CN106323158A

CN106323158A - Device for testing three-dimensional strain state inside soil mass and testing method

Info

Publication number: CN106323158A
Application number: CN201610917550.9A
Authority: CN
Inventors: 李顺群; 潘林娜; 王彦洋; 柴寿喜; 郭林坪; 张彦; 冯彦芳
Original assignee: Tianjin Chengjian University
Current assignee: Tianjin Chengjian University
Priority date: 2016-10-21
Filing date: 2016-10-21
Publication date: 2017-01-11

Abstract

The invention provides a device for testing the three-dimensional strain state inside the soil. The six common strain gauges of the device are sequentially fixed on the strain gauge bases on the surfaces of the rhombus dodecahedron with six normal vectors irrelevant. The centers of the six faces with irrelevant normal vectors of the dihedron are all provided with wire holes leading to the centroid of the rhombic dodecahedron, and are connected to the data acquisition system through measuring wires. At the same time, it provides a testing method of a device for testing the three-dimensional strain state inside the soil. The beneficial effect is that the three-dimensional strain state at a certain position of the soil can be measured more accurately, and the linear strain in the direction of the maximum principal strain can be obtained. Among the measured values of the six strain gauges, the test accuracy of the three principal strains is 1.22ρ, and the test accuracy of the three shear gauges is 1.22ρ. The test accuracy of the strain is 0.71ρ, and the average test accuracy is 0.97ρ, which improves the test accuracy of the strain gauge in one direction and changes the previous limitation that only the surface strain can be tested and the test position is not accurate. The device intuitively reflects the deformation state inside the soil and improves the safety reserve of engineering construction.

Description

Device and test method for testing three-dimensional strain state inside soil

技术领域technical field

本发明属于工程中的变形和应变测试技术领域，具体为一种测试土体内部三维应变状态的装置及测试方法，通过该装置获得菱形十二面体上六个法向向量不相关的面上的线应变，经计算便可得到测试土体处的三维应变状态。The invention belongs to the technical field of deformation and strain testing in engineering, and specifically relates to a device and a testing method for testing the three-dimensional strain state inside the soil, through which the six normal vectors on the rhombic dodecahedron are obtained. The linear strain can be calculated to obtain the three-dimensional strain state of the test soil.

背景技术Background technique

物体的变形和应变测试是土木工程、水利工程以及交通工程中的一项基础性工作。是进行工程健康诊断和量化力学分析的前提。深入认识材料的力学性能，研究土体的应力、应变，准确了解其受力状态和工作状况，是工程建设中质量评估和加固维修的关键。Deformation and strain testing of objects is a basic work in civil engineering, water conservancy engineering and traffic engineering. It is the prerequisite for engineering health diagnosis and quantitative mechanical analysis. In-depth understanding of the mechanical properties of materials, the study of soil stress and strain, and an accurate understanding of its stress state and working conditions are the key to quality assessment and reinforcement maintenance in engineering construction.

一般情况下，受力体的单向应变测试和单向应力测试可以通过应变片和应力计完成。当研究某一确定方向上的应变或应力时，可以采用在该方向上布置应变片、应力计或其他传感器的方式获得该方向上的力学参数。对于平面应力和应变问题，可通过在物体表面粘贴常规应变片组成的应变花测得。常规应变花由三个应变片组成，只能测得某一平面内的应变状况，而在实际工程中岩土体内部的应变和应力状态比较复杂，难以简化为一维或二维的简单状态。往往需要获得某一物体内部的三维应变状态。In general, the unidirectional strain test and unidirectional stress test of the force-bearing body can be completed by strain gauges and stress gauges. When studying the strain or stress in a certain direction, the mechanical parameters in that direction can be obtained by arranging strain gauges, strain gauges or other sensors in that direction. For plane stress and strain problems, it can be measured by pasting a strain rosette composed of conventional strain gauges on the surface of the object. Conventional strain rosettes are composed of three strain gauges, which can only measure the strain state in a certain plane, but in actual engineering, the strain and stress state inside the rock and soil are relatively complicated, and it is difficult to simplify it into a simple one-dimensional or two-dimensional state . It is often necessary to obtain the three-dimensional strain state inside an object.

目前岩土体内部的三维应变状态尚无广泛使用的有效办法，其中专利《用于测试三维应变状态的测试装置及其测试方法》(公布号：CN104482913A)是基于正四面体六条棱的三维应变花装置。该装置与土体接触面较小，粘贴应变片的骨架易随着土体的变形而发生变形，不易固定其在受力体中的位置，从而导致其测试方位存在偏差，不能准确测定岩土体中某一确定位置的三维应变状态。该装置基座的材料选用弹性模量小于待测受力体材料的杆状塑料，将该装置置于受力体中受力变形后将不能再重复使用，属于一次性装置。材料浪费严重，与所提倡的环保理念相违背。为了获得真实有效的应变状态，有必要对土体内部的应变状态进行更加直接稳定的测试。比如基坑工程中，不同位置处土体的应力、应变状态各不相同，且依赖于施工方式、施工进程、天气状况等难以量化的诸多因素的影响。因此，加强三维状态条件下受力体内部应变状态的准确监测，不但对保障工程质量和施工安全非常重要，也是对土木工程信息化施工的基本要求。At present, there is no widely used effective method for the three-dimensional strain state inside the rock and soil mass. Among them, the patent "Testing device for testing the three-dimensional strain state and its testing method" (publication number: CN104482913A) is based on the three-dimensional strain of the six edges of the regular tetrahedron. Flower device. The contact surface between the device and the soil is small, and the skeleton of the strain gauge is easily deformed with the deformation of the soil, and it is not easy to fix its position in the force-bearing body, which leads to deviations in its test orientation and cannot accurately measure the rock and soil The three-dimensional strain state at a certain position in the body. The material of the base of the device is a rod-shaped plastic whose modulus of elasticity is smaller than that of the material of the force-bearing body to be tested. After the device is placed in the force-bearing body and deformed by force, it cannot be reused and is a disposable device. The waste of materials is serious, which is contrary to the advocated environmental protection concept. In order to obtain a true and effective strain state, it is necessary to conduct a more direct and stable test of the strain state inside the soil. For example, in foundation pit engineering, the stress and strain states of the soil at different locations are different, and depend on the influence of many factors that are difficult to quantify, such as construction methods, construction progress, and weather conditions. Therefore, strengthening the accurate monitoring of the internal strain state of the force-bearing body under the condition of three-dimensional state is not only very important to ensure the quality of the project and construction safety, but also a basic requirement for the information construction of civil engineering.

发明内容Contents of the invention

本发明的目的是提供一种用于测试土体内部三维应变状态的装置及测试方法，以实现测试土体内部任意一点的三维应变状态直接准确地测试。The object of the present invention is to provide a device and a testing method for testing the three-dimensional strain state inside the soil, so as to realize direct and accurate testing of the three-dimensional strain state at any point inside the soil.

为实现上述目的，本发明采用的技术方案是：提供一种测试土体内部三维应变状态的装置。其中该装置包括菱形十二面体、六个普通应变片、测量导线、面心导线孔、导线汇总孔、应变片基座。将六个普通应变片固定在菱形十二面体六个法向量不相关的面的应变片基座上，六个普通应变片的测量导线通过面心导线孔，从菱形十二面体的形心导线汇总孔导出后与应变片数据采集系统相连接，形成三维应变状态测试装置。利用数据采集系统测试六个应变片的读数，根据六个不同方向上应变片的读数与各应变片方向余弦值确定出与转换矩阵之间的数学关系式，进而计算得到土体中任意一点的三维应变状态。In order to achieve the above purpose, the technical solution adopted by the present invention is to provide a device for testing the three-dimensional strain state inside the soil. Wherein the device comprises a rhombic dodecahedron, six common strain gauges, measuring wires, face-centered wire holes, wire summary holes, and strain gauge bases. Fix the six ordinary strain gauges on the strain gauge bases on the six faces of the rhombic dodecahedron with irrelevant normal vectors. After the summary hole is exported, it is connected with the strain gauge data acquisition system to form a three-dimensional strain state test device. Use the data acquisition system to test the readings of six strain gauges, and determine the mathematical relationship with the transformation matrix according to the readings of the strain gauges in six different directions and the cosine value of each strain gauge direction, and then calculate the temperature of any point in the soil 3D strain state.

同时提供一种用于测试土体内部三维应变状态的装置的测试方法。At the same time, it provides a testing method of a device for testing the three-dimensional strain state inside the soil.

本发明的效果是：该装置采用菱形十二面体为粘贴应变片的底座，菱形十二面体的制作方法便捷，是由正方体直接截取获得，且菱形十二面体有12个全相等的面组成，每个面粘贴应变片方向的向量与面法线的夹角均相等且唯一。因此将菱形十二面体作为本发明的底座，可使得测试直观且测试位置准确、克服了单个应变片测试精度不高、测试位置存在偏差、测试方向单一、无法获得三维应变状态等技术局限。另外该方法计算原理明确，计算精度较高。假设普通应变片的精度为ρ，计算得到的三个主应变方向上的应变测试精度分别为1.22ρ，三个剪应力的测试精度为0.71ρ，平均测试精度为0.97ρ，精度上得到提高，更加准确、直观的被测物体内部的变形状态，且该装置可以重复使用，复合绿色环保理念，并且提高工程施工的安全储备，为应变测试技术领域相关研究提供了新的思路和途径。The effect of the present invention is: the device adopts a rhombic dodecahedron as the base for pasting strain gauges, and the manufacturing method of the rhombohedral dodecahedron is convenient. The angle between the vector of the direction of pasting the strain gauge on each surface and the surface normal is equal and unique. Therefore, using the rhombic dodecahedron as the base of the present invention can make the test intuitive and the test position is accurate, and overcome technical limitations such as low test accuracy of a single strain gauge, deviation of the test position, single test direction, and inability to obtain a three-dimensional strain state. In addition, the calculation principle of this method is clear and the calculation accuracy is high. Assuming that the accuracy of ordinary strain gauges is ρ, the calculated strain test accuracy in the three principal strain directions is 1.22ρ, the test accuracy of the three shear stresses is 0.71ρ, and the average test accuracy is 0.97ρ, which improves the accuracy. More accurate and intuitive internal deformation state of the measured object, and the device can be reused, combining the concept of green environmental protection, and improving the safety reserve of engineering construction, providing new ideas and approaches for related research in the field of strain testing technology.

附图说明Description of drawings

图1为本发明的应变片的方向向量；Fig. 1 is the direction vector of the strain gauge of the present invention;

图2为本发明的菱形十二面体的制作图；Fig. 2 is the making figure of rhombic dodecahedron of the present invention;

图3为本发明的菱形十二面体；Fig. 3 is rhombic dodecahedron of the present invention;

图4为本发明的安放应变片的菱形十二面体骨架；Fig. 4 is the rhombic dodecahedral framework of placing strain gauges of the present invention;

图5为本发明的三维应变测试装置的俯视图；Fig. 5 is the top view of three-dimensional strain testing device of the present invention;

图6为本发明的三维应变测试装置效果图。Fig. 6 is an effect diagram of the three-dimensional strain testing device of the present invention.

图中：In the picture:

1.菱形十二面体 2.应变片 3.测量导线1. Rhombic dodecahedron 2. Strain gauge 3. Measuring wire

4.面心导线孔 5.导线汇总孔 6.应变片基座4. Surface center wire hole 5. Wire summary hole 6. Strain gauge base

具体的实施方式specific implementation

结合附图对本发明的一种用于测试土体内部三维应变状态的装置及测试方法加以详细说明。A device and testing method for testing the three-dimensional strain state inside the soil mass according to the present invention will be described in detail with reference to the accompanying drawings.

本发明的用于测试土体内部三维应变状态的装置结构是，该装置包括有菱形十二面体1、六个应变片2、测量导线3、面心导线孔4、导线汇总孔5、应变片基座6；将六个应变片2固定在菱形十二面体1六个法向量不相关的面的应变片基座6上，其中应变片基座采用弹性模量小于待测土体材料。六个普通应变片的测量导线3通过面心导线孔4从菱形十二面体的形心导线汇总孔5导出后与应变片数据采集系统相连接，形成三维应变状态测试装置；利用数据采集系统测试六个应变片的读数，根据六个不同方向上应变片的读数与各应变片方向余弦值确定出与转换矩阵之间的数学关系式，进而计算得到土体中任意一点的三维应变状态。The structure of the device for testing the three-dimensional strain state inside the soil body of the present invention is that the device includes a rhombic dodecahedron 1, six strain gauges 2, a measuring wire 3, a face-centered wire hole 4, a wire collection hole 5, and a strain gauge Base 6: Fix the six strain gauges 2 on the strain gauge base 6 on the six normal vector irrelevant surfaces of the rhombic dodecahedron 1, wherein the strain gauge base adopts a material whose elastic modulus is smaller than that of the soil to be measured. The measuring wires 3 of six ordinary strain gauges are derived from the centroid wire summary hole 5 of the rhombic dodecahedron through the face-centered wire hole 4 and then connected with the strain gauge data acquisition system to form a three-dimensional strain state testing device; use the data acquisition system to test The readings of the six strain gauges, according to the readings of the strain gauges in six different directions and the cosine value of each strain gauge direction, determine the mathematical relationship with the transformation matrix, and then calculate the three-dimensional strain state of any point in the soil.

用于测试土体三维应变状态的装置的测试方法包括以下步骤：The test method of the device for testing the three-dimensional strain state of soil comprises the following steps:

(1)首先将测量导线3从每个应变片2底面开始，穿过面心导线孔4在菱形十二面体形心处汇合后由导线汇总孔5引出；将每个应变片2固定在六个应变片基座上，接着将聚氨酯泡沫填缝剂压入填充至导线汇总孔5中，用来充填测量导线与导线孔之间的空隙，形成测试土体内部三维应变状态的装置，并将该装置置于被测土体中。(1) First, the measuring wire 3 starts from the bottom surface of each strain gauge 2, passes through the face-centered wire hole 4 and converges at the centroid of the rhombus dodecahedron, and then leads out from the wire collection hole 5; each strain gauge 2 is fixed on six On a strain gauge base, the polyurethane foam sealant is then pressed and filled into the wire collection hole 5 to fill the gap between the measuring wire and the wire hole to form a device for testing the three-dimensional strain state inside the soil, and The device is placed in the soil to be tested.

(2)以菱形十二面体的形心O为原点，以OO₁、OO₂、OO₃为x轴、y轴、z轴建立三维坐标系。(2) A three-dimensional coordinate system is established with the centroid O of the rhombic dodecahedron as the origin, and OO ₁ , OO ₂ , and OO ₃ as the x-axis, y-axis, and z-axis.

(3)依据步骤(2)所建立的坐标系求得α₁、α₂、α₃、α₄的四个面应变片的方向向量(1,0,1)、(0,1,1)、(-1,0,1)、(0,-1,1)与面β₁、β₂的应变片方向向量(1,1,0)、(-1,1,0)线性无关，即这六个面为方向向量不相关的面。(3) Obtain the direction vectors (1,0,1), (0,1,1) of the four surface strain gauges of α ₁ , α ₂ , α ₃ , and α ₄ according to the coordinate system established in step (2) , (-1,0,1), (0,-1,1) are linearly independent from the direction vectors (1,1,0) and (-1,1,0) of the strain gauges on the surfaces β ₁ , β ₂ , namely These six faces are the faces for which the direction vectors are not correlated.

(4)根据六个普通应变片的轴线方向与x轴、y轴、z轴的夹角计算各应变片的方向余弦l、m、n，并由此确定矩阵A。(4) Calculate the direction cosines l, m, and n of each strain gauge according to the angles between the axis directions of the six common strain gauges and the x-axis, y-axis, and z-axis, and then determine the matrix A.

(5)利用数据采集系统测试六个应变片(2)的读数，根据六个不同方向上应变片的读数与各应变片方向余弦值确定出与转换矩阵之间的数学关系式{ε_j}＝A^-1{ε_i}，进而计算得到土体中任意一点的三维应变状态。(5) Use the data acquisition system to test the readings of six strain gauges (2), and determine the mathematical relationship between the transformation matrix {ε _j } according to the readings of the strain gauges in six different directions and the cosine value of each strain gauge direction ＝A ^-1 {ε _i }, and then calculate the three-dimensional strain state of any point in the soil.

{ε_j}＝A^-1{ε_i} (1){ε _j }＝A ^-1 {ε _i } (1)

其中A^-1为where A ^-1 is

${A A}^{- - 11} = = \{\begin{matrix} 0.5 0.5 & - - 0.5 0.5 & 0.5 0.5 & - - 0.5 0.5 & 0.5 0.5 & 0.5 0.5 \\ - - 0.5 0.5 & 0.5 0.5 & - - 0.5 0.5 & 0.5 0.5 & 0.5 0.5 & 0.5 0.5 \\ 0.5 0.5 & 0.5 0.5 & 0.5 0.5 & 0.5 0.5 & - - 0.5 0.5 & - - 0.5 0.5 \\ 00 & 00 & 00 & 00 & 11 & - - 11 \\ 00 & 11 & 00 & - - 11 & 00 & 00 \\ 11 & 00 & - - 11 & 00 & 00 & 00 \end{matrix}\} - - - - - - ((22))$

本发明的测试土体内部三维应变状态的装置及测试方法是这样实现的：The device and the testing method of the three-dimensional strain state inside the test soil body of the present invention are realized in this way:

1、安放应变片的菱形十二面体骨架制作：1. Fabrication of rhombic dodecahedral skeleton for placing strain gauges:

在六个粘贴应变片的面中心设置直径为1cm的圆孔，该圆孔垂直通向菱形十二面体的形心，选择菱形十二面体1的未粘贴应变片的面并在其上开直径为2cm通向形心的圆孔，以容纳六个普通应变片测量导线的通道。在菱形十二面体六个法向量不相关的面即面α₁、α₂、α₃、α₄和面β₁、β₂中心应变片基座上粘贴应变片，必要时在应变片底部和侧面涂抹粘结剂以保证应变片受力均匀。A round hole with a diameter of 1 cm is set in the center of the six faces where the strain gauges are pasted, and the round hole is vertically leading to the centroid of the rhombic dodecahedron. 2cm circular hole leading to the centroid to accommodate the passage of six common strain gauge measuring wires. Paste the strain gauge on the base of the central strain gauge of the six normal vectors of the rhombic dodecahedron, namely the surfaces α ₁ , α ₂ , α ₃ , α ₄ and the surfaces β ₁ and β ₂ , and if necessary, attach the strain gauge to the bottom of the strain gauge and Adhesive is applied to the side to ensure that the strain gauge is evenly stressed.

2、三维应变测试装置的装配过程：2. The assembly process of the three-dimensional strain test device:

首先将测量导线3从每个应变片2底面开始，穿过面心导线孔4在菱形十二面体形心处汇合后由导线汇总孔5引出；将每个应变片2固定在六个应变片基座上，接着将聚氨酯泡沫填缝剂压入填充至导线汇总孔5中，用来充填测量导线与导线孔之间的空隙，形成基于应变片2的三维应变状态测试装置。First, the measuring wire 3 starts from the bottom surface of each strain gauge 2, passes through the face-centered wire hole 4 and converges at the centroid of the rhombic dodecahedron, and then leads out from the wire summary hole 5; each strain gauge 2 is fixed on six strain gauges On the base, polyurethane foam caulking agent is then pressed and filled into the lead collection hole 5 to fill the gap between the measuring lead and the lead hole to form a three-dimensional strain state testing device based on the strain gauge 2 .

3、将该装置埋置于土体的待测位置，通过应变数据采集系统测得六个主应变方向的应变值，根据式(1)得到常规三维应变状态。3. Embed the device in the position to be measured in the soil, measure the strain values in six principal strain directions through the strain data acquisition system, and obtain the conventional three-dimensional strain state according to formula (1).

基于普通应变片和菱形十二面体的三维应变状态测试装置，计算理论式(1)的推导过程如下：Based on the three-dimensional strain state test device of ordinary strain gauges and rhombic dodecahedrons, the derivation process of the theoretical formula (1) is as follows:

假设三维空间中的一条直线OA，如图1所示。则该直线在x、y、z方向的方向余弦l、m、n分别为Assume a straight line OA in three-dimensional space, as shown in Figure 1. Then the direction cosines l, m and n of the straight line in the x, y and z directions are respectively

n＝cosσ (5)n = cosσ (5)

式中σ为直线与z轴的夹角，为该直线在平面xOy上的投影与x轴的夹角。若已知一点的应变状态为ε_j＝{ε_x,ε_y,ε_z,ε_xy,ε_yz,ε_zx}，则OA方向的线应变为：where σ is the angle between the straight line and the z-axis, is the angle between the projection of the line on the plane xOy and the x-axis. If the strain state of a point is known as ε _j ＝{ε _x ,ε _y ,ε _z ,ε _xy ,ε _yz ,ε _zx }, then the linear strain in the OA direction is:

ε_n＝ε_xl²+ε_ym²+ε_zn²+ε_xylm+ε_yzmn+ε_zxnl (6)ε _n = ε _x l ² + ε _y m ² + ε _z n ² + ε _xy lm + ε _yz mn + ε _zx nl (6)

亦即，如果知道一点的应变状态，则任意方向的线应变均可通过式(6)得到。相应的，若已知六个不同方向上的线应变，则也可以得到其常规应变表示方法。设已知六个不同方向上的线应变分别为：That is, if the strain state of a point is known, the linear strain in any direction can be obtained by formula (6). Correspondingly, if the linear strains in six different directions are known, the conventional strain expression method can also be obtained. Assume that the linear strains in six different directions are known as:

${ϵ ϵ}_{i i} = = {ϵ ϵ}_{x x} {l l}_{i i}^{22} + + {ϵ ϵ}_{y the y}^{22} {m m}_{i i}^{22} + + {ϵ ϵ}_{z z} {n no}_{i i}^{22} + + {ϵ ϵ}_{x x y the y} {l l}_{i i} {m m}_{i i} + + {ϵ ϵ}_{y the y z z} {m m}_{i i} {n no}_{i i} + + {ϵ ϵ}_{z z x x} {n no}_{i i} {l l}_{i i} - - - - - - ((77))$

其中i＝1，2，3，4，5，6，由一般应变状态到不同方向线应变的映射关系为：Where i=1, 2, 3, 4, 5, 6, the mapping relationship from the general strain state to the line strain in different directions is:

$\{\begin{matrix} {ϵ ϵ}_{11} \\ {ϵ ϵ}_{22} \\ {ϵ ϵ}_{33} \\ {ϵ ϵ}_{44} \\ {ϵ ϵ}_{55} \\ {ϵ ϵ}_{66} \end{matrix}\} \{\begin{matrix} {l l}_{11}^{22} & {m m}_{11}^{22} & {n no}_{11}^{22} & {l l}_{11} {m m}_{11} & {m m}_{11} {n no}_{11} & {n no}_{11} {l l}_{11} \\ {l l}_{22}^{22} & {m m}_{22}^{22} & {n no}_{22}^{22} & {l l}_{22} {m m}_{22} & {m m}_{22} {n no}_{22} & {n no}_{22} {l l}_{22} \\ {l l}_{33}^{22} & {m m}_{33}^{22} & {n no}_{33}^{22} & {l l}_{33} {m m}_{33} & {m m}_{33} {n no}_{33} & {n no}_{33} {l l}_{33} \\ {l l}_{44}^{22} & {m m}_{44}^{22} & {n no}_{44}^{22} & {l l}_{44} {m m}_{44} & {m m}_{44} {n no}_{44} & {n no}_{44} {l l}_{44} \\ {l l}_{55}^{22} & {m m}_{55}^{22} & {n no}_{55}^{22} & {l l}_{55} {m m}_{55} & {m m}_{55} {n no}_{55} & {n no}_{55} {l l}_{55} \\ {l l}_{66}^{22} & {m m}_{66}^{22} & {n no}_{66}^{22} & {l l}_{66} {m m}_{66} & {m m}_{66} {n no}_{66} & {n no}_{66} {l l}_{66} \end{matrix}\} \{\begin{matrix} {ϵ ϵ}_{x x} \\ {ϵ ϵ}_{y the y} \\ {ϵ ϵ}_{z z} \\ {ϵ ϵ}_{x x y the y} \\ {ϵ ϵ}_{y the y z z} \\ {ϵ ϵ}_{z z x x} \end{matrix}\} - - - - - - ((88))$

或简写为{ε_i}＝A{ε_j}，其中j＝x，y，z，xy，yz，zx。且有Or simply {ε _i }=A{ε _j }, where j=x, y, z, xy, yz, zx. and have

$A A = = \{\begin{matrix} {l l}_{11}^{22} & {m m}_{11}^{22} & {n no}_{11}^{22} & {l l}_{11} {m m}_{11} & {m m}_{11} {n no}_{11} & {n no}_{11} {l l}_{11} \\ {l l}_{22}^{22} & {m m}_{22}^{22} & {n no}_{22}^{22} & {l l}_{22} {m m}_{22} & {m m}_{22} {n no}_{22} & {n no}_{22} {l l}_{22} \\ {l l}_{33}^{22} & {m m}_{33}^{22} & {n no}_{33}^{22} & {l l}_{33} {m m}_{33} & {m m}_{33} {n no}_{33} & {n no}_{33} {l l}_{33} \\ {l l}_{44}^{22} & {m m}_{44}^{22} & {n no}_{44}^{22} & {l l}_{44} {m m}_{44} & {m m}_{44} {n no}_{44} & {n no}_{44} {l l}_{44} \\ {l l}_{55}^{22} & {m m}_{55}^{22} & {n no}_{55}^{22} & {l l}_{55} {m m}_{55} & {m m}_{55} {n no}_{55} & {n no}_{55} {l l}_{55} \\ {l l}_{66}^{22} & {m m}_{66}^{22} & {n no}_{66}^{22} & {l l}_{66} {m m}_{66} & {m m}_{66} {n no}_{66} & {n no}_{66} {l l}_{66} \end{matrix}\} - - - - - - ((99))$

由图2得到，各应变片的方向向量如表1所示Obtained from Figure 2, the direction vector of each strain gauge is shown in Table 1

表1十二面体各面应变片的方向向量 Table 1 Direction vectors of strain gauges on each face of dodecahedron

因此therefore

$A A = = \frac{11}{22} \{\begin{matrix} 11 & 00 & 11 & 00 & 00 & 11 \\ 00 & 11 & 11 & 00 & 11 & 00 \\ 11 & 00 & 11 & 00 & 00 & - - 11 \\ 00 & 11 & 11 & 00 & - - 11 & 00 \\ 11 & 11 & 00 & 11 & 00 & 00 \\ 11 & 11 & 00 & - - 11 & 00 & 00 \end{matrix}\} - - - - - - ((1010))$

所以so

{ε_i}＝A{ε_j} (11){ε _i }＝A{ε _j } (11)

其中i＝1，2，3，4，5，6。因此where i=1, 2, 3, 4, 5, 6. therefore

$\{\begin{matrix} {ϵ ϵ}_{11} \\ {ϵ ϵ}_{22} \\ {ϵ ϵ}_{33} \\ {ϵ ϵ}_{44} \\ {ϵ ϵ}_{55} \\ {ϵ ϵ}_{66} \end{matrix}\} = = \frac{11}{22} \{\begin{matrix} 11 & 00 & 11 & 00 & 00 & 11 \\ 00 & 11 & 11 & 00 & 11 & 00 \\ 11 & 00 & 11 & 00 & 00 & - - 11 \\ 00 & 11 & 11 & 00 & - - 11 & 00 \\ 11 & 11 & 00 & 11 & 00 & 00 \\ 11 & 11 & 00 & - - 11 & 00 & 00 \end{matrix}\} \{\begin{matrix} {ϵ ϵ}_{x x} \\ {ϵ ϵ}_{y the y} \\ {ϵ ϵ}_{z z} \\ {ϵ ϵ}_{x x y the y} \\ {ϵ ϵ}_{y the y z z} \\ {ϵ ϵ}_{z z x x} \end{matrix}\} - - - - - - ((1212))$

A的逆阵A^-1为The inverse matrix A ^-1 of A is

${A A}^{- - 11} = = \{\begin{matrix} 0.5 0.5 & - - 0.5 0.5 & 0.5 0.5 & - - 0.5 0.5 & 0.5 0.5 & 0.5 0.5 \\ - - 0.5 0.5 & 0.5 0.5 & - - 0.5 0.5 & 0.5 0.5 & 0.5 0.5 & 0.5 0.5 \\ 0.5 0.5 & 0.5 0.5 & 0.5 0.5 & 0.5 0.5 & - - 0.5 0.5 & - - 0.5 0.5 \\ 00 & 00 & 00 & 00 & 11 & - - 11 \\ 00 & 11 & 00 & - - 11 & 00 & 00 \\ 11 & 00 & - - 11 & 00 & 00 & 00 \end{matrix}\} - - - - - - ((1313))$

因此，可以得到三维应变状态为：Therefore, the three-dimensional strain state can be obtained as:

{ε_j}＝A^-1{ε_i} (14){ε _j }＝A ^-1 {ε _i } (14)

针对上述叙述计算推导过程，现举例对测试结果进行计算，假设测得六个面的应变分别为：320、260、370、400、500、350(με)。In view of the calculation and derivation process described above, the test results are calculated as examples, assuming that the measured strains of the six surfaces are: 320, 260, 370, 400, 500, 350 (με).

即：which is:

${ϵ ϵ}_{ξ ξ} = = \{\begin{matrix} {ϵ ϵ}_{11} \\ {ϵ ϵ}_{22} \\ {ϵ ϵ}_{33} \\ {ϵ ϵ}_{44} \\ {ϵ ϵ}_{55} \\ {ϵ ϵ}_{66} \end{matrix}\} = = \{\begin{matrix} 320320 \\ 260260 \\ 370370 \\ 400400 \\ 500500 \\ 350350 \end{matrix}\} - - - - - - ((1515))$

根据三维应变状态计算公式(1)及(2)、(3)、(4)式得：According to the calculation formula (1) and (2), (3) and (4) of the three-dimensional strain state:

$\{\begin{matrix} {ϵ ϵ}_{x x} \\ {ϵ ϵ}_{y the y} \\ {ϵ ϵ}_{z z} \\ {ϵ ϵ}_{x x y the y} \\ {ϵ ϵ}_{y the y z z} \\ {ϵ ϵ}_{z z x x} \end{matrix}\} = = \{\begin{matrix} 0.5 0.5 & - - 0.5 0.5 & 0.5 0.5 & - - 0.5 0.5 & 0.5 0.5 & 0.5 0.5 \\ - - 0.5 0.5 & 0.5 0.5 & - - 0.5 0.5 & 0.5 0.5 & 0.5 0.5 & 0.5 0.5 \\ 0.5 0.5 & 0.5 0.5 & 0.5 0.5 & 0.5 0.5 & - - 0.5 0.5 & - - 0.5 0.5 \\ 00 & 00 & 00 & 00 & 11 & - - 11 \\ 00 & 11 & 00 & - - 11 & 00 & 00 \\ 11 & 00 & - - 11 & 00 & 00 & 00 \end{matrix}\} \times \times \{\begin{matrix} {ϵ ϵ}_{11} \\ {ϵ ϵ}_{22} \\ {ϵ ϵ}_{33} \\ {ϵ ϵ}_{44} \\ {ϵ ϵ}_{55} \\ {ϵ ϵ}_{66} \end{matrix}\} - - - - - - ((1616))$

即：which is:

$\begin{matrix} {ϵ ϵ}_{x x} = = 0.5 0.5 {ϵ ϵ}_{11} - - 0.5 0.5 {ϵ ϵ}_{22} + + 0.5 0.5 {ϵ ϵ}_{33} - - 0.5 0.5 {ϵ ϵ}_{44} + + 0.5 0.5 {ϵ ϵ}_{55} + + 0.5 0.5 {ϵ ϵ}_{66} \\ {ϵ ϵ}_{y the y} = = - - 0.5 0.5 {ϵ ϵ}_{11} + + 0.5 0.5 {ϵ ϵ}_{22} - - 0.5 0.5 {ϵ ϵ}_{33} + + 0.5 0.5 {ϵ ϵ}_{44} + + 0.5 0.5 {ϵ ϵ}_{55} + + 0.5 0.5 {ϵ ϵ}_{66} \\ {ϵ ϵ}_{z z} = = 0.5 0.5 {ϵ ϵ}_{11} + + 0.5 0.5 {ϵ ϵ}_{22} + + 0.5 0.5 {ϵ ϵ}_{33} + + 0.5 0.5 {ϵ ϵ}_{44} - - 0.5 0.5 {ϵ ϵ}_{55} - - 0.5 0.5 {ϵ ϵ}_{66} \\ {ϵ ϵ}_{x x y the y} = = 11 {ϵ ϵ}_{55} - - 11 {ϵ ϵ}_{66} \\ {ϵ ϵ}_{y the y z z} = = 11 {ϵ ϵ}_{22} - - 11 {ϵ ϵ}_{44} \\ {ϵ ϵ}_{z z x x} = = 11 {ϵ ϵ}_{11} - - 11 {ϵ ϵ}_{33} \end{matrix} - - - - - - ((1717))$

土体中测试位置处的三维微应变为：The three-dimensional micro-strain at the test position in the soil is:

${ϵ ϵ}_{j j} = = \{\begin{matrix} {ϵ ϵ}_{x x} \\ {ϵ ϵ}_{y the y} \\ {ϵ ϵ}_{z z} \\ {ϵ ϵ}_{x x y the y} \\ {ϵ ϵ}_{y the y z z} \\ {ϵ ϵ}_{z z x x} \end{matrix}\} = = \{\begin{matrix} 440440 \\ 410410 \\ 250250 \\ 150150 \\ - - 140140 \\ - - 5050 \end{matrix}\} . .$

本发明的用于测试土体内部三维应变状态的装置及测试方法，能够更准确地获取待测土体内部某一点处真实的应变状态，以加强对土体内部的应变状态的稳定监测。本发明的具备的特点是：采用的菱形十二面体底座由弹性模量大于待测土体的材料制成，因此该底座不因土体受力变形而发生变形，使得测试位置更加稳定。菱形十二面体上的应变片基座由弹性模量小于待测土体的材料制成，从而使得应变片随着受力土体一起变形，更加准确地反应受力土体产生的应变量。另外菱形十二面体由正方体直接截取而成，制作简便。且该菱形十二面体12个表面全相等，每个面粘贴应变片方向的向量与面法线的夹角均相等且唯一，因此等菱形十二面体测试精度高于其它十二面体底座。The device and testing method for testing the three-dimensional strain state inside the soil body of the present invention can more accurately obtain the real strain state at a certain point inside the soil body to be tested, so as to strengthen the stable monitoring of the strain state inside the soil body. The characteristic of the present invention is that the rhombohedral dodecahedron base is made of a material whose elastic modulus is greater than that of the soil to be tested, so the base will not be deformed due to stress deformation of the soil, making the test position more stable. The base of the strain gauge on the rhombic dodecahedron is made of a material whose elastic modulus is smaller than that of the soil to be tested, so that the strain gauge deforms together with the stressed soil and more accurately reflects the strain generated by the stressed soil. In addition, the rhombic dodecahedron is directly intercepted from a cube, which is easy to make. Moreover, the 12 surfaces of the rhombic dodecahedron are all equal, and the angle between the vector of the direction of attaching the strain gauge on each surface and the surface normal is equal and unique, so the test accuracy of the rhombohedral dodecahedron is higher than that of other dodecahedron bases.

Claims

1. A device for testing the three-dimensional strain state inside the soil, the device is connected with a data acquisition system, and it is characterized in that: the test device includes a base rhombohedral dodecahedron (1), six strain gauges (2) , measuring wire (3), surface-centered wire hole (4), wire summary hole (5), strain gauge base (6); fix the six strain gauges (2) on six diamond-shaped dodecahedrons (1) On the strain gauge base (6) of the normal vector irrelevant surface, the measuring wires (3) of the six strain gauges are derived from the centroid wire summary hole (5) of the rhombic dodecahedron through the face center wire hole (4) and then connected with The strain gauge data acquisition system is connected to form a three-dimensional strain state test device.

2. the testing method of the device of a kind of test soil interior three-dimensional strain state according to claim 1, the testing method of this device comprises the following steps:

(1) First, the measuring wire (3) starts from the bottom surface of each common strain gauge (2), passes through the face-centered wire hole (4) and converges at the centroid of the rhombic dodecahedron, and then leads out from the wire summary hole (5); Fix the six common strain gauges (2) on the strain gauge bases (6) on the six faces with irrelevant normal vectors, and then press and fill the polyurethane foam sealant into the wire summary hole (5), and use To fill the gap between the measuring wire and the wire hole, form a three-dimensional strain state testing device based on the ordinary strain gauge (2) and the rhombic dodecahedron (1), and place the device in the soil to be tested;

(2) Establish a three-dimensional coordinate system with the centroid O of the rhombic dodecahedron as the origin, and OO ₁ , OO ₂ , and OO ₃ as the x-axis, y-axis, and z-axis;

( ₃ ) According to the coordinate system established in ( ₂ ), the vectors ( _1,0,1 ), ( _0,1,1 ), (0,1,1), (-1,0,1), (0,-1,1) are linearly independent from the vectors (1,1,0) and (-1,1,0) of the strain gauge directions of the surfaces β ₁ and β ₂ , that is These six faces are faces whose direction vectors are irrelevant;

(4) Calculate the direction cosines l, m, and n of each strain gauge according to the angles between the axis directions of the six common strain gauges and the x-axis, y-axis, and z-axis, and determine the matrix A accordingly;

(5) Use the data acquisition system to test the readings of six strain gauges (2), and determine the mathematical relationship between the transformation matrix {ε _j } according to the readings of the strain gauges in six different directions and the cosine value of each strain gauge direction ＝A ^-1 {ε _i }, and then calculate the three-dimensional strain state of any point in the soil.

{ε _j }＝A ^-1 {ε _i } (1)

where A ^-1 is

{A A}^{- - 11} = = \{\begin{matrix} 0.5 0.5 & - - 0.5 0.5 & 0.5 0.5 & - - 0.5 0.5 & 0.5 0.5 & 0.5 0.5 \\ - - 0.5 0.5 & 0.5 0.5 & - - 0.5 0.5 & 0.5 0.5 & 0.5 0.5 & 0.5 0.5 \\ 0.5 0.5 & 0.5 0.5 & 0.5 0.5 & 0.5 0.5 & - - 0.5 0.5 & - - 0.5 0.5 \\ 00 & 00 & 00 & 00 & 11 & - - 11 \\ 00 & 11 & 00 & - - 11 & 00 & 00 \\ 11 & 00 & - - 11 & 00 & 00 & 00 \end{matrix}\} - - - - - - ((22))