral pressure distribution intensity fluctuation of granular material is not greatly affected by particle size and particle friction coefficient, and the distribution range is between 1.17 and 1.29.

At present, it is difficult to fully obtain the lateral pressure distribution of granular materials after stable accumulation in engineering practice and physical tests. However, the discrete element method DEM numerical simulation can refine the lateral pressure distribution information of granular materials. The method of the invention is mainly applied to quantitatively describe the lateral pressure distribution position density and distribution intensity fluctuation of granular materials obtained by the discrete element method DEM numerical simulation, and is helpful for guiding engineering design of retaining walls and foundation pits from a mesoscopic level. The method of the invention is based on the idea of fractal theory, further clarifies the range of the measurement size for describing the lateral pressure characteristics of the granular material, the description parameters are simple and effective, the physical meaning is clear, the applicability is strong, and the lateral pressure of the granular material can be truly reflected. Discrete features of the pressure distribution.

Table 1 DEM numerical simulation calculation parameters

Table 2 Quantitative description of the location density of lateral pressure distribution under different particle size s and particle friction coefficient μ

Table 3 Quantitative description of lateral pressure distribution intensity fluctuation under different particle size s and particle friction coefficient μ

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 r_i(i ═ 1, 2, … n), where r_iSatisfy the requirement of

The conditions of (1).

Step 2, obtaining the measurement number of the lateral pressure distribution position concentration under different measurement scales: measurement scale r_iDividing the retaining wall into equal number

A pitch length of r_iThe statistical subgroup contains the subgroup number n of lateral pressure action points_i。

Step 3, solving a parameter d for describing the lateral pressure distribution position concentration: a series of r obtained in step 2_iAnd corresponding n_iDrawing in a log-log coordinate system, and fitting log r_iAnd log n_iLinear 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 respectively_upAnd P_downSelecting a series of scale parameters R_i(i ═ 1, 2, … n), where R is_iSatisfy the requirement of

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 material_upAs a circle center, with R_iDrawing 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 R_iIs 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 P_nAnd P_downThe distance l on the lateral pressure distribution broken line is less than or equal to R_iWhen the measurement is finished, the final result is R_iMeasuring the number N of lateral pressure distribution polylines for a scale_i＝n+l/R_i。

And 6, solving the fluctuation parameters for describing the lateral pressure distribution strength. Subjecting step 5 to obtain a series of R_iAnd corresponding N_iDrawing in a log-log coordinate system, and fitting log R_iAnd log N_iLinear 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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