Shallow-buried loess tunnel arch load calculation method considering vertical joint influence

Abstract

The invention discloses a shallow-buried loess tunnel arch load calculation method considering vertical joint influence. The method comprises the following steps: S1, establishing a vertical joint error dynamic model; s2, based on the vertical joint fault dynamical model, decomposing the vertical joint fault dynamical model into a plurality of soil column unit bodies, and establishing a mechanical equilibrium equation in the horizontal and vertical directions; s3, based on the soil column unit bodies, stress analysis is conducted on the contact faces of the adjacent soil column unit bodies, and friction force between the soil column unit bodies is determined; s4, on the basis of the vertical joint fault dynamic model, in combination with the curve slope of stratum settlement, an angle expression between thrust between soil column unit bodies and the horizontal direction is determined; and S5, determining the vertical load of the tunnel arch part. According to the method, the loess vertical joint mechanical model is introduced, the vertical joints are simplified into a plurality of independent soil column unit bodies, and the accuracy of tunnel arch load calculation is improved.

Description

Technical Field

[0001] The invention relates to the technical field of shallow buried tunnels, and in particular to a method for calculating the arch load of a shallow buried loess tunnel taking into account the influence of vertical joints. Background Art

[0002] As a special soil, loess has unique physical and mechanical properties that are different from the soft soil in the south and even more different from rocks. However, most of the current calculation methods for the surrounding rock pressure of shallow loess tunnels do not take into account the structural characteristics of loess. Therefore, it is necessary to find a calculation method for the surrounding rock pressure of shallow loess tunnels that conforms to the actual situation, and objectively and reasonably analyze and calculate the surrounding rock pressure acting on shallow loess tunnels, so as to carry out more scientific design and construction. Summary of the invention

[0003] The purpose of the present invention is to overcome the deficiencies in the above-mentioned prior art and provide a method for calculating the arch load of a shallow loess tunnel taking into account the influence of vertical joints. The mechanical model of loess vertical joints is introduced, the vertical joints are simplified into a plurality of independent soil column units, and the force analysis of the plurality of soil column units is performed to obtain the mechanical equilibrium equations of the soil column unit in the horizontal and vertical directions when the soil column unit is separated from the tunnel centerline by a certain distance, thereby improving the accuracy of the tunnel arch load calculation.

[0004] To achieve the above object, the technical solution adopted by the present invention is: a method for calculating the arch load of a shallow loess tunnel considering the influence of vertical joints, comprising the following steps:

[0005] Step S1: Based on the mechanical model established by Xie Jiawu method, vertical joints of loess are introduced to establish a vertical joint dislocation dynamics model;

[0006] Step S2: Based on the vertical joint dislocation dynamics model in step S1, the vertical joint dislocation dynamics model is decomposed into a plurality of soil column units, a force analysis is performed on the soil column units, and mechanical equilibrium equations in the horizontal and vertical directions are established;

[0007] Step S3: Based on the soil column unit body in step S2, the contact surface of the adjacent soil column unit bodies is subjected to force analysis to determine the friction force M between the soil column unit bodies. x ;

[0008] Step S4: Based on the vertical joint dislocation dynamics model described in step S2 and combined with the slope of the ground settlement curve, determine the angle θ between the thrust of the soil column unit and the horizontal direction. x Expression of

[0009] Step S5: Based on the mechanical equilibrium equations in the horizontal and vertical directions in step S2 and the friction force M between the soil column units in step S3 xand the angle θ between the thrust between the soil column units and the horizontal direction in step S4 x , determine the vertical load P(x) on the tunnel arch.

[0010] Preferably, the vertical joint dislocation dynamic model in step S1 includes the tunnel overlying rock mass BDGI, the triangular rock mass ABJ on the left side of the overlying rock mass BDGI, and the triangular rock mass DEF on the right side of the overlying rock mass BDGI.

[0011] Preferably, establishing the mechanical equilibrium equations in the horizontal and vertical directions in step S2 comprises the following steps:

[0012] Step S201: decomposing the rock mass BCHI into a plurality of soil column units by using a strip method;

[0013] Step S202: performing force analysis on the soil column unit body decomposed in step S201 in the horizontal direction and the vertical direction;

[0014] Step S203: Based on the force analysis of the soil column unit body in step S202, the mechanical equilibrium equations of the soil column unit body at a distance x from the tunnel centerline are obtained in the horizontal and vertical directions.

[0015] Preferably, the mechanical equilibrium equation in the horizontal direction is expressed by the following formula:

[0016] T H =N x (16)

[0017] Where: N x is the normal force between soil column units.

[0018] Preferably, the mechanical equilibrium equation in the vertical direction is expressed by the following formula:

[0019]

[0020] Where: γ is the soil weight, H a is the distance from the ground surface to the dome, M x is the friction force between soil column units; P(x) is the force exerted by the supporting structure on the soil column unit.

[0021] Preferably, the friction force M between the soil column units in step S3 is x It is expressed by the following formula:

[0022] M x =N x tanθ x (18)

[0023] Where: N x is the normal force between soil column units, θ xIt represents the angle between the thrust between soil column units and the horizontal direction.

[0024] Preferably, the angle θ between the thrust between the soil column units and the horizontal direction in step S4 is x The calculation process includes the following steps:

[0025] Step S401: Calculate the friction angle based on the soil Establish the angle θ between the thrust force between the soil column units and the horizontal direction x The expression is:

[0026]

[0027] Where: k is the actual friction angle correction coefficient;

[0028] Step 402: Based on the foundation settlement curve, determine the actual friction angle correction coefficient k:

[0029]

[0030] Step S403: Based on the actual friction angle correction coefficient k in step S402, determine the θ in step S401 x :

[0031]

[0032] Where: x is the horizontal distance from any point to the tunnel axis; i is the horizontal distance from the tunnel centerline to the inflection point of the settlement curve; Z is the distance from the selected stratum to the surface, Z=0.5Z0.

[0033] Preferably, the vertical load P(x) of the tunnel arch in step S5 is expressed by the following formula:

[0034]

[0035] Where: γ is the soil weight, H a is the distance from the ground surface to the dome, h is the length of BJ in the three-sided rock mass ABJ or the length of DF in DEF, λ is the lateral pressure coefficient, is the friction angle of the soil, i is the width of the settlement trough, Z is the distance from the selected stratum to the surface, let Z = 0.5Z0.

[0036] Compared with the prior art, the present invention has the following advantages:

[0037] 1. The present invention introduces a mechanical model of loess vertical joints, simplifies the vertical joints into multiple independent soil column units, and performs force analysis on the multiple soil column units to obtain the mechanical equilibrium equations of the soil column units in the horizontal and vertical directions when the soil column units are separated from the tunnel centerline by a certain distance, thereby improving the accuracy of the tunnel arch load calculation.

[0038] 2. The present invention introduces a friction angle correction coefficient into the angle between the thrust and the horizontal direction between the soil column units, and corrects the relative dislocation force between the soil column units by the correction coefficient, thereby improving the accuracy of the tunnel arch load calculation.

[0039] 3. The maximum radial surrounding rock pressure calculated by the theoretical formula proposed in the present invention is located at about 60° of the arch ring, which is close to the data distribution law obtained by actual measurement statistics. The maximum radial surrounding rock pressure calculated by Xie Jiawei's method is located at about 40° of the arch ring.

[0040] 4. The calculation method of the present invention can more accurately calculate the tunnel arch load and better guide the tunnel lining design.

[0041] The present invention is further described in detail below through the accompanying drawings and examples. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a schematic diagram of the calculation of surrounding rock pressure of shallow buried tunnels using the Xiejiawu method;

[0043] Figure 2 This is a schematic diagram of the forces acting on the soil column inside the BCHI soil mass above the tunnel;

[0044] Figure 3 It is a triangle diagram of the force of triangular prism block DEF;

[0045] Figure 4 Schematic diagram of the mechanical model considering vertical joint dislocation. DETAILED DESCRIPTION

[0046] like Figures 1 to 4 As shown, the present invention discloses a method for calculating the arch load of a shallow loess tunnel considering the influence of vertical joints, comprising the following steps:

[0047] Step S1: Based on the mechanical model established by Xie Jiawu method, vertical joints of loess are introduced to establish a vertical joint dislocation dynamics model;

[0048] In the mechanical model of vertical joint dislocation, Figures 1 to 4 As shown in the figure, W is the gravity of the overlying rock mass BDGI of the tunnel; W wis the gravity of the triangular rock mass ABJ or DEF; E is the lateral pressure; F is the resistance of the undisturbed soil to the entire sliding soil; T is the thrust generated by the triangular rock masses ABJ and DEF on the upper overlying rock mass BDGI; H a is the distance from the ground surface to the vault; Z is the distance from the selected stratum to the ground surface; Z0 is the buried depth of the horizontal axis of the tunnel; θ is the friction angle on the BI and DG surfaces; λ is the lateral pressure coefficient; W i is the gravity of each soil column unit; T x is the thrust between soil column units; P i is the force exerted by the supporting structure on the soil column unit; M i and M i ′ is the friction force between soil column units; N i and N i ′ is the normal force between soil column units.

[0049] The vertical joint dislocation dynamic model in step S1 includes the tunnel overlying rock mass BDGI, the triangular rock mass ABJ on the left side of the overlying rock mass BDGI, and the triangular rock mass DEF on the right side of the overlying rock mass BDGI.

[0050] The triangular rock bodies ABJ and DEF on the left and right sides of the overlying rock mass BDGI both generate thrust T on the overlying rock mass BDGI.

[0051] The deadweight of a triangular rock mass ABJ or DEF is expressed by the following formula:

[0052]

[0053] Where: γ is the weight of soil; h is the height of BJ in triangular rock mass ABJ or the height of DF in triangular rock mass DEF; β is the angle between the fracture surface and the horizontal line.

[0054] For the force analysis of the triangular rock mass ABJ or DEF, according to the sine theorem, the thrust T is expressed by the following formula:

[0055]

[0056] Where: is the internal friction angle of soil; θ is the angle between the thrust T and the horizontal direction.

[0057] Substituting formula (1) into formula (2), the thrust T can be obtained as:

[0058]

[0059] Where: λ is the lateral pressure coefficient, Calculate the friction angle for the soil, c is the soil cohesion; δ is the compressive stress when determining the shear strength of the soil; β is the angle between the fracture surface and the horizontal line,

[0060] Decompose the thrust T in the horizontal and vertical directions to obtain the horizontal thrust T H and vertical thrust T V The expression is:

[0061]

[0062] Step S2: Based on the vertical joint dislocation dynamics model in step S1, the vertical joint dislocation dynamics model is decomposed into a plurality of soil column units, a force analysis is performed on the soil column units, and mechanical equilibrium equations in the horizontal and vertical directions are established;

[0063] Step S201: decomposing the rock mass BCHI into multiple groups of soil column units by using the strip method;

[0064] As loess has significant structural characteristics, the vertical joints are simplified into multiple independent soil column units. The strip method is used to analyze the mechanical behavior of the soil above the tunnel, and the rock mass BCHI is decomposed into multiple groups of interacting soil column units, such as Figure 2 As shown, soil column units are KCHL, MKLN, etc.

[0065] Step S202: performing force analysis on the soil column unit body decomposed in step S201 in the horizontal direction and the vertical direction;

[0066] right Figure 2 The stress analysis of the soil column unit KCHL shows:

[0067] E=N1′ (6)

[0068]

[0069] Where: N1' is the normal force between the soil column unit KCHL and the soil column unit MKLN, P0 is the force of the supporting structure on the soil column unit KCHL, and M1' is the upward friction force between the soil column unit KCHL and the soil column unit MKLN.

[0070] The stress analysis of the soil column unit MKLN shows:

[0071] N2′=N1 (8)

[0072] W1=P1dx-M1+M2′ (9)

[0073] Where: N1 is the normal force between the soil column unit MKLN and the soil column unit KCHL, P1 is the force acting on the soil column unit MKLN by the supporting structure, M1 is the downward friction force between the soil column unit MKLN and the soil column unit KCHL, and M'2 is the upward friction force between the side of the soil column unit MKLN away from the soil column unit KCHL and the adjacent soil column unit.

[0074] The stress analysis of the soil column unit QOPR yields:

[0075] N x+1 ′=N x (10)

[0076] W x =P x dx-M x +M x+1 ′ (11)

[0077] The stress analysis of the soil column unit BSTI yields:

[0078] T H =N j (12)

[0079] W j =P j dx-M j +T V (13)

[0080] Where: T H is the thrust T in the horizontal direction.

[0081] The overall stress analysis of the soil column BCHI shows that:

[0082] T H =N j ···=N x =E (14)

[0083]

[0084] Step S203: Based on the force analysis of the soil column unit body in step S202, the mechanical equilibrium equations of the soil column unit body at a distance x from the tunnel centerline are obtained in the horizontal and vertical directions.

[0085] In summary, when the distance between the soil column unit and the tunnel centerline is x, the mechanical equilibrium equation in the horizontal direction is expressed by the following formula:

[0086] T H =N x (16)

[0087] Where: N xis the normal force between soil column units.

[0088] When the distance between the soil column unit and the tunnel centerline is x, the mechanical equilibrium equation in the vertical direction is expressed by the following formula:

[0089]

[0090] Where: γ is the soil weight, H a is the distance from the ground surface to the dome, M x is the friction force between soil column units; P(x) is the force exerted by the supporting structure on the soil column unit.

[0091] Step S3: Based on the soil column unit body in step S2, the contact surface of the adjacent soil column unit bodies is subjected to force analysis to determine the friction force M between the soil column unit bodies. x ;

[0092] like Figure 4 As shown in the figure, the friction force M between the soil column units is x is the friction force between the soil column unit at position x and the soil column unit at position x+1, M x It is expressed by the following formula:

[0093] M x =N x tanθ x (18)

[0094] Where: N x is the normal force between soil column units; θ x It is the angle between the thrust between soil column units and the horizontal direction.

[0095] Step S4: Based on the vertical joint dislocation dynamics model described in step S2 and combined with the slope of the ground settlement curve, determine the angle θ between the thrust of the soil column unit and the horizontal direction. x Expression of

[0096] Step S401: Calculate the friction angle based on the soil Establish the angle θ between the thrust force between the soil column units and the horizontal direction x The expression is:

[0097] like Figure 4 As shown in the figure, the thrust T between soil column units is x The angle θ with the horizontal direction x Take soil from the stratum fracture surface AJ to calculate the friction angle The closer to the tunnel centerline, the smaller the relative displacement between the soil column units is, until the θ x The value is 0; based on the above rules, θ xAssociated with the slope of the formation settlement curve, the following expression is established:

[0098]

[0099] Where: k is the actual friction angle correction coefficient;

[0100] Step 402: Based on the foundation settlement curve, determine the actual friction angle correction coefficient k:

[0101] The formation subsidence curve S(x) is expressed by the following formula:

[0102]

[0103] Where: m = 1.256-0.332Z / Z0, V L is the stratum volume loss or ground loss rate; D is the tunnel diameter; Z is the distance from the selected stratum to the surface, let Z = 0.5Z0; x is the horizontal distance from any point to the tunnel axis.

[0104] According to the formation settlement curve S(x), the expression of k is obtained:

[0105]

[0106] Where: i is the horizontal distance from the tunnel centerline to the inflection point of the settlement curve, also known as the width of the settlement trough, i = K (Z0-Z);

[0107] Step S403: Based on the actual friction angle correction coefficient k in step S402, determine the θ in step S401 x :

[0108]

[0109] Where: x is the horizontal distance from any point to the tunnel axis; i is the horizontal distance from the tunnel centerline to the inflection point of the settlement curve; Z is the distance from the selected stratum to the surface, let Z = 0.5Z0.

[0110] Step S5: Based on the mechanical equilibrium equations in the horizontal and vertical directions in step S2 and the friction force M between the soil column units in step S3 x and the angle θ between the thrust between the soil column units and the horizontal direction in step S4 x , determine the vertical load P(x) on the tunnel arch.

[0111] Substituting equations (18) and (22) into equation (17) and transforming the equations, we can obtain the vertical load P(x) of the tunnel arch in step S5:

[0112]

[0113] Where: γ is the soil weight, H a is the distance from the ground surface to the dome, λ is the lateral pressure coefficient, is the friction angle of the soil, i is the width of the settlement trough, Z is the distance from the selected stratum to the surface, Z=0.5Z0.

[0114] The following is a method for calculating the arch load of a shallow loess tunnel considering the influence of vertical joints disclosed in the present invention, in combination with a specific example:

[0115] Tujiawan Tunnel is located in Lanzhou City, Gansu Province. It is located on the loess ridge and the surface is covered by thick loess. The construction method adopts the method of arch first and wall later with positive steps. The tunnel excavation span is 13.4m. According to the engineering exploration data, the strata distributed at the tunnel location are composed of the Quaternary Upper Pleistocene old loess, the Quaternary Middle Pleistocene old loess and the Upper Pliocene mudstone of the Upper Tertiary System. The vertical joints and joint fissures are developed, and the surrounding rock stability is poor, belonging to the V-level surrounding rock. The tunnel burial depth is H a =28m, Z0=34.7m, h=41.4m, width of sedimentation trough i=K(Z0-Z), K is 0.5 according to engineering experience, surrounding rock density γ=20kN / m 3 , soil cohesion c = 29kPa, soil internal friction angle The parameters of the tunnel arch vertical load P(x) are all known, and the tunnel arch vertical load P(x) can be obtained. The tunnel arch vertical load P(x) is calculated by using the Xie Jiawu method and the calculation method proposed by the present invention, as shown in Table 1 and Table 2;

[0116] Table 1: Calculation of vertical load on tunnel arch based on Xiejiawu surrounding rock pressure calculation formula (kPa):

[0117] Force position dome Arch 30° Arch 45° Arch 60° Arched waist P(x) 418.84186 502.44534 502.44534 468.92666 335.54327

[0118] Table 2: Calculation of vertical load on tunnel arch based on the calculation method of the present invention (kPa):

[0119] Force position dome Arch 30° Arch 45° Arch 60° Arched waist P(x) 108.86128 267.97173 346.6637 382.43353 354.37492

[0120] Compared with the measured data, the calculation method proposed in the present invention is more consistent with the measured data, which means that the surrounding rock pressure calculation method proposed in the present invention is more accurate and can be used to guide engineering practice.

[0121] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent structural transformation made to the above embodiment based on the technical essence of the present invention still falls within the protection scope of the technical solution of the present invention.

Claims

1. A method for calculating the arch load of a shallow loess tunnel considering the influence of vertical joints, characterized in that: The following steps are involved: Step S1: Based on the mechanical model established by Xie Jiawu method, vertical joints of loess are introduced to establish a vertical joint dislocation dynamics model; Step S2: Based on the vertical joint dislocation dynamics model in step S1, the vertical joint dislocation dynamics model is decomposed into a plurality of soil column units, a force analysis is performed on the soil column units, and mechanical equilibrium equations in the horizontal and vertical directions are established; Step S3: Based on the soil column unit body in step S2, the contact surface of the adjacent soil column unit bodies is subjected to force analysis to determine the friction force M between the soil column unit bodies. x ; Step S4: Based on the vertical joint dislocation dynamics model described in step S2 and combined with the slope of the ground settlement curve, determine the angle θ between the thrust of the soil column unit and the horizontal direction. x Expression of Step S5: Based on the mechanical equilibrium equations in the horizontal and vertical directions in step S2 and the friction force M between the soil column units in step S3 x and the angle θ between the thrust between the soil column units and the horizontal direction in step S4 x , determine the vertical load P(x) on the tunnel arch.

2. A method for calculating the arch load of a shallow loess tunnel considering the influence of vertical joints according to claim 1, characterized in that: The vertical joint dislocation dynamic model in step S1 includes the tunnel overlying rock mass BDGI, the triangular rock mass ABJ on the left side of the overlying rock mass BDGI, and the triangular rock mass DEF on the right side of the overlying rock mass BDGI.

3. A method for calculating the arch load of a shallow loess tunnel considering the influence of vertical joints according to claim 2, characterized in that: Establishing the mechanical equilibrium equations in the horizontal and vertical directions in step S2 includes the following steps: Step S201: decomposing the rock mass BCHI into a plurality of soil column units by using a strip method; Step S202: performing force analysis on the soil column unit body decomposed in step S201 in the horizontal direction and the vertical direction; Step S203: Based on the force analysis of the soil column unit body in step S202, the mechanical equilibrium equations of the soil column unit body at a distance x from the tunnel centerline are obtained in the horizontal and vertical directions.

4. A method for calculating the arch load of a shallow loess tunnel considering the influence of vertical joints according to claim 3, characterized in that: The mechanical equilibrium equation in the horizontal direction is expressed by the following formula: T H =N x (16) Where: N x is the normal force between soil column units.

5. A method for calculating the arch load of a shallow loess tunnel considering the influence of vertical joints according to claim 3, characterized in that: The mechanical equilibrium equation in the vertical direction is expressed by the following formula: Where: γ is soil weight, H a is the distance from the ground surface to the dome, M x is the friction force between soil column units; P(x) is the force exerted by the supporting structure on the soil column unit.

6. A method for calculating the arch load of a shallow loess tunnel considering the influence of vertical joints according to claim 1, characterized in that: The friction force M between the soil column units in step S3 x It is expressed by the following formula: M x =N x tanθ x (18) Where: N x is the normal force between soil column units, θ x It represents the angle between the thrust between soil column units and the horizontal direction.

7. A method for calculating the arch load of a shallow loess tunnel taking into account the influence of vertical joints according to claim 1, characterized in that: The angle θ between the thrust between the soil column units and the horizontal direction in step S4 x The calculation process includes the following steps: Step S401: Calculate the friction angle based on the soil Establish the angle θ between the thrust of the soil column unit and the horizontal direction x The expression is: Where: k is the actual friction angle correction coefficient; Step 402: Based on the foundation settlement curve, determine the actual friction angle correction coefficient k: Step S403: Based on the actual friction angle correction coefficient k in step S402, determine the θ in step S401 x : Where: x is the horizontal distance from any point to the tunnel axis; i is the horizontal distance from the tunnel centerline to the inflection point of the settlement curve; Z is the distance from the selected stratum to the surface, Z=0.5Z0.

8. A method for calculating the arch load of a shallow loess tunnel taking into account the influence of vertical joints according to claim 1, characterized in that: The vertical load P(x) of the tunnel arch in step S5 is expressed by the following formula: Where: γ is soil weight, H a is the distance from the ground surface to the dome, h is the length of BJ in the three-sided rock mass ABJ or the length of DF in DEF, λ is the lateral pressure coefficient, is the friction angle of the soil, i is the width of the settlement trough, Z is the distance from the selected stratum to the surface, let Z = 0.5Z0.

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