CN106442104B - Three-dimensional stress state testing device and operation method based on regular dodecahedron - Google Patents

Abstract

The invention provides a device based on a regular dodecahedron base and six common earth pressure cells. The six non-parallel surfaces of the regular dodecahedron base of the device are provided with earth pressure cell grooves, and the The six common earth pressure cells are respectively fixed on the six grooves; the gap between each groove and the common earth pressure cell is filled with an expansion water stop ring; each groove is provided with a data wire leading to the common earth pressure cell. Conductor hole in the body center of the regular dodecahedron; on any surface of the regular dodecahedron base where the groove is not provided, a conductor summary hole is arranged to connect the data conductor with the earth pressure cell measuring and reading element. At the same time, an operation method of a three-dimensional stress state testing device based on a regular dodecahedron is provided. The beneficial effect is that the stress state of a point inside the soil body can be obtained accurately and conveniently, the error caused by the past method of reflecting the stress by pasting strain rosettes is improved, and the average test accuracy is 0.81ρ. The improvement of the accuracy can more accurately reflect the conventional stress state of the soil and improve the safety reserve of the project.

Description

Three-dimensional stress state testing device and operation method based on regular dodecahedron

technical field

The invention belongs to the field of soil stress testing, in particular to a three-dimensional stress state testing device and an operating method based on a regular dodecahedron.

Background technique

Soils have different thickness and properties, so the stress test is a difficult but basic work. In order to deeply study the strength and deformation of soil, it is first necessary to have a full understanding of the stress state of soil. In practical engineering construction such as civil engineering, hydraulic engineering and environmental engineering, the intuitive and accurate acquisition of the stress state of soil is of great value for soil safety analysis, structural protection and scientific research.

At present, the stress testing of soil can be done by earth pressure cells and stress gauges. The stress state in a certain direction can be obtained by arranging the earth pressure cell and the stress gauge in a certain direction. To obtain the three-dimensional stress state of a point in the rock and soil mass, the three-dimensional stress state can be inferred from the strain state by arranging three-dimensional strain rosettes. However, it is difficult to measure the Poisson's ratio of soil under the action of complex forces, and it is difficult to paste strain rosettes on loose rock and soil, so this method has great defects. In many engineering practices, it is often necessary to measure the three-dimensional stress state of the rock and soil mass, while the conventional stress test element can only test the stress in a single direction, and the principal stress direction of the soil mass is difficult to determine. It is arranged in a direction parallel to the principal stress direction, and the result of this arrangement method is that the measured value differs greatly from the actual value, and the practicability is small.

Under normal circumstances, the earth pressure cell is buried in the artificially assumed maximum principal stress direction, and the soil has the characteristics of compressive deformation and unstable properties, so the measured earth pressure value has no application value. In order to obtain the three-dimensional stress state of a point in the soil, it is possible to embed multiple independent earth pressure cells in the soil, but this method ignores the influence of the interaction between the various test data, and there is a large error. Furthermore, the existing three-dimensional stress testing devices based on the rhombic dodecahedron skeleton and the ordinary earth pressure cell, and the three-dimensional stress testing device based on the octahedral skeleton and the ordinary earth pressure cell, due to the asymmetric geometry of the rhombic dodecahedron and the octahedron. As a result, the production process is complicated, and when it is placed in the soil, the center position is not easy to determine, so further improvement is required. Aiming at the defects of the existing testing methods, a practical, intuitive and convenient device for testing the three-dimensional stress state of a point inside the soil is required.

SUMMARY OF THE INVENTION

The invention provides a three-dimensional stress state testing device and operation method based on a regular dodecahedron, which aims to intuitively test the stress state of a point in the soil, and provides a solution for testing the stress state of a point in the soil in the past, which can accurately and conveniently test the stress state of a point in the soil. Test the stress state at a point in the soil.

In order to achieve the above purpose, what the present invention adopts is a device based on a regular dodecahedron base and six common earth pressure cells, wherein: the device includes six common earth pressure cells, a regular dodecahedron base, an expansion Water stop ring, polyurethane foam filler, earth pressure box data wire; earth pressure box grooves are arranged on the six non-parallel surfaces of the regular dodecahedron base, and the six ordinary earth pressure boxes are respectively fixed On the six grooves, the gap between each groove and the ordinary earth pressure cell is filled with an expansion water stop; each groove is provided with a data wire leading the data wire of the ordinary earth pressure cell to the body center of the regular dodecahedron. Conductor holes, on any surface of the regular dodecahedron base without grooves, are provided with a conductor summary hole to connect the data conductor with the earth pressure box measuring and reading element; that is, the invention is used to test a little stress inside the soil body. state of the device.

At the same time, an operation method of a three-dimensional stress state testing device based on a regular dodecahedron is provided.

The effect of the invention is to provide the possibility to obtain the stress state of a point inside the soil body accurately and conveniently, and the device has the characteristics of clear calculation principle, low cost, convenient operation, etc. error. Assuming that the accuracy of the conventional earth pressure cell is ρ, the calculated test accuracy of the three principal stresses is 1.0ρ, the test accuracy of the three shear stresses is 0.62ρ, and the average test accuracy is 0.81ρ. The improvement of the accuracy can more accurately reflect the conventional stress state of the soil and improve the safety reserve of the project.

Description of drawings

Fig. 1 is the calculation method of the direction vector of the earth pressure cell test direction in the device involved in the present invention;

Fig. 2 is the shape of the regular dodecahedron involved in the present invention;

Fig. 3 is the regular dodecahedron skeleton of the six earth pressure cells that the present invention relates to;

Fig. 4 is the overall effect diagram of the device involved in the present invention;

Fig. 5 is the effect diagram before cutting the regular dodecahedron skeleton involved in the present invention;

6 is a cross-sectional view of the O ₁ plane and the A ₁ plane in the process of making the regular dodecahedron skeleton involved in the present invention, wherein the O ₁ plane refers to the plane where the circle is located, the A ₁ plane refers to the plane where the regular pentagon is located, and O The ₁ side is coplanar with the A ₁ side.

In the picture:

1. Data wire hole 2. Groove 3. Earth pressure box 4. Data wire 5. Wire summary hole 6. Expansion water stop ring 7. Regular dodecahedron base

Detailed ways

The three-dimensional earth pressure testing device and operation method based on a regular dodecahedron of the present invention will be described with reference to the accompanying drawings.

The design principle of the present invention: the three-dimensional stress state at a point in the soil includes three normal stresses and three shear stresses, so a geometric body with at least six faces is required to arrange the earth pressure cell. The three-dimensional earth pressure testing device based on the regular dodecahedron of the present invention is embedded in the soil body, and the data wire of the earth pressure box is connected to the reading element to obtain six stress readings. According to the angle between the test direction of the earth pressure cell and the x, y and z axes, the direction cosine of the earth pressure cell is obtained, and then the transformation matrix and its inverse matrix are obtained. Finally, the three-dimensional stress state at that point in the soil is obtained by multiplying the six stress readings by the inverse matrix.

The three-dimensional earth pressure test device based on a regular dodecahedron of the present invention is shown in Figures 2, 3, and 4, and specifically includes: six ordinary earth pressure cells 3, a regular dodecahedron base 7, an expansion water stop ring 6, Polyurethane foam filler, earth pressure box data wire 4; Earth pressure box grooves 2 are provided on the six non-parallel surfaces of the regular dodecahedron base, and the six ordinary earth pressure boxes 3 are fixed On the six grooves, the gap between each groove 2 and the common earth pressure cell 3 is filled with an expansion water stop ring 6; each groove is provided with a data wire leading to the regular dodecahedron of the common earth pressure cell 3 The wire hole 1 of the body center of the base 7, on the regular dodecahedron base 7, is not provided with any surface of the groove, such as the _A8 face is provided with a wire summary hole 5, and the data wire 4 and the earth pressure box are measured and read The elements are connected; that is, the device of the present invention is used to test the stress state of a point inside the soil.

The operating method of the three-dimensional stress testing device based on the regular dodecahedron of the present invention comprises the following steps:

(1) bury the above-mentioned three-dimensional stress state testing device based on regular dodecahedron into the soil;

(2) Calculate the direction cosine of six different test directions according to the angle between the test direction of the ordinary earth pressure cell and the x, y and z axes of the established coordinate system, and obtain the transformation matrix T and its inverse matrix T based on the obtained direction cosine ^-1 ;

(3) Obtain six stress readings, namely σ ₁ , σ ₂ , σ ₃ , σ ₄ , σ ₅ , σ ₆ , according to the earth pressure cell reading element;

(4) According to the inverse matrix T ^-1 obtained in step (2) and the six stress readings obtained in step (3), calculate the three-dimensional stress state of a point in the soil body. The specific formula is:

{σ _j }=T ^-1 {σ _K } (1)

In formula (1), σ _j is the three-dimensional stress state of the measured point, namely

σ _x , σ _y , σ _z , σ _xy , σ _yz , σ _zx represent the three normal stress components and the three shear stress components of the normal stress state of the test point, respectively;

σ _k is the measured value of ordinary earth pressure cell 3, namely

σ ₁ , σ ₂ , σ ₃ , σ ₄ , σ ₅ , and σ ₆ represent the measured values of the ordinary earth pressure cell (3) in six different directions, respectively;

In formula (1), T ^-1 is:

The operating method of the three-dimensional stress testing device based on the regular dodecahedron of the present invention is specifically implemented as follows:

First, make a regular dodecahedron base. The regular dodecahedron is cut from a sphere. The specific cutting method is as follows:

(1) Select a sphere with a known radius of a, select any diameter on the sphere and mark it as AB, and draw a plane O ₁ with the straight line AB as the normal at the position of the line AB at a distance of μcm from point A, where The sphere is cut through the plane O ₁ , and the inscribed regular pentagon abcde of the cut surface is made, that is, the A ₁ surface of the regular dodecahedron skeleton is formed, as shown in Figure 6.

(2) Correspondingly, cut the same surface at a distance of μcm from point B on the other side of the sphere, and make the inscribed regular pentagon kjlst of the cutting surface, and the pentagon kjlst and the direction of the abcde figure form 180°, that is, form A ₈ surface, as shown in Figure 5.

(3) Cross the side ab of the regular pentagon abcde and form an angle α with the plane O ₁ to make the plane O ₃ and cut the sphere through the plane O ₃ to make the inscribed regular pentagon bchgf of the plane O ₃ , where α= 116°33′54″, that is, the A ₂ face is formed; in the same way, the other four faces of the regular dodecahedron skeleton, namely the A ₃ , A ₄ , A ₅ and A ₆ faces, are made in turn, as shown in Figure 5 .

(4) Cross the side gh of the regular pentagon bchgf and form an angle α with the plane O ₃ to make the plane O ₄ and cut the sphere through the plane O ₄ to make the inscribed regular pentagon ghijk of the plane O ₄ , where α= 116°33′54″, that is, the A ₇ plane is formed; in the same way, make similar planes and regular pentagons through the line segments fg, gh, hi, im, mn, no, op, pq, qr and rf, that is The remaining 4 faces of the regular dodecahedron can be obtained, as shown in Figure 5.

(5) Cut off the overlapping part between the surfaces and the residual part outside the outline of the regular dodecahedron, that is, a regular dodecahedron model is formed.

(6) Finally, the earth pressure cell groove 2 is set at the center position of the regular dodecahedron A ₂ surface, the groove 2 and the A ₂ surface are parallel to each other and the bottom surface of the groove is flat, and the center of the groove 2 is provided with a wire hole 1; The diameter of groove 2 is the diameter of the earth pressure box plus 1-2mm, and the depth of the groove is 2/3-1/3 of the thickness of the earth pressure box; the remaining five earth pressure boxes are placed in the corresponding dodecahedron skeleton A ₁ , A ₃ , A4, _A5 and _{A6 .} That is to form a regular dodecahedron skeleton, as shown in Figure 2.

Second, install a three-dimensional earth pressure cell. The data wires connected to the conventional earth pressure box are passed through the data wire hole 1, and finally through the wire collection hole 5. The conventional earth pressure box 3 is fixed on the groove 2 of the regular dodecahedron base, the expansion water stop ring 6 is stuck in the gap between the earth pressure box 3 and the groove 2, and finally the three are fully filled with waterproof colloid. Fix; install the remaining five earth pressure boxes in sequence in this way. After installation, use polyurethane foam filler to waterproof the gap between the earth pressure box data wire 4 and the wire summary hole 5, and seal the data wire 4 with the soil. The pressure cell reading element is connected. That is, a three-dimensional earth pressure testing device based on a regular dodecahedron and an ordinary earth pressure cell is formed.

Third, the earth pressure testing device fabricated in the above steps (1) and (2) is embedded in the soil body.

Fourth, the earth pressure values in six different directions, namely σ ₁ , σ ₂ , σ ₃ , σ ₄ , σ ₅ , σ ₆ , are obtained through the earth pressure box reading element, expressed as σ _k ={σ ₁ ,σ ₂ , σ ₃ , σ ₄ , σ ₅ , σ ₆ } ^T .

Fifth, the direction cosine of each earth pressure cell is calculated according to the angle between the test directions of the six conventional earth pressure cells and the x, y and z axes of the established coordinate system. As shown in Figure 1, OA is the test direction of the conventional earth pressure cell, OA' is the projection of OA on the xoy plane, δ is the angle between the test direction of the earth pressure cell and the z-axis, The test direction for the earth pressure box represents the angle between the projection of the line on the xoy plane and the x-axis. The specific expression of the direction cosine is as follows:

n=cosδ (6)

Sixth, the transformation matrix T is obtained based on the direction cosine of the test direction of the earth pressure cell, and then the inverse matrix T ^-1 of the transformation matrix is obtained.

Seventh, the conventional stress state at a point in the soil is calculated according to the formula {σ _j }=T ^-1 {σ _k }. In the formula: σ _j = {σ _x , σ _y , σ _z , σ _xy , σ _yz , σ _zx } ^T , σ _x , σ _y , σ _z , σ _xy , σ _yz , σ _zx represent the measured points respectively. Three normal stress components and three shear stress components for the normal stress state.

The three-dimensional stress state of a point O(x, y, z) in the soil can be expressed as

According to the shear stress reciprocal theorem, in formula (7), σ _xy =σ _yx , σ _xz =σ _zx , σ _yz =σ _zy , that is, three normal stresses and three shear stresses total 6 stress components can express the stress of a point state. Assuming that the stress state of a point in space is σ _ij (equation (7)), the normal stress of the axis where the element is located is

If the normal stresses in six different directions are known, the stress state at a point in the medium can be obtained. Then the normal stress in any direction can be obtained by formula (8). Assuming that the normal stress in 6 different directions is, then σ _k can be expressed as:

where k=1, 2, 3, 4, 5, 6. Then the algebraic relationship between the conventional earth pressure state and the measured stress reading is as follows:

or abbreviated as

{σ _k }=T{σ _j } (11)

where j=x, y, z, xy, yz, zx. The matrix T is

but

{σ _j }=T ^-1 {σ _k } (13)

The direction cosine of the test direction of each earth pressure cell in this device can be obtained from Figure 2, see Table 1:

Table 1. Direction cosines of three-dimensional earth pressure cells

From equation (12) and Table 1, the inverse matrix T ^-1 of the matrix T can be determined, that is,

In view of the above derivation process, a specific example is now given to further illustrate the application of the three-dimensional earth pressure cell testing device and the operation method: measuring the conventional stress state of soil during the seepage process of the earth-rock dam. The above-mentioned device based on a regular dodecahedron base and six common earth pressure cells is embedded in the soil to be tested, and the device is connected with the earth pressure cell reading element to observe the soil mass in the seepage process of the earth-rock dam. The experimental data obtained are only for the reference of relevant project construction parties.

Take the earth pressure reading at a certain stage for verification. The readings of earth pressure values measured on six non-parallel surfaces are: 1.25, 0.89, 1.35, 1.06, 1.02, 0.96, and the unit is (kpa). which is

o _θ = {σ ₁ , σ ₂ , σ ₃ , σ ₄ , σ ₅ , σ ₆ } = {1.25, 0.89, 1.35, 1.06, 1.02, 0.96}

Obtained from the measured three-dimensional values and the above formulas (1)(2)(3)(4):

in

which is

σ _x = -0.2501σ ₁ +0.7514σ ₂ -0.1546σ ₃ +0.4047σ ₄ +0.4047σ _{5 -0.1546σ}

σ _y = -0.2495σ ₁ -0.2505σ ₂ +0.6544σ ₃ +0.0954σ ₄ +0.0954σ ₅

+0.6544σ ₆

σ _z =σ ₁

σ _xy =0.2938σ ₃ -0.4754σ ₄ +0.4754σ ₅ -0.2938σ ₆

σ _yz =0.4757σ ₃ +0.2940σ ₄ -0.2940σ ₅ -0.4757σ ₆

σ _xz = -0.0003σ ₁ +0.5012σ ₂ +0.1545σ ₃ -0.4045σ ₄ -0.4045σ ₅

+0.1545σ ₆

After calculation, the three-dimensional stress state in the soil is:

The device and the calculation method for testing the three-dimensional stress state of a point in the soil provided by the invention have the characteristics of simple operation, clear principle and low cost. The previous method of reflecting the three-dimensional stress state of soil through three-dimensional strain rosettes is further improved, and provides reference value for soil stress testing in related projects.

The above description is only for description in conjunction with this production process, and is not limited to this device. For those skilled in the art, some changes may occur in the present invention, such as changes in the shape of the regular dodecahedron base, changes in the materials used. change etc. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (2)

1. a three-dimensional stress state testing device based on a regular dodecahedron, the device includes six common earth pressure cells (3), a regular dodecahedron base (7), it is characterized in that: the device also includes expansion A water stop ring (6), a polyurethane foam filler, an earth pressure box data wire (4), and earth pressure box grooves ( 2), fix the six common earth pressure cells (3) on the six grooves respectively, and the gap between each groove (2) and the common earth pressure cell (3) is filled with an expansion water stop ring (6); A wire hole (1) for connecting the data wire of the common earth pressure cell (3) to the body center of the regular dodecahedron base (7) is arranged on the groove. A wire collecting hole (5) is provided on any surface of the setting groove, and the data wire (4) is connected with the measuring and reading element of the soil pressure box; that is, a device for testing the stress state of a point in the soil is formed. 2. The operation method of the three-dimensional stress state testing device based on a regular dodecahedron according to claim 1, the method comprising the following steps: (1) bury the above-mentioned three-dimensional stress state testing device based on regular dodecahedron into the soil; (2) Calculate the direction cosine of six different test directions according to the angle between the test direction of the ordinary earth pressure cell and the x, y and z axes of the established coordinate system, and obtain the transformation matrix T and its inverse matrix T based on the obtained direction cosine ^-1 ; (3) Obtain six stress readings, namely σ ₁ , σ ₂ , σ ₃ , σ ₄ , σ ₅ , σ ₆ , according to the earth pressure cell reading element; (4) According to the inverse matrix T ^-1 obtained in step (2) and the six stress readings obtained in step (3), calculate the three-dimensional stress state of a point in the soil body. The specific formula is: {σ _j }=T ^-1 {σ _K } (1) In formula (1), σ _j is the three-dimensional stress state of the measured point, namely σ _x , σ _y , σ _z , σ _xy , σ _yz , σ _zx represent the three normal stress components and the three shear stress components of the normal stress state of the test point, respectively; σ _k is the measured value of the ordinary earth pressure cell (3), namely σ ₁ , σ ₂ , σ ₃ , σ ₄ , σ ₅ , and σ ₆ represent the measured values of the ordinary earth pressure cell (3) in six different directions, respectively; In formula (1), T ^-1 is: