Method for predicting collapse height of weak interlayer rock mass with steep dip angle of tunnel based on Principh pressure arch theory

Abstract

A tunnel steep dip angle weak intercalated rock mass collapse height prediction method based on the Principh pressure arch theory comprises the steps that after a tunnel is excavated, a weak intercalated layer is revealed; recording the characters of rock masses in and around the weak intercalated layer, and measuring the occurrence of the weak intercalated layer and the thickness l of the weak intercalated layer; calculating a firmness coefficient f of the rock mass in the weak intercalated layer; if the trend of the weak intercalated layer intersects with the axis of the tunnel at a small angle, and the quality grade of the surrounding rock mass of the weak intercalated layer can reach a preset quality grade or above, an included angle alpha between the arch foot connecting line of the pressure arch and the normal of the wall of the weak intercalated layer is obtained; deriving a prediction formula of the collapse height of the weak intercalated rock mass on the basis of the Principal pressure arch theory, and substituting l, f and alpha into the prediction formula to obtain the collapse height h of the weak intercalated rock mass; the # imgabs0 # imgabs1 # has the advantages that the prediction formula can accurately predict the collapse height of the weak intercalated rock mass, reference can be provided for design and construction of a tunnel containing the weak intercalated rock mass, and the prediction formula has important significance.

Description

Technical Field

[0001] The invention relates to the technical field of collapse height prediction, and in particular to a method for predicting the collapse height of a soft interlayer rock mass with a steep inclination angle in a tunnel based on the Proctor pressure arch theory. Background Art

[0002] Accurate prediction of collapse height is of great significance for tunnel surrounding rock stability evaluation, support scheme design, and construction risk control. At present, scholars at home and abroad mainly predict the collapse height of tunnel surrounding rock through model tests, theoretical analysis, and numerical simulation methods. Among the theoretical analysis models, the Pugh pressure arch theory is the most commonly used. This theory is based on bulk mechanics. Through simple static equilibrium analysis, the pressure arch axis equation and collapse height are derived, and then the surrounding rock loosening pressure can be determined. For example, some scholars have used the pressure arch theory to derive the limit equilibrium height formula of the critical soil cave in karst collapse; some scholars have calculated the loose soil pressure on the top pipe under deep burial conditions based on this theory.

[0003] However, existing research mainly focuses on homogeneous surrounding rocks. For tunnels with weak interlayers, especially the collapse height of weak interlayers, there are few studies and a lack of simple and feasible prediction formulas. However, it is of great significance to study this issue, because weak interlayers, such as small and medium-sized fault fracture zones and interlayer dislocation zones, are quite common in rock masses. As the weak link in the rock mass, they are often the most susceptible to damage. Therefore, it is necessary to further improve the existing technology. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a method for predicting the collapse height of soft interlayer rock mass at steep inclination angle in tunnels based on the Proctor pressure arch theory, with the aim of accurately predicting the collapse height of soft interlayer rock mass in the above-mentioned prior art.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a method for predicting the collapse height of a tunnel with steep inclination and weak interlayer rock mass based on the Proctor pressure arch theory, which is characterized by comprising the following steps:

[0006] Step 1: After tunnel excavation, reveal the weak interlayer;

[0007] Step 2, record the properties of the rock mass in and around the weak interlayer, and measure the occurrence and thickness l of the weak interlayer;

[0008] Step 3: Calculate the strength coefficient f of the rock mass in the weak interlayer. is the internal friction angle of the rock mass in the weak interlayer;

[0009] Step 4: If the direction of the weak interlayer intersects the tunnel axis at a small angle, and the quality grade of the rock mass around the weak interlayer can reach or exceed the preset quality grade, then obtain the angle α between the line connecting the arch foot of the pressure arch and the normal line of the weak interlayer wall, and the arch foot of the pressure arch is located on the intersection line of the weak interlayer wall and the tunnel contour; derive the prediction formula for the collapse height of the weak interlayer rock mass based on the Pugh pressure arch theory, and substitute the thickness of the weak interlayer l, the firmness coefficient f of the rock mass in the weak interlayer and the angle α between the line connecting the arch foot of the pressure arch and the normal line of the weak interlayer wall into the prediction formula, that is, the collapse height h of the weak interlayer rock mass is predicted; the calculation formula of h is:

[0010]

[0011] Preferably, the basic assumptions that the prediction formula needs to meet are:

[0012] Condition 1: The rock mass inside the weak interlayer is a loose medium with a certain cohesive force, and the quality grade of the rock mass around the weak interlayer can reach or exceed the preset quality grade;

[0013] Condition 2: The direction of the weak interlayer intersects the tunnel axis at a small angle;

[0014] Condition 3: The arch foot of the pressure arch is located at the intersection of the weak interlayer wall and the tunnel contour, and the rock mass at the arch foot is stable;

[0015] Condition 4: Do not consider the lateral stress effect.

[0016] In order to obtain a more accurate prediction effect, step 2 also includes the following process:

[0017] Determine whether the properties of the recorded weak interlayer and the surrounding rock mass meet condition one, and determine whether the measured occurrence of the weak interlayer meets condition two. If the properties of the recorded weak interlayer and the surrounding rock mass meet condition one, and the measured occurrence of the weak interlayer meets condition two, execute steps 3 and 4.

[0018] Preferably, in step 4, if the direction of the weak interlayer intersects the tunnel axis at a non-small angle, or the quality grade of the rock mass around the weak interlayer does not reach above the preset quality grade, a numerical simulation method is required to predict the collapse height of the rock mass in the weak interlayer.

[0019] Preferably, the numerical simulation method is a finite element numerical simulation method or a discrete element numerical simulation method.

[0020] Preferably, the quality grade of the rock mass around the weak interlayer in step 4 is obtained through the "Engineering Rock Mass Classification Standard" (GB / T 50218-2014) or the "Specification for Geological Investigation of Hydropower Engineering" (GB 50287-2016).

[0021] Compared with the prior art, the advantages of the present invention are as follows: a prediction formula for the collapse height of the weak interlayer rock mass is derived based on the Proctor pressure arch theory, and according to the prediction formula, it can be known that the collapse height is proportional to the thickness of the weak interlayer; as the properties of the weak interlayer deteriorate (the Proctor strength coefficient decreases), the collapse height first increases slowly and then increases rapidly; as the angle between the line connecting the arch foot of the pressure arch and the normal line of the weak interlayer wall increases, the collapse height shows a trend of first being gentle and then dropping sharply. Therefore, for steeply inclined weak interlayers, when they are exposed on the side walls of the tunnel, collapse is not likely to occur. In general, these conclusions are consistent with engineering knowledge, and the prediction formula can more accurately predict the collapse height of the weak interlayer rock mass, which can provide a reference for the design and construction of tunnels containing weak interlayers, and is of great significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 A typical pattern diagram of the collapse of a steeply inclined weak interlayer rock mass in a tunnel according to an embodiment of the present invention;

[0023] Figure 2 This is a diagram of the mechanical model established in an embodiment of the present invention. DETAILED DESCRIPTION

[0024] The present invention is further described in detail below with reference to the accompanying drawings.

[0025] In this embodiment, the method for predicting the collapse height of a tunnel steep-angle weak interlayer rock mass based on the Proctor pressure arch theory includes the following steps:

[0026] Step 1: After tunnel excavation, reveal the weak interlayer;

[0027] Step 2, record the properties of the rock mass in and around the weak interlayer, and measure the occurrence and thickness l of the weak interlayer;

[0028] Step 3: Calculate the strength coefficient f of the rock mass in the weak interlayer. is the internal friction angle of the rock mass in the weak interlayer;

[0029] Step 4: If the weak interlayer strikes and intersects the tunnel axis at a small angle, and the quality grade of the rock mass around the weak interlayer can reach or exceed the preset quality grade, then obtain the angle α between the line connecting the arch foot of the pressure arch and the normal line of the weak interlayer wall (the arch foot of the pressure arch is located on the intersection line of the weak interlayer wall and the tunnel contour foot); derive the prediction formula for the collapse height of the weak interlayer rock mass based on the Pugh pressure arch theory, and substitute the thickness of the weak interlayer l, the firmness coefficient f of the rock mass in the weak interlayer and the angle α between the line connecting the arch foot of the pressure arch and the normal line of the weak interlayer wall into the prediction formula, that is, the collapse height h of the weak interlayer rock mass is predicted; the calculation formula of h is:

[0030]

[0031] In this embodiment, the quality grade of the rock mass around the weak interlayer is obtained through the Engineering Rock Mass Classification Standard (GB / T50218-2014) or the Hydropower Engineering Site Investigation Specification (GB 50287-2016). The above-mentioned weak interlayer is produced at a steep angle (usually >60°); in this embodiment, the direction of the weak interlayer needs to intersect the tunnel axis at a small angle, which can be simplified to a plane strain situation for analysis, that is, the following condition 2 is met.

[0032] In this embodiment, the typical mode of collapse of the steep-angle weak interlayer rock mass in the tunnel is as follows: Figure 1 As shown in the figure, before tunnel excavation, the rock mass is in a state of stress balance; after tunnel excavation, the stress balance is broken and a loose zone is formed around the tunnel. The weak interlayer has a larger loose zone due to its weak properties (stage one); when the residual strength of the material in the weak interlayer is not enough to support its own loose load, collapse will occur (stage two); for deep buried tunnels, collapse will stabilize after reaching a certain height because an arched bearing structure, namely a pressure arch, is formed in the rock mass.

[0033] The assumptions that need to be met by the above prediction formula are:

[0034] Condition 1: The rock mass inside the weak interlayer is a loose medium with a certain cohesive force, and the quality grade of the rock mass around the weak interlayer can reach or exceed the preset quality grade;

[0035] Condition 2: The direction of the weak interlayer intersects the tunnel axis at a small angle, so it can be analyzed according to the plane strain condition;

[0036] Condition 3: The arch foot of the pressure arch is located at the intersection of the weak interlayer wall and the tunnel contour, and the rock mass at the arch foot is stable;

[0037] Condition 4: Do not consider the lateral stress effect.

[0038] The acquisition theory of the prediction formula in this embodiment is:

[0039] Establish as Figure 2 The mechanical model shown in the figure establishes a rectangular coordinate system with the normal direction of the weak interlayer wall as the x-axis and the direction parallel to the weak interlayer wall as the z-axis; points A and B are the arch feet, and point C is the highest point of the arch; l is the true thickness of the weak interlayer, l c is the span of the right half of the arch; α is the angle between the AB line (arch foot line) and the normal of the weak interlayer wall. Assume that the loose load of the rock mass in the weak interlayer is q, which acts on the pressure arch in a uniformly distributed manner. Different from the conventional symmetric problem, the pressure arch considered in this embodiment is an inclined arch. Through the arch-shaped bearing structure, the loose load of the rock mass in the weak interlayer is converted into an inclined thrust acting on the arch foot.

[0040] Since the pressure arch is in a state of equilibrium, according to the static equilibrium equation,

[0041]

[0042] Where ∑M A Indicates the moment taken about point A; ∑F z It means to find the resultant force of the component forces in the z direction.

[0043] get:

[0044]

[0045] in is the reaction force acting on point A and parallel to the z direction, is the reaction force acting on point B and parallel to the z direction;

[0046] Since the bending moment at any point M(x,z) on the axis of the pressure arch is 0, that is:

[0047] ∑M M =0 (3)

[0048]

[0049] Among them, M M Indicates the moment taken at point M; V B for The sum of the force component of T′ in the z direction, that is, T′ is the oblique thrust acting on the arch foot, and its line of action coincides with the line connecting the arch foot; x represents the x coordinate of point M; z represents the z coordinate of point M; T B is the component of force T′ acting on point B in the x-axis direction, that is, T B =T′cosα.

[0050] get:

[0051]

[0052] dz / dx=(V B -qx) / T B (6)

[0053] When x = l c When dz / dx=0, then:

[0054] V B =ql c (7)

[0055] According to Platts' theory:

[0056] T B ≤V B f (8)

[0057] in, f is the solidity coefficient of the rock mass in the weak interlayer, is the friction angle; to ensure that the pressure arch has sufficient stability in the x-axis direction, take:

[0058] 2T B =V B f (9)

[0059] Substituting formula (7) into formula (9), we get:

[0060]

[0061] because but:

[0062]

[0063] Substituting formula (11) into formula (7), we have:

[0064]

[0065] Let x = l c ,but:

[0066]

[0067] So the landslide height is approximately:

[0068]

[0069] Step 2 also includes the following process:

[0070] Determine whether the recorded properties of the rock mass in and around the weak interlayers meet condition 1, and determine whether the measured occurrence of the weak interlayers meets condition 2. If the recorded properties of the rock mass in and around the weak interlayers meet condition 1, and the measured occurrence of the weak interlayers meet condition 2, then execute steps 3 and 4. On the contrary, if the recorded properties of the rock mass in and around the weak interlayers do not meet condition 1, or the measured occurrence of the weak interlayers does not meet condition 2, the above prediction formula cannot be used to predict the rock collapse height.

[0071] In addition, in step 4, if the weak interlayer strikes and the tunnel axis at a non-small angle, or the quality grade of the rock mass around the weak interlayer does not reach the preset quality grade, a numerical simulation method is required to predict the collapse height of the weak interlayer rock mass. The numerical simulation method in this embodiment is a finite element numerical simulation method or a discrete element numerical simulation method.

[0072] During the construction of the water diversion tunnel, landslides occurred many times due to weak interlayers. Taking 8 typical landslides as examples, the proposed landslide height prediction formula was verified. The basic situation of the landslide cases is shown in Table 1.

[0073] Table 1 Basic information of typical collapse cases

[0074]

[0075] The collapse height is predicted using formula (15) and compared with the actual situation. The results are shown in Table 2. It can be seen that the prediction results have a high accuracy, the absolute error between the predicted value and the actual value is between -0.9 and +0.6m, and the relative error is between -13.9% and 18.2%. Among them, the relative error of 5 collapses is within 10%. It can be seen that the collapse height prediction formula for surrounding rock collapse in tunnels with weak interlayers proposed in the present invention is applicable.

[0076] Table 2 Prediction accuracy evaluation table

[0077]

[0078] According to the prediction formula, the collapse height is proportional to the thickness of the weak interlayer; as the properties of the weak interlayer deteriorate (the Proctor's strength coefficient decreases), the collapse height first increases slowly and then increases rapidly; as the angle between the arch foot of the pressure arch and the normal line of the weak interlayer wall increases, the collapse height shows a trend of first being gentle and then falling sharply. Therefore, for steeply inclined weak interlayers, when they are exposed on the side walls of the tunnel, collapse is not likely to occur. In general, these conclusions are consistent with engineering knowledge.

[0079] This embodiment also involves a computer-readable storage medium, which stores a computer program and can be read and executed by a processor. When the computer program is executed by the processor, the above-mentioned method for predicting the collapse height of soft interlayer rock mass with steep inclination in a tunnel based on the Proctor pressure arch theory is implemented.

[0080] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for predicting the collapse height of soft interlayer rock mass with steep inclination in tunnels based on the Pugh pressure arch theory, which is characterized by The steps include: Step 1: After tunnel excavation, reveal the weak interlayer; Step 2, record the properties of the rock mass in and around the weak interlayer, and measure the occurrence and thickness l of the weak interlayer; Step 3: Calculate the strength coefficient f of the rock mass in the weak interlayer. is the internal friction angle of the rock mass in the weak interlayer; Step 4: If the weak interlayer strikes and intersects the tunnel axis at a small angle, and the quality grade of the rock mass around the weak interlayer can reach or exceed the preset quality grade, then obtain the angle α between the connecting line of the pressure arch foot and the normal line of the weak interlayer wall, and the pressure arch foot is located on the intersection line of the weak interlayer wall and the tunnel contour; Based on the Pugh pressure arch theory, the prediction formula for the collapse height of the weak interlayer rock mass is derived, and the thickness of the weak interlayer l, the strength coefficient f of the rock mass in the weak interlayer and the angle α between the arch foot of the pressure arch and the normal line of the weak interlayer wall are substituted into the prediction formula, that is, the collapse height h of the weak interlayer rock mass is predicted; the calculation formula of h is:

2. The method for predicting collapse height of steeply inclined soft interlayer rock mass in a tunnel according to claim 1 is characterized by: The assumptions that the prediction formula needs to meet are: Condition 1: The rock mass inside the weak interlayer is a loose medium with a certain cohesive force, and the quality grade of the rock mass around the weak interlayer can reach or exceed the preset quality grade; Condition 2: The direction of the weak interlayer intersects the tunnel axis at a small angle; Condition 3: The arch foot of the pressure arch is located at the intersection of the weak interlayer wall and the tunnel contour, and the rock mass at the arch foot is stable; Condition 4: Do not consider the lateral stress effect.

3. The method for predicting collapse height of steeply inclined soft interlayer rock mass in a tunnel according to claim 2 is characterized by: The step 2 also includes the following process: Determine whether the properties of the recorded weak interlayer and the surrounding rock mass meet condition one, and determine whether the measured occurrence of the weak interlayer meets condition two. If the properties of the recorded weak interlayer and the surrounding rock mass meet condition one, and the measured occurrence of the weak interlayer meets condition two, execute steps 3 and 4.

4. The method for predicting collapse height of steep-angle weak interlayer rock mass in a tunnel according to any one of claims 1 to 3, characterized in that: In step 4, if the direction of the weak interlayer intersects the tunnel axis at a non-small angle, or the quality grade of the rock mass around the weak interlayer does not reach the preset quality grade, it is necessary to use a numerical simulation method to predict the collapse height of the rock mass in the weak interlayer.

5. The method for predicting collapse height of soft interlayer rock mass with steep inclination in tunnel according to claim 4 is characterized by: The numerical simulation method is a finite element numerical simulation method or a discrete element numerical simulation method.

6. The method for predicting collapse height of soft interlayer rock mass with steep inclination in tunnel according to claim 4 is characterized by: The quality grade of the rock mass around the weak interlayer in step 4 is obtained through the "Engineering Rock Mass Classification Standard" (GB / T50218-2014) or the "Specification for Site Investigation of Hydropower Engineering" (GB 50287-2016).

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