A method for determining a characteristic curve of surrounding rock considering temperature correction

Abstract

This invention discloses a method for determining the characteristic curve of surrounding rock considering temperature correction, relating to the field of mining construction engineering. It provides an effective method for more accurate determination of the characteristic curve of surrounding rock in deep variable-temperature environments, thus laying the foundation for the design of the shared load-bearing structure of surrounding rock in variable-temperature environments. Step 1: Sampling and testing the physical properties of surrounding rock; Step 2: On-site parameter testing; Step 3: Calculating the temperature field distribution at time t; Step 4: Determining the displacement corresponding to the inner side of the surrounding rock under a certain support pressure at time t; Step 5: Plotting a family of characteristic curves of surrounding rock considering temperature correction. Compared with conventional characteristic curves of surrounding rock, this method corrects for errors caused by the heat transfer and temperature variation process, avoiding material waste due to overestimating the wellbore load and preventing safety hazards caused by underestimating the wellbore load.

Description

Technical Field

[0001] This invention relates to the field of mining construction engineering. Background Technology

[0002] As national resource extraction gradually shifts from shallow to deep, high-temperature surrounding rocks will inevitably be encountered during the construction of shafts and tunnels. With increasing depth, the geothermal gradient is typically 1-3℃ / 100m, and in some strata with high geothermal gradients, the stratum temperature at 2500m may reach over 90℃.

[0003] In high-temperature environments, the temperature of shafts and tunnels during construction needs to be controlled, typically around the human body's thermal comfort temperature of 28°C. This creates a significant temperature gradient from the surrounding rock to the working area, causing the surrounding rock to cool down. This cooling process leads to shrinkage and deformation of the surrounding rock. Therefore, the characteristic curve of the surrounding rock is a crucial basis for the design of the rock-support structure's shared load-bearing capacity. However, the shrinkage and deformation of the surrounding rock caused by the large temperature gradient alters this characteristic curve. Thus, determining the characteristic curve of the surrounding rock becomes a pressing technical problem for those skilled in the art. Summary of the Invention

[0004] To address the above problems, this invention proposes a method for determining the characteristic curve of surrounding rock that takes temperature correction into account. This provides an effective method for determining the characteristic curve of surrounding rock in deep variable temperature environments, thereby laying the foundation for the design of the joint load-bearing structure of surrounding rock and support structure in variable temperature environments.

[0005] The technical solution of this invention is as follows: It is carried out according to the following steps:

[0006] Step 1: Sampling and physical property testing of surrounding rock;

[0007] Samples were taken from the surrounding rock excavated on site, and the elastic modulus E and Poisson's ratio of the surrounding rock samples were measured. The thermal conductivity k, density ρ, specific heat c, and coefficient of thermal expansion a of the sample were tested in the laboratory.

[0008] Calculate the thermal diffusivity of the surrounding rock based on the test parameters. , ;

[0009] Step 2: On-site parameter testing;

[0010] At the working face, the initial in-situ stress P0 and initial temperature of the surrounding rock were measured. Average air temperature at the working face The convective heat transfer coefficient h on the inner side of the surrounding rock was tested.

[0011] Step 3: Calculate the temperature field distribution at time t;

[0012] Select the surrounding rock calculation area, where the inner side of the surrounding rock is... , refers to the rough excavation path of a shaft or tunnel, and the outer boundary of the surrounding rock. It needs to be outside the excavation impact zone. The calculation area for the surrounding rock is selected above 50m. .

[0013] Given Given a sequence of equally spaced position coordinates r, determine the temperature field at each position coordinate at time t, and determine the temperature gradient at each position coordinate at time t.

[0014] Step 4: Determine the displacement of the inner side of the surrounding rock under a certain support pressure at time t. ;

[0015] Step 5: Draw a family of surrounding rock characteristic curves considering temperature correction;

[0016] Select multiple support pressures between 0 and P0. Determine the displacement corresponding to the inner side of the surrounding rock according to step four. Plot in rectangular coordinates ~ The relationship curve is the characteristic curve of the surrounding rock at time t.

[0017] The specific steps for determining the temperature field at each coordinate at time t and the temperature gradient at each coordinate at time t in step three are as follows:

[0018] Determine the coefficients according to the following formula. , :

[0019] ;

[0020] Calculate and determine the steady-state temperature distribution sequence:

[0021] ;

[0022] The root sequence of the following characteristic equation is solved using a search method:

[0023] ;

[0024] ;

[0025] ;

[0026] In the formula, J0(∙) and Y0(∙) are the first and second type Bessel functions of order 0, respectively, and J1(∙) and Y1(∙) are the first and second type Bessel functions of order 1, respectively. These are the eigenvalues ​​to be solved; (∙) is the derivative of the function J0(∙); (∙) is the derivative of the function Y0(∙);

[0027] These root sequences are ordered as follows Arrange the i values ​​(i=1,2,3,…) in ascending order, and for each i, calculate the following sequence of characteristic function values:

[0028] ;

[0029] Numerical integration is used to calculate the following sequence of characteristic function chord lengths:

[0030] ;

[0031] For each i, the corresponding coefficients are calculated and determined through numerical integration:

[0032] ;

[0033] Determine the temperature field at each coordinate at time t using the following formula:

[0034] ,in It is the thermal diffusivity of the surrounding rock calculated in step one;

[0035] The number of terms M in the series can be selected according to the required precision.

[0036] At the same time, determine the temperature gradient at each coordinate at time t;

[0037] ,in, It is the symbol for solving partial derivatives.

[0038] Step 4: Determine the displacement of the inner side of the surrounding rock under a certain support pressure at time t using the following steps. ;

[0039] Determine the plane strain parameters of elastic modulus, Poisson's ratio, and coefficient of thermal expansion;

[0040] ;

[0041] ;

[0042] ;

[0043] Calculate the temperature rise inside the surrounding rock:

[0044] ;

[0045] Based on the temperature gradient determined in step three, calculate the following relevant variables:

[0046] ;

[0047] Calculate and determine the following two numerical integrals:

[0048] ;

[0049] ;

[0050] Given the inner support pressure of the surrounding rock Determine the following two coefficients:

[0051] ;

[0052] ;

[0053] The coefficients are determined according to the following formula. , :

[0054]

[0055]

[0056] Apply the following formula to calculate the support pressure. Corresponding displacement of the inner side of the surrounding rock:

[0057] .

[0058] After step five, select another time point and repeat the process from step three to step five to obtain the surrounding rock characteristic curve at another heat transfer time point. By repeating this process, a family of surrounding rock characteristic curves considering heat transfer temperature correction at multiple times can be obtained.

[0059] This invention facilitates more accurate plotting of surrounding rock characteristic curves in variable temperature environments, laying the foundation for the design of shared load-bearing capacity between surrounding rock and support structures in such environments. Considering that high-temperature surrounding rock conditions are frequently encountered during deep shaft and tunnel construction, while the construction environment must be kept at a comfortable human temperature, this results in the cooling of the high-temperature surrounding rock. In such variable temperature environments, the surrounding rock characteristic curve needs to consider temperature correction; otherwise, the load acting on the support structure may be overestimated or underestimated, leading to material waste or reduced engineering safety.

[0060] This invention involves testing the initial ground stress, initial temperature, working area air temperature, and convective heat transfer coefficient of the surrounding rock wall at the engineering site. Simultaneously, samples are taken and tested in the laboratory for parameters such as thermal conductivity, specific heat, density, and thermal expansion coefficient of the surrounding rock. Then, according to the process, a series of formulas are used to calculate the displacement of the surrounding rock under different support pressures at a given heat transfer moment. The support pressure-displacement relationship of the surrounding rock at that moment is plotted, and a characteristic curve of the surrounding rock considering temperature correction can be obtained at that moment. By plotting the characteristic curves of the surrounding rock at different moments, a family of characteristic curves of the surrounding rock considering temperature correction can be obtained.

[0061] This invention utilizes laboratory tests on the thermal and mechanical properties of excavated rock samples, along with on-site tests of initial ground pressure, ground temperature, and working area parameters. Through procedural formula calculations and curve plotting, it generates characteristic curves of the surrounding rock considering temperature corrections at different heat transfer stages. This method offers advantages such as a simple process, high operability, and wide applicability. Compared to conventional surrounding rock characteristic curves, it corrects for errors caused by temperature variations during heat transfer, avoiding material waste due to overestimating wellbore loads and preventing safety hazards caused by underestimating wellbore loads. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the calculation model;

[0063] Figure 2 These are characteristic curves of the surrounding rock at typical heat transfer moments;

[0064] In the diagram: 1-High-temperature surrounding rock zone; 2-Temperature-controlled working area. Detailed Implementation

[0065] To clearly illustrate the technical features of this patent, the following detailed description is provided through specific embodiments and in conjunction with the accompanying drawings.

[0066] The specific implementation steps are as follows:

[0067] Step 1: Sampling and physical property testing of surrounding rock;

[0068] Sampling was conducted on the surrounding rock excavated at the site. Due to the favorable conditions of the surrounding rock in the deeper strata, larger rock blocks were selected and processed into standard specimens in the laboratory. Mechanical and thermal parameters were tested according to standard procedures. These tests all follow standard procedures and were conducted in accordance with those procedures. The laboratory tests yielded an elastic modulus of the surrounding rock of E=60GPa and a Poisson's ratio. =0.3, thermal conductivity k=1.5W / (m·K), density ρ=2000kg / m³ 3 Specific heat c = 2100 J / (kg·K), coefficient of thermal expansion a = 1.5 10 -5 K-1 .

[0069] Calculate the thermal diffusivity of the surrounding rock using the following formula. , .

[0070] Step 2: On-site parameter testing;

[0071] Field parameter testing can be conducted, with multiple tests performed at various locations and the average value taken. The final test results show an initial rock stress P0 = 50 MPa and an initial temperature... =80℃, working face air temperature =28℃, convection heat transfer coefficient inside the surrounding rock h=20 W / (m²) 2 ·K);

[0072] Step 3: Calculate the temperature field distribution at time t;

[0073] The rough diameter of the well shaft excavation is 10m, therefore the inner side of the surrounding rock =5m, while the outer boundary of the surrounding rock is taken as =50m.

[0074] Given The coordinate sequence r is evenly spaced, because numerical integration of the computational domain will be performed later, requiring a relatively large number of points; preferably more than 1000 points. The coordinates are determined by equal intervals between 2000 coordinates, which is the vector sequence r. In other words, the vector sequence r = (r... a , r a +δ, r a +2δ, r a +3δ,…, r b ), where δ=(r b -r a ) / 2000.

[0075] Determine the coefficients according to the following formula. , ;

[0076] ;

[0077] Calculate and determine the steady-state temperature distribution sequence;

[0078] ;

[0079] The root sequence of the following characteristic equation is solved using a search method;

[0080] ;

[0081] ;

[0082] ;

[0083] In the formula, J0(∙) and Y0(∙) are the first and second type Bessel functions of order 0, respectively, and J1(∙) and Y1(∙) are the first and second type Bessel functions of order 1, respectively.

[0084] These root sequences are ordered as follows (i=1,2,3,…) arranged in ascending order. For each i, calculate the following sequence of characteristic function values;

[0085] ;

[0086] The following sequence of characteristic function chord lengths is calculated using numerical integration;

[0087] ;

[0088] For each i, the corresponding coefficients are calculated and determined through numerical integration;

[0089] ;

[0090] Determine the temperature at each coordinate in the vector r at time t using the following formula;

[0091] ;

[0092] The number of terms M in the above formula is 2000.

[0093] At the same time, determine the temperature gradient at each position coordinate in the r vector at time t;

[0094] .

[0095] Step 4: Determine the displacement of the surrounding rock under a certain support pressure at time t;

[0096] Determine the plane strain parameters of elastic modulus, Poisson's ratio, and coefficient of thermal expansion;

[0097] ;

[0098] ;

[0099] ;

[0100] Calculate the temperature rise inside the surrounding rock;

[0101] ;

[0102] Based on the temperature gradient determined in step three, calculate the following relevant variables;

[0103] ;

[0104] Calculate and determine the following two numerical integrals;

[0105] ;

[0106] ;

[0107] In 0~ Between, select a certain support pressure on the inner side of the surrounding rock. Determine the following two coefficients;

[0108] ;

[0109] ;

[0110] The coefficients are determined according to the following formula. , ;

[0111] ;

[0112] ;

[0113] Apply the following formula to calculate the support pressure. The corresponding displacement of the inner side of the surrounding rock;

[0114] ;

[0115] Step 5: Draw a family of surrounding rock characteristic curves considering temperature correction;

[0116] Select multiple support pressures between 0 and P0. The interval [0, P0] can be divided into several equal parts, selected sequentially from smallest to largest. The displacement corresponding to the inner side of the surrounding rock is determined according to step four. Plot in rectangular coordinates ~ The relationship curve is the characteristic curve of the surrounding rock at time t.

[0117] Choose another moment and repeat steps three through five to obtain the surrounding rock characteristic curve at another heat transfer moment. By repeating this process, a family of surrounding rock characteristic curves considering heat transfer temperature corrections at multiple moments can be obtained. Figure 2 The figure shows the characteristic curves of the surrounding rock at 0.1 hours and 20 hours of heat transfer.

[0118] There are many specific ways to implement this invention. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A method for determining the characteristic curve of surrounding rock considering temperature correction, characterized in that, Follow these steps: Step 1: Sampling and physical property testing of surrounding rock; Samples were taken from the surrounding rock excavated on site, and the elastic modulus E and Poisson's ratio of the surrounding rock samples were measured. The thermal conductivity k, density ρ, specific heat c, and coefficient of thermal expansion a of the sample were tested in the laboratory. Calculate the thermal diffusivity of the surrounding rock based on the test parameters. , ; Step 2: On-site parameter testing; At the working face, the initial in-situ stress P0 and initial temperature of the surrounding rock were measured. Average air temperature at the working face The convective heat transfer coefficient h on the inner side of the surrounding rock was tested. Step 3: Calculate the temperature field distribution at time t; Select the surrounding rock calculation area, where the inner side of the surrounding rock is... , refers to the rough excavation path of a shaft or tunnel, and the outer boundary of the surrounding rock. It needs to be outside the excavation impact zone. The calculation area for the surrounding rock is selected above 50m. . Given Given a sequence of equally spaced position coordinates r, determine the temperature field at each position coordinate at time t, and determine the temperature gradient at each position coordinate at time t. Step 4: Determine the displacement of the inner side of the surrounding rock under a certain support pressure at time t. ; Step 5: Draw a family of surrounding rock characteristic curves considering temperature correction; Select multiple support pressures between 0 and P0. Determine the displacement corresponding to the inner side of the surrounding rock according to step four. Plot in rectangular coordinates ~ The relationship curve is the characteristic curve of the surrounding rock at time t.

2. The method for determining the characteristic curve of surrounding rock considering temperature correction according to claim 1, characterized in that, The specific steps for determining the temperature field at each coordinate at time t and the temperature gradient at each coordinate at time t in step three are as follows: Determine the coefficients according to the following formula. , : ； Calculate and determine the steady-state temperature distribution sequence: ； The root sequence of the following characteristic equation is solved using a search method: ； ； ； In the formula, J0(∙) and Y0(∙) are the first and second type Bessel functions of order 0, respectively, and J1(∙) and Y1(∙) are the first and second type Bessel functions of order 1, respectively. These are the eigenvalues ​​to be solved; (∙) is the derivative of the function J0(∙); (∙) is the derivative of the function Y0(∙); These root sequences are ordered as follows Arrange the i values ​​(i=1,2,3,…) in ascending order, and for each i, calculate the following sequence of characteristic function values: ； Numerical integration is used to calculate the following sequence of characteristic function chord lengths: ； For each i, the corresponding coefficients are calculated and determined through numerical integration: ； Determine the temperature field at each coordinate at time t using the following formula: ,in It is the thermal diffusivity of the surrounding rock calculated in step one; The number of terms M in the series can be selected according to the required precision. At the same time, determine the temperature gradient at each coordinate at time t; ,in, It is the symbol for solving partial derivatives.

3. The method for determining the characteristic curve of surrounding rock considering temperature correction according to claim 1, characterized in that, Step 4: Determine the displacement of the inner side of the surrounding rock under a certain support pressure at time t using the following steps. ; Determine the plane strain parameters of elastic modulus, Poisson's ratio, and coefficient of thermal expansion; ； ； ； Calculate the temperature rise inside the surrounding rock: ； Based on the temperature gradient determined in step three, calculate the following relevant variables: ； Calculate and determine the following two numerical integrals: ； ； Given the inner support pressure of the surrounding rock Determine the following two coefficients: ； ； The coefficients are determined according to the following formula. , : Apply the following formula to calculate the support pressure. Corresponding displacement of the inner side of the surrounding rock: 。 4. The method for determining the characteristic curve of surrounding rock considering temperature correction according to claim 1, characterized in that, After step five, select another time point and repeat the process from step three to step five to obtain the surrounding rock characteristic curve at another heat transfer time point. By repeating this process, a family of surrounding rock characteristic curves considering heat transfer temperature correction at multiple times can be obtained.

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