Load calculation method for shallow-buried loess tunnel arch considering influence of vertical joint

Abstract

The application discloses a shallow-buried loess tunnel arch load calculation method considering the influence of vertical joints, and comprises the following steps: step S1, a vertical joint dislocation mechanical model is established; step S2, based on the vertical joint dislocation mechanical model, the vertical joint dislocation mechanical model is decomposed into multiple soil column unit bodies, and horizontal and vertical direction mechanical balance equations are established; step S3, based on the soil column unit body, force analysis is carried out on the contact surface of adjacent soil column unit bodies, and the friction force between the soil column unit bodies is determined; step S4, based on the vertical joint dislocation mechanical model, in combination with the curve slope of stratum settlement, an angle expression between the thrust between the soil column unit bodies and the horizontal direction is determined; and step S5, the vertical load of the tunnel arch is determined. The application introduces a loess vertical joint mechanical model, simplifies the vertical joints into multiple independent soil column unit bodies, and improves the accuracy of tunnel arch load calculation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of shallow-buried tunnel, in particular to a shallow-buried loess tunnel arch load calculation method considering the influence of vertical joints. BACKGROUND

[0002] Loess is a special soil, which has different physical and mechanical properties from the soft soil in the south and from the rock. However, the current calculation method of the surrounding rock pressure of shallow-buried loess tunnel does not consider the structural characteristics of loess. Therefore, it is necessary to find a calculation method of the surrounding rock pressure of shallow-buried loess tunnel which is in line with the actual situation, objectively and reasonably analyzes and calculates the surrounding rock pressure acting on the shallow-buried loess tunnel, so as to design and construct more scientifically. SUMMARY

[0003] The present application aims to overcome the deficiencies in the prior art, and provides a shallow-buried loess tunnel arch load calculation method considering the influence of vertical joints, which introduces a loess vertical joint mechanical model, simplifies the vertical joint into multiple independent soil column unit bodies, and analyzes the stress of the multiple soil column unit bodies to obtain the mechanical equilibrium equations of the soil column unit bodies in the horizontal and vertical directions when the soil column unit bodies are separated from the tunnel central axis by a certain distance, thereby improving the accuracy of the tunnel arch load calculation.

[0004] To achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows: a shallow-buried loess tunnel arch load calculation method considering the influence of vertical joints, comprising the following steps:

[0005] Step S1: based on the mechanical model established by Xie Jiaxiao method, introducing loess vertical joints, and establishing a vertical joint dislocation mechanical model;

[0006] Step S2: based on the vertical joint dislocation mechanical model in step S1, decomposing the vertical joint dislocation mechanical model into multiple soil column unit bodies, analyzing the stress of the soil column unit bodies, and establishing the mechanical equilibrium equations in the horizontal and vertical directions;

[0007] Step S3: based on the soil column unit bodies in step S2, analyzing the stress of the contact surface of adjacent soil column unit bodies, and determining the friction force M x between the soil column unit bodies;

[0008] Step S4: based on the vertical joint dislocation mechanical model in step S2, combining the curve slope of stratum settlement, and determining the expression of the angle θ x between the thrust between the soil column unit bodies and the horizontal direction;

[0009] Step S5: based on the mechanical equilibrium equations in the horizontal and vertical directions in step S2 and the friction force M x between the soil column unit bodies in step S3, calculating the tunnel arch load.The angle θ between the pushing force between the soil column units and the horizontal direction in step S4 x The vertical load P(x) of the tunnel arch is determined.

[0010] Preferably, the vertical joint dislocation mechanics model in step S1 comprises the overburden rock mass BDGI, the triangular rock mass ABJ on the left side of the overburden rock mass BDGI, and the triangular rock mass DEF on the right side of the overburden rock mass BDGI.

[0011] Preferably, the establishment of the mechanics balance equation in the horizontal and vertical directions in step S2 comprises the following steps:

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

[0013] Step S202: The soil column units divided in step S201 are subjected to stress analysis in the horizontal and vertical directions;

[0014] Step S203: Based on the stress analysis of the soil column units in step S202, the mechanics balance equation in the horizontal and vertical directions of the soil column units with a distance of x from the tunnel central axis is obtained.

[0015] Preferably, the mechanics balance equation in the horizontal direction is represented by the following formula:

[0016] T H =N x (16)

[0017] In the formula, N x is the normal force between the soil column units.

[0018] Preferably, the mechanics balance equation in the vertical direction is represented by the following formula:

[0019]

[0020] In the formula, γ is the specific weight of the soil mass, H a is the distance from the ground surface to the arch top, M x is the friction force between the soil column units, and P(x) is the acting force of the supporting structure on the soil column units.

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

[0022] M x =N x tanθ x (18)

[0023] In the formula, N x is the normal force between the soil column units, and θ xThis 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 in step S4 and the horizontal direction 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 between soil column elements and the horizontal direction. x The expression:

[0026]

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

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

[0029]

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

[0031]

[0032] In the formula: x is the horizontal distance of any point from 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 Earth's 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] In the formula: γ is the soil unit weight, H a λ is the distance from the ground surface to the crown, h is the length of BJ in the triangular rock mass ABJ or the length of DF in DEF, and λ is the lateral pressure coefficient. Calculate the friction angle for the soil, where i is the width of the settlement trough. Z is the distance from the selected stratum to the Earth's surface, let Z = 0.5Z0.

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

[0037] 1、The loess vertical joint mechanical model is introduced, the vertical joint is simplified into multiple independent soil column unit bodies, stress analysis is carried out on the multiple soil column unit bodies, the mechanical equilibrium equations of the soil column unit bodies in the horizontal direction and the vertical direction when the soil column unit bodies are separated from the tunnel central axis by a certain distance are obtained, and the accuracy of tunnel arch load calculation is improved.

[0038] 2、The friction angle correction coefficient is introduced in the angle between the thrust between the soil column unit bodies and the horizontal direction, the relative dislocation force between the soil column unit bodies is corrected through the correction coefficient, and the accuracy of tunnel arch load calculation is improved.

[0039] 3、The maximum radial surrounding rock pressure calculated by the theoretical formula of the present application is located at about 60° of the arch ring, which is close to the data distribution law obtained by actual measurement, and the maximum radial surrounding rock pressure calculated by the method of Xie Jiaoxio is located at about 40° of the arch ring.

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

[0041] The present application will be further described in detail below with reference to the drawings and examples. DESCRIPTION OF DRAWINGS

[0042] Figure 1 It is a schematic diagram for calculating the surrounding rock pressure of a shallow-buried tunnel by the method of Xie Jiaoxio;

[0043] Figure 2 It is a schematic diagram of the force of the internal soil column of the tunnel upper soil body BCHI;

[0044] Figure 3 It is a schematic diagram of the force triangle of the three-prism soil block DEF;

[0045] Figure 4 It is a schematic diagram of the mechanical model considering the vertical joint dislocation. DETAILED DESCRIPTION

[0046] As shown in Figures 1 to 4 , the present application discloses a shallow-buried loess tunnel arch load calculation method considering the influence of vertical joints, which comprises the following steps:

[0047] Step S1: based on the mechanical model established by the method of Xie Jiaoxio, the loess vertical joint is introduced, and the vertical joint dislocation mechanical model is established;

[0048] In the mechanical model of the vertical joint dislocation, as shown in Figures 1 to 4 , W is the gravity of the tunnel overburden rock body BDGI; 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 whole sliding soil; T is the thrust of 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 depth of the tunnel horizontal axis; θ is the friction angle on the BI and DG planes; λ is the lateral pressure coefficient; W i is the gravity of each soil column unit; T x is the thrust between the soil column units; P i is the force of the supporting structure on the soil column unit; M i and M i ′ are the friction forces between the soil column units; N i and N i ′ are the normal forces between the soil column units.

[0049] The vertical joint dislocation mechanics model in step S1 includes the 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 masses ABJ and DEF on the left and right sides of the overlying rock mass BDGI generate a thrust T on the overlying rock mass BDGI.

[0051] The self-weight of the triangular rock mass ABJ or DEF is represented by the following formula:

[0052]

[0053] In the formula, γ is the soil bulk density; h is the height of BJ in the triangular rock mass ABJ or the height of DF in the triangular rock mass DEF; and β is the angle between the fracture surface and the horizontal line.

[0054] According to the sine theorem, the thrust T is represented by the following formula through stress analysis of the triangular rock mass ABJ or DEF:

[0055]

[0056] In the formula, is the internal friction angle of the soil; and θ is the angle between the thrust T and the horizontal direction.

[0057] The thrust T is obtained by substituting formula (1) into formula (2):

[0058]

[0059] In the formula, λ is the lateral pressure coefficient, is the calculated friction angle of the soil, c is the cohesion of the soil mass; δ is the pressure stress when the shear strength of the soil mass is determined; β is the angle between the fracture surface and the horizontal line,

[0060] The horizontal and vertical components of the thrust T are decomposed to obtain the expressions of the horizontal thrust T H and the vertical thrust T V

[0061]

[0062] Step S2: based on the vertical joint dislocation mechanics model described in step S1, the vertical joint dislocation mechanics model is decomposed into a plurality of soil column unit bodies, the stress analysis of the soil column unit bodies is carried out, and the mechanical equilibrium equations in the horizontal and vertical directions are established;

[0063] Step S201: the rock mass BCHI is decomposed into a plurality of groups of soil column unit bodies by using the strip method;

[0064] Since the loess has significant structural characteristics, the vertical joint is simplified into a plurality of independent soil column unit bodies, the strip method is used to analyze the mechanical behavior of the soil mass above the tunnel, the rock mass BCHI is decomposed into a plurality of groups of interacting soil column unit bodies, as shown in Figure 2 the soil column unit bodies KCHL, MKLN, etc.

[0065] Step S202: the stress analysis of the soil column unit bodies decomposed in step S201 in the horizontal and vertical directions is carried out;

[0066] The stress analysis of the soil column unit body KCHL in Figure 2 can obtain:

[0067] E=N1′ (6)

[0068]

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

[0070] The stress analysis of the soil column unit body MKLN can obtain:

[0071] N2′=N1 (8)

[0072] W1=P1dx-M1+M2′ (9)

[0073] ​In the formula: N1 is the normal force between soil column unit MKLN and soil column unit KCHL, P1 is the force exerted by the support structure on soil column unit MKLN, M1 is the downward frictional force between soil column unit MKLN and soil column unit KCHL, and M'2 is the upward frictional force between the side of soil column unit MKLN away from soil column unit KCHL and the adjacent soil column unit.

[0074] Stress analysis of the soil column element QOPR yields the following results:

[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 element by BSTI yields the following results:

[0078] T H =N j (12)

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

[0080] In the formula: T H The thrust T is the force along the horizontal direction.

[0081] The stress analysis of the soil column BCHI as a whole yields the following results:

[0082] T H =N j ···=N x =E (14)

[0083]

[0084] Step S203: Based on the force analysis of the soil column unit described in step S202, the mechanical equilibrium equations of the soil column unit 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 horizontal mechanical equilibrium equation is expressed by the following formula:

[0086] T H =N x (16)

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

[0088] When the distance between the soil column units and the tunnel axis is x, the vertical mechanical equilibrium equation is represented by the following formula:

[0089]

[0090] In the formula, γ is the specific weight of the soil, H a is the distance from the ground to the vault, M x is the friction between the soil column units; P(x) is the force of the supporting structure on the soil column units.

[0091] Step S3: Based on the soil column units described in step S2, the contact surface of the adjacent soil column units is analyzed, and the friction M x between the soil column units is determined.

[0092] As shown in Figure 4 , the friction M x between the soil column units at position x and the soil column units at position x+1 is represented by the following formula:

[0093] M x = N x tanθ x (18)

[0094] In the formula, N x is the normal force between the soil column units; θ x is the angle between the thrust between the soil column units and the horizontal direction.

[0095] Step S4: Based on the vertical joint dislocation mechanical model in step S2, the expression of the angle θ x between the thrust between the soil column units and the horizontal direction is determined in combination with the curve slope of the stratum settlement.

[0096] Step S401: Based on the soil calculation friction angle , the expression of the angle θ x between the thrust between the soil column units and the horizontal direction is established:

[0097] As shown in Figure 4 , the angle θ x between the thrust T x between the soil column units and the horizontal direction is represented by the following formula: The closer the soil column units are to the tunnel axis, the smaller the relative dislocation between the soil column units, and the value of θ x at the tunnel axis is 0; based on the above rule, the expression of θ x ​Associated with the slope of the strata settlement curve, the following expression is established:

[0098]

[0099] In the formula: 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 strata settlement curve S(x) is represented by the following formula:

[0102]

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

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

[0105]

[0106] In the formula: i is the horizontal distance from the tunnel center line to the inflection point of the settlement curve, also known as the settlement groove width, i = K(Z0-Z);

[0107] Step S403: Based on the actual friction angle correction coefficient k in step S402, determine θ x in step s401.

[0108]

[0109] In the formula: x is the horizontal distance of any point from the tunnel axis; i is the horizontal distance from the tunnel center line to the inflection point of the settlement curve; Z is the distance from the selected strata to the ground surface, let Z = 0.5Z0.

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

[0111] Substitute formula (18) and formula (22) into formula (17), and transform the formula to obtain the vertical load P(x) of the tunnel arch in step S5:

[0112]

[0113] wherein: γ is the bulk density of the soil, H a is the distance from the ground to the vault, λ is the lateral pressure coefficient, is the calculated friction angle of the soil, i is the width of the settlement tank, Z is the distance from the selected stratum to the ground surface, Z = 0.5Z0.

[0114] The application discloses a shallow-buried loess tunnel arch load calculation method considering the influence of vertical joints.

[0115] The Tujiawan tunnel is located in Lanzhou City, Gansu Province, and is located in a loess mountain ridge, with a thick layer of loess covering the ground surface. The construction method adopts the method of a positive step, arch first and wall later, and the tunnel excavation span is 13.4 m. According to the engineering exploration data, the stratum distributed at the tunnel position is composed of the old loess of the Quaternary Upper Pleistocene, the old loess of the Quaternary Middle Pleistocene and the mudstone of the Upper Tertiary Upper Neogene, vertical joints and joint fissures are developed, the surrounding rock stability is poor, and belongs to V-grade surrounding rock. The tunnel burial depth H a = 28 m, Z0 = 34.7 m, h = 41.4 m, the width of the settlement tank i = K (Z0-Z), K is valued at 0.5 according to engineering experience, the surrounding rock bulk density γ = 20 kN / m 3 , the soil cohesion c = 29 kPa, and the soil internal friction angle The parameters in 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 calculation method of Xie Jiaoxiao and the application respectively, as shown in Table 1 and Table 2.

[0116] Table 1: Tunnel arch vertical load (kPa) calculated based on the Xie Jiaoxiao surrounding rock pressure calculation formula:

[0117] Stress position Crown Splay 30° Splay 45° Splay 60° Haunch P(x) 418.84186 502.44534 502.44534 468.92666 335.54327

[0118] Table 2: Tunnel arch vertical load (kPa) calculated based on the calculation method of the application:

[0119] Stress position Crown Splay 30° Splay 45° Splay 60° Haunch P(x) 108.86128 267.97173 346.6637 382.43353 354.37492

[0120] Compared with the measured data, the calculation method proposed in the application has higher consistency with the measured data, and the calculation method of the application has higher accuracy, and can be used to guide the engineering practice.

[0121] The above is only a preferred embodiment of the application, and does not limit the application. Any simple modification, change and equivalent structure change made according to the technical essence of the application to the above embodiment still belongs to the protection scope of the technical solution of the application.

Claims

1. A method for calculating the arch load of a shallow-buried loess tunnel considering the influence of vertical joints, characterized in that, Includes the following steps: Step S1: Based on the mechanical model established by Xie Jiaxiao's method, introduce loess vertical joints and establish a dynamic model of vertical joint faults; The vertical joint fault dynamic model includes the tunnel overburden BDGI, the triangular rock mass ABJ to the left of the overburden BDGI, and the triangular rock mass DEF to the right of the overburden BDGI. Step S2: Based on the vertical joint fault dynamic model described in Step S1, the vertical joint fault dynamic model is decomposed into multiple soil column units, and the stress analysis of the soil column units is performed to establish mechanical equilibrium equations in the horizontal and vertical directions. The mechanical equilibrium equations in the horizontal and vertical directions include the following steps: Step S201: Decompose the rock mass BCHI into multiple soil column units using the slice method; Step S202: Perform force analysis on the soil column element decomposed in step S201 in the horizontal and vertical directions; Step S203: Based on the force analysis of the soil column unit described in step S202, obtain the mechanical equilibrium equations of the soil column unit in the horizontal and vertical directions at a distance x from the tunnel centerline; The mechanical equilibrium equation in the horizontal direction is expressed by the following equation: ， In the formula: The normal force between soil column elements; The mechanical equilibrium equation in the vertical direction is expressed by the following equation: ， In the formula: The soil weight, This is the distance from the ground surface to the vault. The frictional force between soil column units; The force exerted by the support structure on the soil column unit; Step S3: Based on the soil column unit described in Step S2, perform a force analysis on the contact surface of adjacent soil column units to determine the frictional force between the soil column units. ; Friction between the soil column units It can be expressed by the following formula: ， In the formula: The normal force between soil column elements. This represents the angle between the thrust between soil column elements and the horizontal direction. Step S4: Based on the vertical joint fault dynamic model described in Step S2, and combined with the slope of the ground settlement curve, determine the angle between the thrust between soil column units and the horizontal direction. The expression; The angle between the thrust between the soil column units and the horizontal direction The calculation process includes the following steps: Step S401: Calculate the friction angle based on the soil. Establish the angle between the thrust between soil column elements and the horizontal direction. The expression: ， In the formula: This is the correction factor for the actual friction angle; Step 402: Determine the actual friction angle correction factor based on the foundation settlement curve. : ， Step S403: Based on the actual friction angle correction coefficient k in step S402, determine the value in step S401. : ， In the formula: The horizontal distance of any point from the tunnel axis; The horizontal distance from the tunnel centerline to the inflection point of the settlement curve; ; To select the distance from the stratum to the Earth's surface, , The depth of the tunnel's horizontal axis; Step S5: Based on the mechanical equilibrium equations in the horizontal and vertical directions described in Step S2, and the frictional force between the soil column units described in Step S3. The angle between the thrust between the soil column units described in step S4 and the horizontal direction Determine the vertical load of the tunnel arch. ; Vertical load of the tunnel arch It can be expressed by the following formula: ， In the formula: The soil weight, This is the distance from the ground surface to the vault. This refers to the length of BJ in the triangular rock mass ABJ on both sides, or the length of DF in DEF. The lateral pressure coefficient, Calculate the friction angle for the soil. The width of the settling tank. , To select the distance from the stratum to the surface, let .

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