Calculation method for arch damage area in horizontal layered surrounding rock highway tunnel construction

Abstract

The invention belongs to the technical field of highway tunnel engineering, and discloses a horizontal layered surrounding rock highway tunnel construction arch damage area calculation method, which comprises the following steps of judging a first damage position and calculating a damage length; judging a secondary damage position and calculating a damage length; and judging N (N is greater than 2) damage positions and calculating the damage length. According to the method, the length of the damage area of the arch surrounding rock can be rapidly calculated, so that design of prevention and control measures is guided, and the problems of local chipping, collapse and the like of the horizontal layered surrounding rock are solved.

Description

Technical Field

[0001] The invention belongs to the technical field of highway tunnel engineering, and in particular relates to a method for calculating the arch failure zone during construction of a horizontal layered surrounding rock highway tunnel. Technical Background

[0002] With the rapid development of my country's highway transportation industry, the number of highway tunnels has increased year by year, and it is inevitable that new tunnels will be built in horizontal layered rock formations. Horizontal layered rock has a parallel distribution of bedding structure, and its deformation characteristics and failure mode are affected by the bedding. Unlike other rock masses, it often becomes a very complicated problem under construction disturbance. Engineering practice shows that during the construction of horizontal layered surrounding rock tunnels, the arch is very likely to have engineering problems such as delamination, bending, and even large-scale collapse, which seriously threatens the lives of construction workers, affects the construction progress, and causes huge economic losses.

[0003] At present, many scholars have conducted extensive theoretical research on the top plate of horizontal layered rock tunnels, abstracting it into a beam model or a plate model, analyzing the mechanical properties and failure characteristics of the top plate after tunnel excavation, and proposing corresponding prevention and control measures; however, engineering problems in the construction process still exist and have not been completely solved. Engineering practice shows that during the construction of horizontal layered rock tunnels, the arch surrounding rock is very easy to be damaged under the action of the upper loose load, resulting in a certain span of free surface in the upper surrounding rock, thereby inducing large-scale surrounding rock collapse failure. It can be seen that the destruction of the surrounding rock structure begins with the rupture of the arch surrounding rock. The destruction of the arch surrounding rock is a necessary condition for the collapse of the upper surrounding rock. Maintaining the stability of the arch surrounding rock can essentially solve the problem of collapse failure of horizontal layered surrounding rock. Therefore, how to calculate the length of the arch failure zone in the construction of horizontal layered surrounding rock has become a key issue that needs to be solved urgently. Summary of the invention

[0004] The purpose of the present invention is to overcome the deficiencies in the above-mentioned prior art and to provide a method for calculating the arch failure zone during the construction of a highway tunnel with horizontal layered surrounding rock, so as to guide the design of prevention and control measures during the construction of a highway tunnel with horizontal layered surrounding rock and solve the problems of local block falling and collapse of the horizontal layered surrounding rock.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] According to the stress characteristics, the surrounding rock of the arch is divided into two areas: area I is a variable-section cantilever beam structure, and area II is a cantilever stacked beam structure.

[0007] It is assumed that each rock layer has the same physical and mechanical properties and thickness, fits tightly, maintains coordinated deformation under external loads, has the same bending curvature, and only undergoes multiple orderly linear failures according to the laws of mechanics.

[0008] Step 1: determine the first failure position of the arch surrounding rock and calculate the first failure length of the arch surrounding rock;

[0009] Step 2: determine the secondary failure position of the arch surrounding rock and calculate the secondary failure length of the arch surrounding rock;

[0010] Step 3: Determine the N-time (N>2) failure position of the surrounding rock of the arch, and calculate the N-time failure length of the surrounding rock of the arch.

[0011] The above-mentioned method for calculating the arch failure zone of a horizontal layered surrounding rock highway tunnel construction is characterized in that the judgment condition for the first failure position of the arch surrounding rock in step 1 is:

[0012] The first damage occurs in region I: σ 1-I (x)≥[σ];

[0013] The first damage occurs in region II: σ 1-II (x)≥[σ];

[0014] The surrounding rock of the arch does not fail: σ 1-I (x)<[σ],σ 1-II (x)<[σ];

[0015] Among them, σ 1-I (x) is calculated using formula (2), σ 1-II (x) is calculated using formula (3), [σ] is the ultimate tensile strength of the surrounding rock,

[0016]

[0017] Among them, M z-1 (x) is the bending moment borne by the surrounding rock of the arch under load; σ 1-I (x) is the tensile stress of the surrounding rock in area I; σ 1-II (x) is the tensile stress of each layer of the surrounding rock in area II; x is the horizontal distance of a certain section from the origin of the coordinate system; γ is the weight of the surrounding rock; q is the loose load on the upper part of the tunnel; R is the radius of the circular curve of the tunnel contour; h1 is the vertical distance between the vertex of the tunnel contour and the upper boundary line of the intersecting (tangent) rock layer; [σ] is the tensile strength of the surrounding rock; b is the width of the surrounding rock; h is the thickness of the rock layer; l is the length of area I; n is the number of rock layers on the failure surface, calculated using formula (4); a is the process value in the derivation, calculated using formula (5);

[0018]

[0019] z is the first letter of the pinyin of “total”, Mz means total bending moment, and Mz-1 represents the total bending moment of the first failure.

[0020] The above-mentioned method for calculating the arch failure zone of a horizontal layered surrounding rock highway tunnel construction is characterized in that the first failure length of the arch surrounding rock in step 1 is calculated according to the following method:

[0021] When damage occurs in Area I:

[0022] σ 1-I (x) intersects with the function graph of [σ], and the horizontal coordinate of the intersection point is x=l 1-I , then the first failure length of the arch surrounding rock is l 1-I ;

[0023] σ 1-I The function graph of (x) is always above the function graph of [σ], then the first failure length of the surrounding rock of the arch is l;

[0024] When damage occurs in Area II:

[0025] σ 1-II The graph of (x) intersects with the graph of [σ], and the horizontal coordinate of the intersection point is x=l 1-II , then the first failure length of the arch surrounding rock is l 1-II .

[0026] The above-mentioned method for calculating the arch failure zone of a horizontal layered surrounding rock highway tunnel construction is characterized in that the judgment condition for the secondary failure position of the arch surrounding rock in step 2 is:

[0027] Secondary damage occurs in region I: σ 2-I (x)≥[σ];

[0028] Secondary damage occurs in region II: σ 2-II (x)≥[σ];

[0029] The surrounding rock of the arch is no longer damaged: σ 2-I (x)<[σ],σ 2-II (x)<[σ];

[0030] Among them, σ 1-I (x) is calculated using formula (7), σ 1-II (x) is calculated using formula (8);

[0031]

[0032] Among them, M z-2 (x) is the bending moment borne by the surrounding rock of the arch under the load after the first failure; σ 2-I (x) is the tensile stress of the surrounding rock in area I after the first failure; σ 2-II (x) is the tensile stress of each layer of the surrounding rock mass in area II after the first failure; l 1-iis the length of the first failure of the surrounding rock of the arch, and the first failure position is in area I, l 1-i Take l 1-I , the first damage location is in area II, l 1-i Take l 1-II .

[0033] i is I and II, representing area I and area II in the figure respectively, l 1-i is the length of the first failure of the surrounding rock of the arch, and the first failure position is in area I, l 1-i Take l 1-I , the first damage location is in area II, l 1-i Take l 1-II .

[0034] The above-mentioned method for calculating the arch failure zone of a horizontal layered surrounding rock highway tunnel construction is characterized in that the secondary failure length of the arch surrounding rock in step 2 is calculated according to the following method:

[0035] When damage occurs in Area I:

[0036] σ 2-I (x) intersects with the function graph of [σ], and the horizontal coordinate of the intersection point is x=l 2-I , then the secondary failure length of the arch surrounding rock is l 2-I ;

[0037] σ 2-I The function graph of (x) is always above the function graph of [σ], then the secondary failure length of the surrounding rock of the arch is l;

[0038] When damage occurs in Area II:

[0039] σ 2-II The graph of (x) intersects with the graph of [σ], and the horizontal coordinate of the intersection point is x=l 2-II , then the secondary failure length of the arch surrounding rock is l 2-II .

[0040] The above-mentioned method for calculating the arch damage zone of a horizontal layered surrounding rock highway tunnel construction is characterized in that the calculation method of step two is applicable to step three, and when the Nth calculation meets the judgment condition that the surrounding rock is not damaged, the N-1th calculation result can be used as the length of the damage zone of the arch surrounding rock.

[0041] The beneficial effects of the present invention are:

[0042] 1. The present invention can quickly calculate the length of the destruction zone of the arch surrounding rock, thereby guiding the design of prevention and control measures and solving problems such as local block falling and collapse of horizontal layered surrounding rock.

[0043] 2. The failure length of the arch surrounding rock is calculated by a simple formula, which is more convenient and faster than numerical calculation.

[0044] 3. The calculation results of the present invention can be used as the lateral span of the upper surrounding rock of the tunnel, and combined with the existing theory, it can predict the damage range of the horizontal layered surrounding rock.

[0045] 4. For the first time, a calculation method for the arch surrounding rock failure zone was proposed, which filled the gap in the calculation theory of the arch failure zone in horizontal layered surrounding rock construction and promoted the development of the layered surrounding rock stability theory. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1a Schematic diagram of the equivalent model of layered surrounding rock after upper step excavation in the construction of a horizontal layered surrounding rock highway tunnel.

[0047] Figure 1b Schematic diagram of the surrounding rock mechanics model for the construction arch of a highway tunnel with horizontal layered surrounding rock.

[0048] Figure 2 This is a schematic diagram of the arch surrounding rock division.

[0049] Figure 3a This is the mechanical model of the arch surrounding rock where the first failure of the surrounding rock occurs in area I.

[0050] Figure 3b This is the mechanical model of the arch surrounding rock where the first failure of the surrounding rock occurs in area II.

[0051] Figure 4 This is a flow chart of the calculation method for the arch surrounding rock failure zone.

[0052] The meanings of the symbols in the figure are as follows: the layered surrounding rock is numbered from 1 to N from top to bottom, h1 is the vertical distance between the vertex of the tunnel contour and the upper boundary line of the intersecting (tangent) rock layer; q is the loose load on the upper part of the tunnel; M is the mid-span bending moment of the first layer of surrounding rock; q1 is the horizontal thrust borne by the first layer of surrounding rock; Q is the shear force borne by the first layer of surrounding rock (according to beam theory, the shear force in the mid-span of the beam is zero); l is the length of area I. DETAILED DESCRIPTION

[0053] The schematic diagram of the construction structure of a highway tunnel with horizontal layered surrounding rock is as follows: Figure 1a , Figure 1b As shown, the framed part in the figure is taken as the isolation body, and the mechanical model of the arch surrounding rock is established.

[0054] It is assumed that each layer of rock has the same physical and mechanical properties and thickness, fits tightly, maintains coordinated deformation under external loads, has the same bending curvature, and only undergoes multiple orderly linear failures according to the laws of mechanics.

[0055] Step 1: Determine the first failure position of the arch surrounding rock and calculate the first failure length of the arch surrounding rock:

[0056] The horizontal layered rock tunnel is excavated by the up-and-down step method. After the up-step excavation, the tunnel contour can be regarded as an arc with a radius of R. Figure 2 In the coordinate system shown, the curve equation of the tunnel contour is:

[0057]

[0058] like Figure 2 As shown in the figure, the surrounding rock structure of the arch is divided into area I and area II. Area I is a cantilever beam structure with a variable cross-section. By comparing the tensile stress of a certain section under the external load with the ultimate tensile strength of the surrounding rock, it is determined whether the section is damaged. The corresponding calculation formula is:

[0059] The first damage occurs in region I: σ 1-I (x)≥[σ];

[0060] The first damage does not occur in region I: σ 1-I (x)<[σ].

[0061]

[0062] Among them, σ 1-I (x) is the tensile stress of the surrounding rock in area I; M z-1 (x) is the bending moment borne by the surrounding rock of the arch under the action of load; γ is the density of the surrounding rock; [σ] is the tensile strength of the surrounding rock; b is the width of the surrounding rock; l is the length of area I.

[0063] Within Region I:

[0064] σ 1-I (x) intersects with the function graph of [σ], and the horizontal coordinate of the intersection point is x=l 1-I , then the first failure length of the arch surrounding rock is l 1-I .

[0065] σ 1-I If the function graph of (x) is always above the function graph of [σ], the first failure length of the surrounding rock of the arch is l.

[0066] σ 1-I If the function graph of (x) is always below the function graph of [σ], the surrounding rock of the arch in region I will not be damaged.

[0067] If the above-mentioned judgment conditions for the first failure in area I are not met, the first failure may occur in area II. According to the stacked beam theory, the tensile stress of each layer of surrounding rock under load is calculated, and the tensile stress is compared with the ultimate tensile strength of the surrounding rock to determine whether the section is damaged. The corresponding formula is:

[0068] The first damage occurs in region II: σ 1-II (x)≥[σ];

[0069] The surrounding rock of the arch does not fail: σ 1-II (x)<[σ].

[0070]

[0071] Among them, σ 1-II (x) is the tensile stress of each layer of the surrounding rock mass in area II; n is the number of rock layers in a certain section, h is the thickness of the rock layer; a is the process value in the derivation, a=y(x)-(n-1)h.

[0072] Within Region II:

[0073] σ 1-II The graph of (x) intersects with the graph of [σ], and the horizontal coordinate of the intersection point is x=l 1-II , then the first failure length of the arch surrounding rock is l 1-II .

[0074] σ 1-II If the image of (x) is always below the image of [σ], the surrounding rock of the arch will not be damaged.

[0075] Step 2: Determine the secondary damage position of the arch and calculate the secondary damage length (the secondary damage length refers to the total length of the first damage length and the second damage length):

[0076] like Figure 3a ,like Figure 3b As shown in the figure, the mechanical model of the surrounding rock of the arch changes after the first failure, and the surrounding rock on the air side is no longer subjected to bending moment. Both regions I and II may experience secondary failure. By comparing the tensile stress of a certain section under load and the ultimate tensile strength of the surrounding rock, it is determined whether region I is damaged. The corresponding formula is:

[0077] Secondary damage occurs in region I: σ 2-I (x)≥[σ];

[0078] Secondary damage does not occur in region I: σ 2-I (x)<[σ].

[0079]

[0080] Among them, M z-2 (x) is the bending moment borne by the surrounding rock of the arch under load; σ 2-I (x) is the tensile stress of the surrounding rock in area I; 1-I is the first failure length of the arch surrounding rock in area I.

[0081] Within Region I:

[0082] σ2-I (x) intersects with the function graph of [σ], and the horizontal coordinate of the intersection point is x=l 2-I , then the secondary failure length of the arch surrounding rock is l 2-I .

[0083] σ 2-I If the function graph of (x) is always above the function graph of [σ], the secondary failure length of the surrounding rock of the arch is l.

[0084] σ 2-I If the function graph of (x) is always below the function graph of [σ], no secondary damage will occur in the surrounding rock of the arch in region I.

[0085] If the above-mentioned secondary damage judgment condition in area I is not met, or the first damage location is in area II, then secondary damage may occur in area II. Whether secondary damage occurs is judged by comparing the tensile stress of each rock layer under load with the ultimate tensile strength of the surrounding rock. The corresponding formula is:

[0086] Secondary damage occurs in region II: σ 2-II (x)≥[σ];

[0087] The surrounding rock of the arch is no longer damaged: σ 2-II (x)<[σ].

[0088]

[0089] Among them, l 1-i is the length of the first failure of the surrounding rock of the arch, and the first failure location is in area I, l 1-i Take l 1-I , the first damage location is in area II, l 1-i Take l 1-II .

[0090] In Region II,

[0091] σ 2-II The graph of (x) intersects with the graph of [σ], and the horizontal coordinate of the intersection point is x=l 2-II , then the secondary failure length of the arch surrounding rock is l 2-II .

[0092] σ 2-II If the image of (x) is always below the image of [σ], the surrounding rock of the arch will no longer be damaged.

[0093] Step 3: Determine the N-time (N>2) failure position of the surrounding rock of the arch and calculate the N-time failure length (the N-time failure length refers to the total length of the length of the N-th failure and all failure lengths before N-1):

[0094] The N-th (N>1) failure position and failure length of the arch surrounding rock can be calculated completely according to the calculation process of step 2. When the N-th calculation meets the judgment condition that the arch surrounding rock is not damaged, the N-1-th calculation result can be used as the length of the failure zone of the arch surrounding rock.

[0095] The following is a specific example of a method for calculating the arch failure zone of a horizontal layered surrounding rock highway tunnel construction proposed by the present invention:

[0096] Baochuan No. 2 Tunnel is located in Yangquan City, Shanxi Province. The tunnel is 533m long and is excavated using the upper and lower steps. The upper step contour is a semicircle with a radius of R = 6m. According to the geological survey report, the tunnel site is composed of medium to strong weathered biotite gneiss, with developed joints, fissures, layers and other structural surfaces. The surrounding rock is relatively stable and belongs to Class V surrounding rock. After excavation, the surrounding rock of the arch was completely destroyed, and the upper surrounding rock collapsed on a large scale, making it difficult to form a tunnel. Surrounding rock weight γ = 20kN / m 3 , tensile strength [σ] = 3.0MPa. According to the on-site geological sketch, the rock layer thickness h = 0.5m, the longitudinal width b of the beam is 1m per unit length, the vertical distance h1 = 0.3m between the vertex of the tunnel contour and the upper boundary line of the tangent rock layer, and the loose load on the upper part of the surrounding rock is calculated as 264.96kPa according to the surrounding rock pressure calculation formula in the "Highway Tunnel Design Code". Substituting it into the calculation formula proposed in the present invention, the final destruction length of the arch surrounding rock is 5.86m, indicating that the arch surrounding rock is basically completely destroyed after excavation, which is consistent with the situation of difficult hole formation at the construction site. This shows that the arch destruction zone calculation method proposed in the present invention is accurate and can be used to guide engineering practice.

[0097] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating the arch failure zone of a horizontal layered surrounding rock highway tunnel construction, characterized in that: The following steps are involved: Step 1: determine the first failure position of the arch surrounding rock and calculate the first failure length of the arch surrounding rock; Step 2: determine the secondary failure position of the arch surrounding rock and calculate the secondary failure length of the arch surrounding rock; Step 3: Determine the N-time (N>2) failure position of the surrounding rock of the arch, and calculate the N-time failure length of the surrounding rock of the arch.

2. The method for calculating the arch failure zone of a horizontal layered surrounding rock highway tunnel construction according to claim 1 is characterized in that: The conditions for determining the first failure position of the surrounding rock of the arch in step 1 are: The first damage occurs in region I: σ 1-I (x)≥[σ]; The first damage occurs in region II: σ 1-II (x)≥[σ]; The surrounding rock of the arch does not fail: σ 1-I (x)<[σ],σ 1-II (x)<[σ]; Among them, M z-1 (x) is the bending moment borne by the surrounding rock of the arch under load; σ 1-I (x) is the tensile stress of the surrounding rock in area I; σ 1-II (x) is the tensile stress of each layer of the surrounding rock in area II; x is the horizontal distance of a certain section from the origin of the coordinate system; γ is the weight of the surrounding rock; q is the loose load on the upper part of the tunnel; R is the radius of the circular curve of the tunnel contour; h1 is the vertical distance between the vertex of the tunnel contour and the upper boundary line of the intersecting or tangent rock layer; [σ] is the ultimate tensile strength of the surrounding rock; b is the width of the surrounding rock; h is the thickness of the rock layer; l is the length of area I; n is the number of rock layers on the failure surface, calculated using formula (4); a is the process value in the derivation, calculated using formula (5); Formula (4) Formula (5) 3. The method for calculating the arch failure zone of a horizontal layered surrounding rock highway tunnel construction according to claim 2 is characterized in that: The first failure length of the surrounding rock of the arch described in step 1 is calculated as follows: When damage occurs in Area I: σ 1-I (x) intersects with the function graph of [σ], and the horizontal coordinate of the intersection point is x=l 1-I , then the first failure length of the arch surrounding rock is l 1-I ; σ 1-I The function graph of (x) is always above the function graph of [σ], then the first failure length of the surrounding rock of the arch is l; When damage occurs in Area II: σ 1-II The graph of (x) intersects with the graph of [σ], and the horizontal coordinate of the intersection point is x=l 1-II , then the first failure length of the arch surrounding rock is l 1-II .

4. The method for calculating the arch failure zone of a horizontal layered surrounding rock highway tunnel construction according to claim 2 is characterized in that: The conditions for determining the secondary failure position of the surrounding rock of the arch in step 2 are: Secondary damage occurs in region I: σ 2-I (x)≥[σ]; Secondary damage occurs in region II: σ 2-II (x)≥[σ]; The surrounding rock of the arch is no longer damaged: σ 2-I (x)<[σ],σ 2-II (x)<[σ]; Among them, M z-2 (x) is the bending moment borne by the surrounding rock of the arch under the load after the first failure; σ 2-I (x) is the tensile stress of the surrounding rock in area I after the first failure; σ 2-II (x) is the tensile stress of surrounding rock layers in area II after the first failure; l 1-i is the length of the first failure of the surrounding rock of the arch, and the first failure position is in area I, l 1-i Take l 1-I , the first damage location is in area II, l 1-i Take l 1-II .

5. The method for calculating the arch failure zone of a horizontal layered surrounding rock highway tunnel construction according to claim 4 is characterized in that: The secondary failure length of the surrounding rock of the arch described in step 2 is calculated as follows: When damage occurs in Area I: σ 2-I (x) intersects with the function graph of [σ], and the horizontal coordinate of the intersection point is x=l 2-I , then the secondary failure length of the arch surrounding rock is l 2-I ; σ 2-I The function graph of (x) is always above the function graph of [σ], then the secondary failure length of the surrounding rock of the arch is l; When damage occurs in Area II: σ 2-II The graph of (x) intersects with the graph of [σ], and the horizontal coordinate of the intersection point is x=l 2-II , then the secondary failure length of the arch surrounding rock is l 2-II .

6. The method for calculating the arch failure zone of a horizontal layered surrounding rock highway tunnel construction according to claim 1 is characterized in that: The calculation method of the N-times (N>2) failure length of the surrounding rock of the arch described in step three is the same as that in step two.

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