Equivalent replacement calculation method acting on unbalanced load around circular roadway hole

Abstract

The invention provides an equivalent replacement calculation method for unbalanced load acting on the periphery of a circular roadway hole, belongs to the technical field of underground engineering, and solves the problem of displacement multi-value performance. The invention relates to an equivalent replacement calculation method for an unbalanced load acting on the periphery of a circular roadway, which comprises the following steps of: equivalently splitting a stress field of the unbalanced load acting on the periphery of the circular roadway; and respectively calculating a stress field of the central point of the hole under the action of equivalent concentrated force and a stress field of the primary surface force and Kelvin stress at the periphery of the hole under the superposed action of release load of the primary surface force and Kelvin stress at the periphery of the hole, so as to finally obtain a stress value of any point outside the circular tunnel under the action of unbalanced load. When the stress field is calculated, the displacement unitary property can be considered, the influence of the displacement multi-valued property on the calculation of the stress field of the circular roadway is thoroughly eliminated, and the calculation process is simple and convenient.

Description

Technical Field

[0001] This invention belongs to the field of underground engineering technology and relates to the calculation of unbalanced loads around tunnels, particularly an equivalent replacement calculation method for unbalanced loads acting around circular tunnels. Background Technology

[0002] In recent years, with the commencement of major national projects, the construction of underground tunnels (groups) and mines has developed rapidly. However, during tunnel construction, the excavation process causes changes in the stress field of the surrounding rock, resulting in significant deformation of the surface and adjacent buildings (structures), which can even lead to engineering accidents in severe cases.

[0003] Therefore, accurate calculation of the stress field of the surrounding rock after tunnel excavation and the stress field of the entire area after support is of great theoretical significance and application value for guiding engineering construction.

[0004] According to the theory of elasticity, when the resultant force on the periphery of a circular tunnel opening is not zero, the single-valuedness of displacement must be considered when calculating the stress field. If the single-valuedness of displacement is not considered, the stress field will cause a certain error.

[0005] To address the aforementioned limitations, this invention employs an equivalent substitution calculation method for unbalanced loads acting around a circular tunnel, which can completely eliminate the influence of displacement multivalues, ensuring that the surface forces around the tunnel are always in equilibrium during the calculation of the tunnel stress field. Summary of the Invention

[0006] The purpose of this invention is to address the aforementioned problems in existing technologies by proposing an equivalent replacement calculation method for unbalanced loads acting around a circular tunnel. This method considers the single-valued nature of displacement, completely eliminates the influence of multi-valued displacement on the stress field calculation of a circular tunnel, and simplifies the calculation process.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] An equivalent replacement calculation method for unbalanced loads acting around a circular tunnel is proposed. The unbalanced loads acting around the circular tunnel are equivalently decomposed into: stress field one generated by the resultant force acting at the center of the tunnel, and stress field two under the superposition of the original surface force and Kelvin stress under the released load around the tunnel, so as to calculate the stress value at any point outside the circular tunnel under the action of unbalanced loads.

[0009] Furthermore, this includes the following steps:

[0010] S1: Based on the superposition principle, the stress field of the unbalanced load acting around the circular tunnel is equivalently decomposed into stress field one and stress field two, where:

[0011] Stress field 1: The stress field at the center point of a circular tunnel opening in an infinite plane, subjected to an equivalent concentrated force;

[0012] Stress field 2: The stress field under the superposition of the original surface force and Kelvin stress around the circular tunnel and the released load around the circular tunnel.

[0013] S2: The resultant force of the stress on the periphery of the circular tunnel at the center of the tunnel in the first stress field calculation;

[0014] S3: In the calculation of stress field one, the stress at any point in the surrounding rock mass of the circular tunnel; in the calculation of stress field two, the radial stress and tangential stress around the circular tunnel.

[0015] S4: Obtain the corresponding stress components in stress field two through the stress function; the stress components are: the stress at any point outside the circular tunnel;

[0016] S5: Based on the equations in S1-S4 above, the final stress value is calculated;

[0017] The final stress value is the stress value at any point outside the circular tunnel under unbalanced load.

[0018] Furthermore, in S2, the resultant force of the stresses acting around the perimeter of the circular tunnel at the center of the tunnel is expressed as follows:

[0019] ;

[0020] The calculation shows that:

[0021] ;

[0022] In the formula:

[0023] The radial stress experienced around the perimeter of a circular tunnel.

[0024] This refers to the tangential stress around the perimeter of a circular tunnel.

[0025] Where U, V, X, and W are constants, L is the radius of the circular tunnel, and α is the angle between the stress application point and the center of the circular tunnel; F x F y These are the resultant forces in the x and y directions, respectively.

[0026] Furthermore, in S3, the stress at any point within the surrounding rock mass of the roadway is expressed as follows:

[0027] ;

[0028] ;

[0029] ;

[0030] In the formula: denoted as , where is the distance from any point within the surrounding rock mass to the center of the circular tunnel, and μ is Poisson's ratio.

[0031] Furthermore, in S3, the radial stress and tangential stress around the circular tunnel are expressed as follows:

[0032] Radial stress:

[0033] ;

[0034] Tangential stress:

[0035] ;

[0036] Right now,

[0037] ;

[0038] ;

[0039] In the formula:

[0040] ;

[0041] .

[0042] Furthermore, in S4, the stress function is expressed as follows:

[0043] ;

[0044] The stress components are obtained through the stress function, that is, the stress at any point outside the circular tunnel is expressed as follows:

[0045] ;

[0046] ;

[0047] ;

[0048] Based on the above calculation formula, the radial stress and tangential stress around the circular tunnel are obtained as follows:

[0049] Radial stress: ;

[0050] Tangential stress: ;

[0051] Based on the above equation, we can conclude that:

[0052] ;

[0053] .

[0054] Furthermore, in S5, the radial normal stress, circumferential normal stress, and shear stress are calculated and expressed as follows:

[0055] ;

[0056] ;

[0057] .

[0058] Compared with the prior art, the present invention has the following advantages:

[0059] This invention performs equivalent decomposition and calculation of the stress field of unbalanced loads acting around a circular tunnel. The calculation process not only considers the single-valuedness of displacement, but also completely eliminates the influence of the multi-valuedness of displacement on the calculation of the stress field of the circular tunnel. The calculation process is simple and the calculation method is straightforward. Attached Figure Description

[0060] Figure 1 This is a schematic diagram of the calculation process of the present invention.

[0061] Figure 2 This is a schematic diagram of the resultant force of the stress on the periphery of a circular tunnel in an infinite plane at the center of the tunnel in S1 of the present invention.

[0062] Figure 3 This is a schematic diagram of how the stress field of the unbalanced load acting on the periphery of the circular tunnel in S2 is equivalently split into stress field one and stress field two in this invention. Detailed Implementation

[0063] The following are specific embodiments of the present invention, which are described in conjunction with the accompanying drawings. However, the present invention is not limited to these embodiments.

[0064] like Figures 1-3 As shown, this embodiment provides an equivalent replacement calculation method for unbalanced loads acting around a circular tunnel. The unbalanced loads acting around the circular tunnel are equivalently decomposed into: a stress field one generated by the resultant force acting at the center of the tunnel, and a stress field two under the superposition of the original surface force and Kelvin stress under the released load around the tunnel, so as to calculate the stress value at any point outside the circular tunnel under the action of unbalanced loads.

[0065] This invention specifically includes the following steps:

[0066] S1: Based on the superposition principle, the stress field of the unbalanced load acting around the circular tunnel is equivalently decomposed into stress field one and stress field two, such as... Figure 3 As shown, where:

[0067] Stress field 1: The stress field at the center point of a circular tunnel opening in an infinite plane, subjected to an equivalent concentrated force;

[0068] Stress field two: The stress field under the superposition of the original surface force and Kelvin stress around the circular tunnel and the released load around the circular tunnel.

[0069] S2: In the calculation of stress field one, the resultant force of the stress on the periphery of the circular roadway at the center of the roadway is expressed as follows:

[0070] ;

[0071] The calculation shows that:

[0072] ;

[0073] In the formula:

[0074] The radial stress experienced around the perimeter of a circular tunnel.

[0075] This refers to the tangential stress around the perimeter of a circular tunnel.

[0076] Where U, V, X, and W are constants, L is the radius of the circular tunnel, and α is the angle between the stress application point and the center of the circular tunnel; F x F y These are the resultant forces in the x and y directions, respectively.

[0077] S3: In the calculation of stress field one, the stress at any point in the surrounding rock mass of the circular tunnel is represented as follows:

[0078] ;

[0079] ;

[0080] ;

[0081] In the formula: denoted as , where is the distance from any point within the surrounding rock mass to the center of the circular tunnel, and μ is Poisson's ratio.

[0082] In the calculation of stress field two, the radial and tangential stresses around the circular tunnel are expressed as follows:

[0083] Radial stress:

[0084] ;

[0085] Tangential stress:

[0086] ;

[0087] Right now,

[0088] ;

[0089] ;

[0090] In the formula:

[0091] ;

[0092] .

[0093] S4: Calculate the stress components corresponding to stress field two, that is, the stress at any point outside the circular tunnel;

[0094] The stress function is expressed as follows:

[0095] ;

[0096] Stress components are represented as follows:

[0097] ;

[0098] ;

[0099] ;

[0100] Based on the above calculation formula, the radial stress and tangential stress around the circular tunnel are obtained as follows:

[0101] Radial stress: ;

[0102] Tangential stress: ;

[0103] Based on the above equation, we can conclude that:

[0104] ;

[0105] .

[0106] S5: Based on the equations in S1-S4 above, the stress value at any point outside the circular tunnel under unbalanced load is calculated.

[0107] The radial normal stress, circumferential normal stress, and shear stress are represented as follows:

[0108] ;

[0109] ;

[0110] .

[0111] In summary, this invention is applicable to calculating the stress value at any point outside a circular tunnel opening when the tunnel is subjected to unbalanced loads. The calculation can take into account the single-valuedness of displacement, completely eliminating the influence of multi-valued displacement on the stress field calculation of the circular tunnel, and the calculation process is simple.

[0112] Example 1:

[0113] like Figure 2 As shown, for a circular tunnel with radius l, a uniformly distributed surface force f in the x-direction acts around the perimeter of the tunnel opening. x and the uniformly distributed surface force f in the y direction y .

[0114] The resultant force at the center of the circular tunnel is:

[0115] ;

[0116] ;

[0117] The radial and tangential stresses along the perimeter of the tunnel are expressed as:

[0118] ;

[0119] Based on step 1, we obtain:

[0120] ;

[0121] Therefore, the stress at any point outside the hole is:

[0122] ;

[0123] ;

[0124] .

[0125] In existing technologies, such as Chen Zimeng's "Analytical Methods in Surrounding Rock Mechanics Analysis" published by the Coal Industry Press, a calculation method using complex variable functions is described, with the following results:

[0126] ;

[0127] ;

[0128] The stress components expressed using complex functions are:

[0129] ;

[0130] ;

[0131] The stress components obtained by substituting are respectively

[0132] ;

[0133] ;

[0134] .

[0135] The results obtained by the complex function method are consistent with those of this invention, but the principle of the complex function method is more complex and the calculation process is more complicated.

[0136] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A method for calculating the equivalent replacement of unbalanced load acting on the circumference of a circular tunnel hole, characterized in that: the unbalanced load acting on the circumference of the circular tunnel is equivalent to the stress field 1 generated by the resultant force acting on the center of the tunnel and the stress field 2 generated by the superimposed action of the release load of the original surface force and Kelvin stress on the circumference of the tunnel, so as to calculate the stress value of any point outside the circular tunnel under the action of the unbalanced load. Comprising the following steps:

2. The equivalent replacement calculation method for unbalanced load acting on the round roadway hole according to claim 1, characterized in that, S1: Based on the superposition principle, the stress field of the unbalanced load acting on the circumference of the circular tunnel is equivalent to the stress field 1 and the stress field 1, wherein: Stress field 1: the stress field of the center point of the circular tunnel hole in the infinite plane under the action of the equivalent concentrated force; Stress field 2: the stress field of the superimposed action of the release load of the original surface force and Kelvin stress on the circumference of the circular tunnel hole; S2: Calculate the resultant force of the stress on the circumference of the circular tunnel in the stress field 1 at the center of the tunnel; S3: Calculate the stress of any point in the surrounding rock mass of the circular tunnel in the stress field 1, and calculate the radial stress and tangential stress of the circumference of the circular tunnel in the stress field 2; S4: Obtain the corresponding stress component in the stress field 2 through the stress function; the stress component is: the stress of any point outside the circular tunnel; S5: Based on the equations in S1-S4 above, the final stress value is calculated; The final stress value is: the stress value of any point outside the circular tunnel under the action of the unbalanced load. In the S2:

3. The equivalent replacement calculation method for unbalanced load acting on the round roadway hole according to claim 2, characterized in that, The resultant force of the stress on the circumference of the circular tunnel at the center of the tunnel is represented as follows: The calculation result is: ； In the S3: ； The stress of any point in the surrounding rock mass of the tunnel is represented as follows: R = radial stress on the circular roadway hole perimeter; T is the tangential stress on the circular roadway hole perimeter; Wherein, U, V, X, W are constants, L is the radius of the circular roadway, and a is the angle between the stress point and the center of the circular roadway; F x , F y are the resultant forces in the x and y directions, respectively.

4. The equivalent replacement calculation method for the unbalanced load acting on the round roadway hole according to claim 3, characterized in that, In the S3: The radial stress and tangential stress of the circumference of the circular tunnel are represented as follows: ； ； ； In the formula: is the distance from any point in the surrounding rock mass to the center of the circular roadway, and μ is the Poisson's ratio.

5. The equivalent replacement calculation method for the unbalanced load acting on the round roadway hole according to claim 4, characterized in that, Radial stress: Tangential stress: That is, ； In the S4: ； The stress function is represented as follows: ； ； The corresponding stress component obtained through the stress function, that is, the stress of any point outside the circular tunnel, is represented as follows: ； 。 6. The equivalent replacement calculation method for the unbalanced load acting on the round roadway hole according to claim 5, characterized in that, According to the above calculation formula, the radial stress and tangential stress of the circumference of the circular tunnel are represented as follows: According to the above equation, we get: ； In the S5, the radial normal stress, hoop normal stress and shear stress are calculated respectively, and represented as follows: ； ； ； ​ Radial stress: ; tangential stress: ; ​ ； 。 7. The method according to claim 6, wherein, ​ ； ； 。

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