Three-dimensional stress calculation method during missing of partial test data of sensor

Abstract

The invention discloses a three-dimensional stress calculation method during missing of partial test data of a sensor. The method comprises the following steps: judging whether the stress characteristic of a soil body is in an axial symmetry state or a one-dimensional compression state; secondly, according to the soil stress characteristics determined in the first step, the stress relation met by the soil stress characteristics is substituted into an existing three-dimensional stress calculation formula to be simplified, and a conversion matrix is obtained; solving a maximum irrelevant group of the conversion matrix; a new conversion matrix is formed by the obtained maximum irrelevant groups, and at the moment, the three-dimensional stress state, meeting the axial symmetry state or one-dimensional compression state condition, of the stress characteristics of the tested soil body can be calculated only through the normal stress on the normal vector corresponding to the new conversion matrix. The method has the advantages that the purpose of obtaining the three-dimensional stress state through residual test data is achieved, the serious influence of sensor test data missing on three-dimensional stress calculation in the axial symmetry and one-dimensional compression state is effectively made up, the data utilization efficiency is improved, and the test cost is reduced.

Description

Technical Field

[0001] The invention belongs to the field of soil stress testing, and in particular relates to a three-dimensional stress calculation method suitable for when part of sensor test data is missing under axisymmetric and one-dimensional compression states. Background Art

[0002] Stress state is an important indicator for evaluating soil stability and safety. Stress testing is a prerequisite for quantitative mechanical analysis and safety evaluation. Therefore, accurate and complete acquisition of the stress state and development trend inside the soil has important engineering value for studying the strength and stability of the soil.

[0003] The common stress state in geotechnical engineering is the three-dimensional stress state. The testing principle is to collect the normal stress of 6 unrelated normal vectors to solve the stress state of the point. However, in soil stress testing, due to the complexity of the site, various uncertain factors such as accidental damage and environmental damage, it is very likely that some sensor data will be missing in a certain period of time. This will cause the previous three-dimensional stress calculation method to fail and fail to accurately and completely obtain the stress state inside the soil. At present, there are two common methods to deal with this situation. One is to delete all the data in the time period, that is, not considering the impact of the time period with some missing data, and only use the test data of the remaining time period for analysis. The second is to invalidate all the test data and retest. The first method will lead to data faults, reduce the integrity and accuracy of the data, and thus have a huge impact on subsequent data analysis and data mining. The second method will not only waste manpower and material resources, but also may cause new errors or even mistakes due to repeated loading, such as super consolidation. Therefore, when data loss is unavoidable, how to scientifically process the existing test data to compensate for the impact of missing test data and improve the overall accuracy of the test data is a hot issue that needs to be urgently resolved in three-dimensional stress testing in geotechnical engineering. Summary of the invention

[0004] In view of this situation, the present invention aims to provide a three-dimensional stress calculation method suitable for when the sensor part test data is missing under the axisymmetric and one-dimensional compression state. It can be used for three-dimensional stress calculation when the sensor part test data is missing and the force characteristics of the test soil body meet the axisymmetric state or one-dimensional compression state conditions to compensate for the impact caused by the missing test data.

[0005] To achieve the above object, the technical solution of the present invention is: a three-dimensional stress calculation method suitable for when part of the sensor test data is missing under axisymmetric and one-dimensional compression state. The method comprises the following steps:

[0006] Step 1: Determine whether the soil is subjected to axial symmetry or one-dimensional compression. In the axial symmetry state, the stress relationship satisfies: xx =σyy , σ yz = σ zx , in the one-dimensional compression state, its stress relationship satisfies: σ xx = σ yy , σ yz = σ zx = σ xy = 0;

[0007] Step 2: According to the stress characteristics of the soil mass determined in Step 1, substitute the stress relationship it satisfies into the existing three-dimensional stress calculation formula (1), and then simplify it to obtain the simplified transformation matrix.

[0008] {σ j} = T -1 {σ i} (1)

[0009] Where: σ j is the stress state of a point, σ j = {σ xx σ yy σ zz σ xy σ yz σ zx}; T is the transformation matrix; σ i is the normal stress in a certain direction, σ i = σ xx l i 2 + σ yy m i 2 + σ zz n i 2 + 2σ xy l i m i + 2σ yz m i n i + 2σ zx n i l i , l i , m i , n i are the cosines of the angles between the i-th normal stress and the coordinate axes x, y, z respectively, i = 1, 2, 3, 4, 5, 6;

[0010] Step 3: According to the transformation matrix obtained in Step 2, find its maximal linearly independent group, and form a new transformation matrix from the obtained maximal linearly independent group. At this time, only the normal stress on the normal vector corresponding to the new transformation matrix is required to calculate the three-dimensional stress state that satisfies the axisymmetric state or one-dimensional compression state condition of the stress characteristics of the tested soil mass. The calculation formula is as shown in Equation (2).

[0011] {σ j} = A -1 {σ k} (2)

[0012] Where: A is the maximal linearly independent group after the simplification of the transformation matrix T;

[0013] The beneficial effects of the present invention are as follows: The provided three-dimensional stress calculation method can effectively make up for the influence of the missing sensor test data on the three-dimensional stress calculation in the axisymmetric and one-dimensional compression states. Without re-testing, reliable three-dimensional stress calculation results can be obtained by scientifically processing the remaining test data, avoiding data waste. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a flow chart of the calculation method of the present invention;

[0015] Figure 2 is a schematic diagram of the stress characteristics of the soil body in the embodiment of the present invention.

[0016] In the figure

[0017] 1. DTS-3 type three-dimensional earth pressure cell 2. Cylinder 3. Concrete cover plate 4. Loading channel 5. Soil body DETAILED DESCRIPTION OF THE INVENTION

[0018] The following combines the drawings and embodiments to elaborate in detail on a three-dimensional stress calculation method of the present invention applicable to the situation where some test data of the sensor is missing in the axisymmetric and one-dimensional compression states.

[0019] The principle of the calculation method of the present invention: Based on the existing three-dimensional stress calculation principle, combined with the stress characteristics of the axisymmetric and one-dimensional compression states, a new low-order transformation matrix is established to realize the calculation of the three-dimensional stress state of the tested soil body by using the remaining non-missing test data.

[0020] Referring to Figure 1 , the present invention provides a three-dimensional stress calculation method applicable to the situation where some test data of the sensor is missing in the axisymmetric and one-dimensional compression states, including the following steps:

[0021] Step 1. Determine whether the stress characteristic of the soil body is the axisymmetric state or the one-dimensional compression; in the axisymmetric state, its stress relationship satisfies: σ xx = σ yy , σ yz = σ zx , in the one-dimensional compression state, its stress relationship satisfies: σ xx = σ yy , σ yz = σ zx = σxy = 0。

[0022] Step 2: According to the stress characteristics of the soil mass determined in Step 1, substitute the stress relationship it satisfies into the existing three-dimensional stress calculation formula (1), and then simplify it to obtain the simplified transformation matrix.

[0023] {σ j} = T -1 {σ i} (1)

[0024] Where: σ j is the stress state of a point, σ j = {σ xx σ yy σ zz σ xy σ yz σ zx}; T is the transformation matrix; σ i is the normal stress in a certain direction, σ i = σ xx l i 2 + σ yy m i 2 + σ zz n i 2 + 2σ xy l i m i + 2σ yz m i n i + 2σ zx n i l i ,l i 、m i 、n i are the cosines of the angles between the i-th normal stress and the coordinate axes x, y, and z respectively, i = 1, 2, 3, 4, 5, 6.

[0025] Step 3: According to the transformation matrix obtained in Step 2, find its maximal independent set. The new transformation matrix is composed of the obtained maximal independent set. At this time, only the normal stress on the normal vector corresponding to the new transformation matrix is required to calculate the three-dimensional stress state that satisfies the axisymmetric state or one-dimensional compression state condition of the stress characteristics of the tested soil mass. The calculation formula is as shown in Equation (2).

[0026] {σ j} = A -1 {σ k} (2)

[0027] Where: A is the maximal independent set after simplifying the transformation matrix T;

[0028] In Step 2, if the stress characteristics of the soil mass determined in Step 1 are in an axisymmetric state, the simplified transformation matrix obtained is T1.

[0029]

[0030] In Step 2, if the stress characteristics of the soil mass determined in Step 1 are in a one-dimensional compression state, the simplified transformation matrix obtained is T2.

[0031]

[0032] In Step 3, if the matrix obtained in Step 2 is T1, the new transformation matrix obtained in Step 3 is A1. At this time, only the normal stresses on the 4 normal vectors corresponding to the transformation matrix A1 need to be transformed to calculate the three-dimensional stress state at this time. The calculation formula is shown in Equation (3).

[0033] {σ j} = A1 -1 {σ k} (3)

[0034] Where:

[0035] In Step 3, if the matrix obtained in Step 2 is T2, the new transformation matrix obtained is A2. At this time, only the normal stresses on the 2 normal vectors corresponding to the transformation matrix A2 need to be transformed to calculate the three-dimensional stress state at this time. The calculation formula is shown in Equation (4).

[0036] {σ j} = A2 -1 {σ k} (4)

[0037] Where:

[0036] Embodiment

[0038] As Figure 1 , Figure 2 shown, the DTS-3 type three-dimensional earth pressure cell 1 is buried in the barrel 2 filled with the soil mass 5. There is a concrete cover plate 3 above the barrel 2, and the force transmission and transformation are realized through the upper loading channel 4. Taking the upper surface of the fill as the horizontal plane and the center of the model box as the origin, an overall coordinate system is established. Select the x-axis direction as any direction on the horizontal plane, the y-axis is perpendicular to the x-axis, and the z-axis is perpendicular downward. The x, y, and z axes are perpendicular to each other. The DTS-3 type three-dimensional earth pressure cell 1 is buried at the position half of the barrel height downward from the origin. When burying, make the coordinate system of the DTS-3 type three-dimensional earth pressure cell 1 consistent with the overall coordinate system. σ xxis the normal stress acting on the plane perpendicular to the x-axis and in the x-axis direction, σ yy is the normal stress acting on the plane perpendicular to the y-axis and in the y-axis direction, σ zz is the normal stress acting on the plane perpendicular to the z-axis and in the z-axis direction, σ xy is the shear stress acting on the plane perpendicular to the x-axis and in the y-axis direction, σ yz is the shear stress acting on the plane perpendicular to the y-axis and in the z-axis direction, σ zx is the shear stress σ acting on the plane perpendicular to the z-axis and in the x-axis direction xx is the normal stress acting on the plane perpendicular to the x-axis and in the x-axis direction, σ yy is the normal stress acting on the plane perpendicular to the y-axis and in the y-axis direction, σ zz is the normal stress acting on the plane perpendicular to the z-axis and in the z-axis direction, σ xy is the shear stress acting on the plane perpendicular to the x-axis and in the y-axis direction, σ yz is the shear stress acting on the plane perpendicular to the y-axis and in the z-axis direction, σ zx is the shear stress acting on the plane perpendicular to the z-axis and in the x-axis direction. In this embodiment, the DTS-3 type three-dimensional earth pressure cell is used as the sensor, and the normal vectors of its 6 normal stresses are shown in Table 1. The force characteristics of the soil mass are as Figure 2 shown

[0039] Table 1 The specific implementation steps are as follows:

[0042] Step 1: Determine whether the force characteristic of the soil mass is an axisymmetric state or one-dimensional compression;

[0043] As can be seen from Figure 2 shown, the force characteristic of the soil mass is an axisymmetric state. Its stress relationship satisfies: σ xx = σ yy , σ yz = σ zx .

[0044] Step 2: According to the force characteristic of the soil mass determined in this embodiment, substitute the stress relationship it satisfies into the existing three-dimensional stress calculation formula, and then simplify it to obtain the simplified transformation matrix T1.

[0045]

[0046] Step 3: According to the transformation matrix T1 obtained in Step 2, find its maximal independent group to obtain the new transformation matrix A1. At this time, only the normal stresses on the 4 normal vectors corresponding to the transformation matrix A1 need to be used to calculate the three-dimensional stress state at this time. The calculation formula is as shown in Equation (3).

[0047] {σ j} = A1 -1 {σ k} (3)

[0048] In the formula:

[0049] Here, for the four normal stress planes corresponding to A1, one is selected from the σ1 and σ2 planes, one is selected from the σ3 and σ4 planes, and the σ5 and σ6 planes. Therefore, for the DTS-3 type three-dimensional earth pressure cell, when facing the 8 data missing situations shown in Table 2 in the axisymmetric state, the three-dimensional stress at this time can be obtained according to the normal stresses on the remaining 4 faces.

[0050] Table 2

[0053] The above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by those skilled in the art within the essence of the present invention should also fall within the protection scope of the present invention.

Claims

1. A three-dimensional stress calculation method when part of the test data of a sensor is missing, characterized in that: It includes the following steps: Step 1: Determine whether the stress characteristics of the soil mass are in an axisymmetric state or a one-dimensional compression state; Under the axisymmetric state, its stress relationship satisfies: σ xx = σ yy , σ yz = σ zx ; under the one-dimensional compression state, its stress relationship satisfies: σ xx = σ yy , σ yz = σ zx = σ xy = 0; Step 2. According to the soil stress characteristics determined in Step 1, substitute the stress relationship it satisfies into the existing three-dimensional stress calculation formula: {σ j} = T -1 {σ i}, and then simplify it to obtain the simplified transformation matrix. Where: σ j is the stress state at a point, and σ j ={σ xx σ yy σ zz σ xy σ yz σ zx}; T is the transformation matrix; σ i is the normal stress in a certain direction, l i 、m i 、n i are the cosines of the angles between the i-th normal stress and the coordinate axes x, y, z respectively, where i = 1, 2, 3, 4, 5, 6; Step 3: According to the transformation matrix obtained in Step 2, find its maximal linearly independent group, and form a new transformation matrix with the obtained maximal linearly independent group. At this time, only the normal stress on the normal vector corresponding to the new transformation matrix is required to calculate the three-dimensional stress state that satisfies the axisymmetric state or the one-dimensional compression state condition of the stress characteristics of the tested soil mass. The calculation formula is as follows. {σ j} = A -1 {σ k} Where: A is the maximal linearly independent group after the simplification of the transformation matrix T; 2. The three-dimensional stress calculation method when part of the test data of the sensor is missing according to claim 1, wherein: The transformation matrix obtained in Step 2 includes: 1) The stress characteristics of the soil mass determined in Step 1 are in an axisymmetric state, and its stress relationship satisfies: σ xx = σ yy , σ yz = σ zx . The simplified transformation matrix obtained is T1. 2) The stress characteristics of the soil mass determined in Step 1 are in a one-dimensional compression state, and its stress relationship satisfies: σ xx = σ yy , σ yz = σ zx = σ xy = 0. The simplified transformation matrix obtained is T2, 3. The three-dimensional stress calculation method when part of the test data of the sensor is missing according to claim 1, characterized in that: The new transformation matrix obtained in Step 3 includes: 1) If the matrix obtained in Step 2 is T1, then the new transformation matrix obtained in Step 3 is A1. At this time, only the normal stress on the 4 normal vectors corresponding to the transformation matrix A1 is required to calculate the three-dimensional stress state at this time. The calculation formula is as follows. Wherein: 2) If the matrix obtained in Step 2 is T2, then the new transformation matrix obtained in Step 3 is A2. At this time, only the normal stress on the 2 normal vectors corresponding to the transformation matrix A2 is required to calculate the three-dimensional stress state at this time. The calculation formula is as follows. Wherein:

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