A calculation method for the comprehensive elastic modulus of rock strata for tunnel stability analysis

Abstract

The present invention belongs to the field of underground engineering construction, and specifically relates to a method for calculating the comprehensive elastic modulus of rock strata for tunnel stability analysis. The method includes the following steps: S100 - Establish a mechanical model of multi-layer rock strata with equal thickness. Each rock stratum in the model is a horizontal rock stratum. The Z-axis of the model restricts the displacement in the Z direction at the vertical boundary surface, and the Y-axis restricts the displacement in the Y direction at the vertical boundary surface. The upper surface of the model is subjected to the vertical pressure of the overlying rock strata, and its numerical value is; S200 - Use the physical equations under plane strain conditions, and combine the boundary conditions and deformation coordination conditions of the rock stratum model to establish the physical equations of each layer of the rock stratum: S300 - Use the characteristic that the action direction is perpendicular to the rock stratum surface to further determine the physical equation of the i-th layer of the rock stratum; S400 - Based on the thickness of each rock stratum and the principle of deformation superposition, obtain the deformation of the total rock stratum in the x direction; S500 - Establish the overall Poisson's ratio formula of the rock stratum and calculate the linear strain of the n-layer rock stratum as a whole in the x direction; S600 - Calculate the overall comprehensive elastic modulus of the rock stratum.

Description

Technical Field

[0001] The present invention belongs to the field of underground engineering construction, and specifically relates to a method for calculating the comprehensive elastic modulus of rock strata for tunnel stability analysis. Background Art

[0002] The mechanical properties of geological bodies are the basis for the design and construction of underground engineering. Due to the sedimentation during the diagenetic process in shallow strata, they have distinct layered structural characteristics. The large number of rock strata and their diverse mechanical properties result in many parameters in design calculations. Tunnel engineering is a typical underground project. There are a large number of tunnel projects under construction and to be built in China. Currently, the main methods for tunnel support design include the design method of standard support models, empirical analogy method, analytical method, and numerical calculation method. The design method of standard support models is applicable when there is a standard support model. When there is no standard support model, the empirical analogy method or analytical method needs to be selected according to the rock mass conditions. The empirical analogy method depends on the knowledge reserve of engineering technicians, etc., and it is easy to cause completely different understandings of the same problem by different technicians. The numerical calculation method is limited by equipment and the skills of engineers and is difficult to be popularized and applied in construction units. The calculation of the analytical method usually brings inconvenience to designers and construction technicians due to numerous calculation parameters. Technicians usually use the empirical method to deal with the problems they face under time constraints.

[0003] Therefore, considering the simplicity of design calculations, the present invention provides a method for calculating the comprehensive elastic modulus of rock strata for tunnel stability analysis, which converts multiple parameters of the original elastic modulus into one parameter, improves the calculation efficiency, reduces the calculation difficulty, and facilitates the application by on-site technicians. Summary of the Invention

[0004] The present invention provides a method for calculating the comprehensive elastic modulus of rock strata for tunnel stability analysis to solve the problems of numerous and complex surrounding rock parameters in tunnel stability calculations and low downstream analysis and calculation efficiency.

[0005] The present invention adopts the following technical solutions: A method for calculating the comprehensive elastic modulus of rock strata for tunnel stability analysis includes the following steps.

[0006] S100 - Establish a mechanical model of multi-layer equal-thickness rock strata ( Figure 1 as shown), each rock stratum in the model is a horizontal rock stratum, the Z-axis vertical boundary of the model restricts the displacement in the Z direction, the Y-axis vertical boundary restricts the displacement in the Y direction, and the upper surface of the model is subjected to the vertical pressure of the overlying rock strata, and its numerical value is .

[0007] S200 - Use the physical equation under plane strain conditions, and combine the boundary conditions and deformation coordination conditions of the rock stratum model to establish the physical equations of each layer of the rock stratum:

[0008]

[0009] (1)

[0010] Where i is the number of the rock layer, is the strain of the ith rock layer in the x direction, is the strain in the y direction of the i-th rock layer, is the normal stress in the x direction of the rock formation, is the normal stress in the y direction of the rock formation, is the elastic modulus of the ith rock layer, is the Poisson's ratio of the ith rock layer.

[0011] S300~Use The characteristic of the action direction being perpendicular to the rock layer is that the physical equation of the i-th rock layer is further determined as:

[0012] (2).

[0013] S400 - Based on the thickness of each rock layer and the deformation superposition principle, the deformation of the total rock layer in the x direction is obtained;

[0014] (3)

[0015] Where D is the total deformation of the rock layer in the x direction, is the thickness of the i-th rock layer;

[0016] Then the comprehensive linear strain of the n-layer rock layer in the x direction is:

[0017] (4).

[0018] S500~Establish the Poisson's ratio formula for the entire rock formation:

[0019] (5)

[0020] Then the linear strain of the n-layer rock layer in the x direction is:

[0021] (6)

[0022] S600~Solve Formula 4 and Formula 6 to obtain the overall comprehensive elastic modulus of the rock formation:

[0023] .

[0024] Compared with the prior art, the present invention has the following beneficial effects: By using the stress and deformation characteristics of the tunnel and combining with the plane strain physical equation, a mechanical model is established to describe the mechanical model and physical equation of the multi-layer rock formation. At the same time, a calculation formula for the comprehensive Poisson's ratio of the multi-layer rock formation is introduced. For different combinations of multi-layer rock formations, it is necessary to determine the elastic modulus, Poisson's ratio, and thickness of each rock layer. The calculation formula of the present invention has a clear physical meaning. The overall comprehensive elastic modulus and Poisson's ratio of the rock formation can be determined by manual calculation, or can be calculated through excel or computer programs. This enables the stress and displacement of the tunnel that could not be calculated and analyzed by the original analytical method to be quickly realized, greatly expanding the scope of application of the method and improving work efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is the mechanical model diagram of the rock formation;

[0026] Figure 2 is the calculation step diagram of the calculation method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0028] A calculation method for the comprehensive elastic modulus of a rock formation for tunnel stability analysis includes the following steps.

[0029] S100 - Establish a mechanical model of multi-layer equal-thickness rock formations ( Figure 1 as shown), each rock layer in the model is a horizontal rock layer, the Z-axis vertical boundary surface of the model restricts the displacement in the Z direction, the Y-axis vertical boundary surface restricts the displacement in the Y direction, and the upper surface of the model is subjected to the vertical pressure of the overlying rock formation, and its numerical value is .

[0030] S200 - Use the physical equation under plane strain conditions, and combine with the boundary conditions and deformation coordination conditions of the rock formation model to establish the physical equations of each layer of the rock formation:

[0031]

[0032] (1)

[0033] where i is the number of the rock layer, is the strain in the x direction of the i-th rock layer, is the strain of the i-th rock stratum in the y direction, is the normal stress of the rock stratum in the x direction, is the normal stress of the rock stratum in the y direction, is the elastic modulus of the i-th rock stratum, is the Poisson's ratio of the i-th rock stratum.

[0034] S300 - Utilize the characteristic that the action direction is perpendicular to the rock stratum surface to further determine the physical equation of the i-th rock stratum as:

[0035] (2).

[0036] S400 - Based on the thickness of each rock stratum and the principle of deformation superposition, obtain the deformation of the total rock stratum in the x direction;

[0037] (3)

[0038] where D is the total deformation of the rock stratum in the x direction, is the thickness of the i-th rock stratum;

[0039] Then the comprehensive linear strain shown by the n-layer rock stratum as a whole in the x direction is:

[0040] (4).

[0041] S500 - Establish the formula for the overall Poisson's ratio of the rock stratum:

[0042] (5)

[0043] Then the linear strain of the n-layer rock stratum as a whole in the x direction is:

[0044] (6)

[0045] S600 - Solve formulas 4 and 6 to obtain the overall comprehensive elastic modulus of the rock stratum:

[0046] .

[0047] A long and small-section circular water conveyance tunnel is located in a rock mass composed of multiple rock strata. The diameter a of the tunnel is 2m. The tunnel is in a uniform stress field with a stress p0 = 20MPa. There are 5 layers of surrounding rock within the influence range of the tunnel. The mechanical parameters (elastic modulus and Poisson's ratio) and thickness of each layer of rock stratum are: E1 = 7000MPa, v 1 = 0.25, d 1 = 1.5m, E2 = 3500MPa, v 2 = 0.20, d 2 = 0.5m, E3 = 800MPa, v 3 = 0.35,d 3 = 0.8 m, E4 = 5000 MPa, v 4 = 0.28, d 4 = 1.0 m, E5 = 2500 MPa, v 5 = 0.23, d 5 = 0.5 m, the comprehensive Poisson's ratio and comprehensive elastic modulus of the rock mass where the tunnel surrounding rock is located are calculated according to Equations (5) and (7):

[0048] ,

[0049] 2089 MPa.

[0050] Therefore, the comprehensive elastic modulus and Poisson's ratio of the tunnel surrounding rock are 0.267 and 2089 MPa.

[0051] On the basis of obtaining the comprehensive elastic modulus and Poisson's ratio of the tunnel surrounding rock, the existing results - the analytical solutions of the stress and displacement of a circular tunnel in a homogeneous rock mass can be used to solve the stress in the tunnel surrounding rock and the displacement on the tunnel surface. Here, taking the calculation of the approach amount of the tunnel roof and floor as an example, the calculation is as follows:

[0052] , is the approach amount of the tunnel roof and floor. Accordingly, the approach amount of the tunnel roof and floor is 2.4 cm.

[0053] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A calculation method for the comprehensive elastic modulus of rock strata for tunnel stability analysis, characterized in that: including the following steps, S100~Establish a mechanical model of multi-layer rock strata with equal thickness. Each rock stratum in the model is a horizontal rock stratum. The Z-axis vertical boundary surface of the model restricts the displacement in the Z direction, and the Y-axis vertical boundary surface restricts the displacement in the Y direction. The upper surface of the model is subjected to the vertical pressure of the overlying rock strata, and its numerical value is ; S200~Utilize the physical equations under plane strain conditions, and combine the boundary conditions and deformation coordination conditions of the rock stratum model to establish the physical equations of each layer of the rock stratum: S300~Utilization By making use of the characteristic that the acting direction is perpendicular to the rock bedding plane, further determine the physical equation of the i-th layer of rock formation; S400~Based on the thickness of each rock stratum and the principle of deformation superposition, obtain the deformation of the total rock stratum in the x direction; In step S400, the deformation of the total rock stratum in the x direction is: （3） where D is the total deformation of the rock formation in the x direction, is the thickness of the i-th rock formation, is the Poisson's ratio of the i-th rock formation, is the elastic modulus of the i-th rock formation; Then the comprehensive linear strain exhibited by the n-layer rock stratum as a whole in the x direction is: （4）； S500~Establish the overall Poisson's ratio formula of the rock stratum and calculate the linear strain of the n-layer rock stratum as a whole in the x direction; In step 500, the overall Poisson's ratio formula of the rock stratum is: （5） Then the linear strain of the n-layer rock stratum as a whole in the x direction is: （6）； S600~Calculate the overall comprehensive elastic modulus of the rock stratum; Solve formulas 4 and 6, and the calculation formula for the overall comprehensive elastic modulus of the rock stratum is: （7）。 2. The method for calculating the comprehensive elastic modulus of rock strata for tunnel stability analysis according to claim 1, wherein: In the described S200, the physical equations of each layer of the rock stratum are: （1） where i is the number of the rock stratum, is the strain of the i-th rock stratum in the x direction, is the strain of the i-th rock stratum in the y direction, is the normal stress of the rock stratum in the x direction, is the normal stress of the rock stratum in the y direction, is the elastic modulus of the i-th rock stratum, is the Poisson's ratio of the i-th rock stratum.

3. The method for calculating the comprehensive elastic modulus of rock strata for tunnel stability analysis according to claim 2, characterized in that: The physical equation of the i-th layer of the rock stratum in the described step S300 is: （2）。

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