A method for calculating earth pressure in deep tunnels considering overbreak effect

Abstract

The present invention discloses a method for calculating the earth pressure of deep tunnels that takes into account the overbreak effect. The method comprises the following steps: determining the overbreak volume of the tunnel under construction disturbance based on shield machine design parameters; constructing a theoretical analysis model, determining the parabola height based on the internal friction angle of the soil and the principal stress deflection theory, and combining the soil volume expansion coefficient with the overbreak volume to determine the height of the rectangular failure zone above the shield tunnel, thereby obtaining the heights of the load-bearing zone and the undisturbed zone; and calculating the undisturbed zone, the load-bearing zone, and the failure zone in sequence from top to bottom based on the principle of mechanical equilibrium to obtain the earth pressure at the crown of the deep shield tunnel. The method can be applied to the calculation and analysis of the earth pressure at the crown of deep shield tunnels, providing a reference for the design of deep shield tunnel segments.

Description

Technical Field

[0001] The invention belongs to the technical field of shield construction, and in particular relates to a method for calculating earth pressure in a deep-buried tunnel taking over-excavation effect into consideration. Background Art

[0002] With the rapid economic development and accelerated urbanization in my country, major cities are constructing numerous urban rail transit lines to alleviate surface traffic congestion. As shield tunnels are buried deeper, the sliding shear zone formed by the overexcavation of the shield machine fails to reach the surface and remains within the stratum. This leads to a strong soil arching effect, resulting in the earth pressure acting on the shield tunnel vault being far less than the deadweight stress of the overlying soil. Therefore, how to reasonably predict the vertical earth pressure acting on the vault of deep shield tunnels and optimize the structural design is a major challenge facing geotechnical engineers today.

[0003] Currently, most calculation methods for soil pressure on the crown of shield tunnels are still for shallow tunnels, and research on the soil pressure on the crown of deep tunnels, which takes into account the over-excavation and soil arching effects of shield machine construction, is still limited. Zhang (2016) proposed that the height of the failure zone is closely related to the stratum loss caused by tunnel construction and derived a calculation method for the soil pressure on the crown of deep tunnels. Chen and Peng (2018) pointed out that the height of the failure zone can be regarded as 0.75 times the tunnel diameter for soft soil strata and believed that the soil pressure acting on the tunnel crown can be assumed to be Gaussian distributed. Based on the limit equilibrium theory, Ji (2018) proposed a modified Protodyakonov arch model and derived an expression for the vertical load on the crown of deep tunnels.

[0004] In the aforementioned models, it is assumed that the soil above the failure zone remains undisturbed, with its own weight stress acting directly on the failure zone. However, based on discrete element simulations of sliding door tests, Lai (2018) pointed out that the soil within a certain range above the failure zone is not under its own weight stress, but rather undergoes stress redistribution. Therefore, it is unreasonable to ignore the transition zone between the failure zone and the undisturbed zone in current theoretical calculation methods. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention provides a method for calculating the earth pressure at the crown of a deep shield tunnel in sand, taking into account both overexcavation and soil arching. This method calculates the failure zone, bearing zone, and undisturbed zone of the soil above the tunnel based on the overexcavation volume of the shield machine. The soil arching effect of sand is also taken into account when calculating the load transfer in the bearing zone and failure zone.

[0006] To achieve the above object, the present invention provides a method for calculating earth pressure in a deep tunnel taking into account the overbreak effect, comprising:

[0007] Determine the over-excavation volume of the tunnel under construction disturbance based on the shield machine design parameters;

[0008] A theoretical analysis model was constructed to determine the parabola height based on the soil internal friction angle and principal stress deflection theory. The height of the rectangular failure zone above the shield tunnel was determined by combining the soil volume expansion coefficient and the over-excavation volume, thereby obtaining the heights of the load-bearing zone and the undisturbed zone.

[0009] According to the principle of mechanical equilibrium, the undisturbed area, the bearing area and the damaged area are calculated in sequence from top to bottom to obtain the earth pressure on the crown of the deep shield tunnel.

[0010] Preferably, the process of determining the over-excavation volume of the tunnel under construction disturbance according to the shield machine design parameters includes:

[0011] The over-excavation volume of the tunnel is obtained based on the relationship between the outer diameter of the shield machine and the outer diameter of the shield tunnel during shield tunnel construction.

[0012] The formula for calculating the over-excavation volume of the tunnel is:

[0013]

[0014] Where: V L is the tunnel over-excavation volume, D m is the outer diameter of the shield machine, and D is the outer diameter of the tunnel.

[0015] Preferably, the process of constructing a theoretical analysis model includes:

[0016] Assuming the soil is homogeneous and isotropic and satisfies the Mohr-Coulomb yield criterion, the soil sinks after the shield machine over-excavates, forming two shear zones within the soil above the tunnel. At this point, a failure zone, a load-bearing zone, and an undisturbed zone are formed from the tunnel top to the surface. A theoretical analysis model corresponding to these failure zones, load-bearing zones, and undisturbed zones is constructed.

[0017] The destruction zone is composed of a rectangle and a parabola; the bearing zone is an irregular shape with a straight line at the top and a parabola at the bottom; and the undisturbed zone is a rectangle.

[0018] Preferably, the formula for determining the parabola height according to the soil internal friction angle and principal stress deflection theory includes:

[0019]

[0020] Where: H3 is the height of the parabola, φ is the internal friction angle of sand, and θ0 is the principal stress deflection angle in the failure zone.

[0021] Preferably, the formula for determining the height of the rectangular damage zone above the shield tunnel by combining the soil volume expansion coefficient and the over-excavation volume is:

[0022]

[0023] Where: H4 is the height of the rectangular failure zone, and α is the soil volume expansion coefficient.

[0024] Preferably, the height of the bearing area is expressed as follows:

[0025] H2=0.4D m

[0026] Where: H2 is the height of the bearing area;

[0027] The formula for the height of the undisturbed zone is:

[0028] H1=C-H2-H3-H4

[0029] Where: C is the burial depth of the top of the shield machine.

[0030] Preferably, according to the principle of mechanical equilibrium, the process of calculating the undisturbed area, the load-bearing area and the damage area from top to bottom includes:

[0031] Calculating the uniformly distributed load of the undisturbed area acting on the upper surface of the load-bearing area;

[0032] Calculating the uniformly distributed load of the bearing area acting on the upper surface of the failure area;

[0033] Calculate the load acting on the top of the rectangular soil mass in the failure zone based on the parabolic soil mass at the upper part of the failure zone acting on the top of the rectangular soil mass with its own weight;

[0034] Based on the principle of mechanical equilibrium, the load acting on the tunnel top is calculated according to the friction force generated between the failure zone and the stable soil on both sides.

[0035] Preferably, the process of calculating the uniformly distributed load of the bearing area acting on the upper surface of the failure area includes:

[0036] The load-bearing area is divided into n three-hinged arch structures with reasonable arch axes. According to the properties of the three-hinged arch with a reasonable arch axis, each three-hinged arch is mechanically balanced, and the finite difference method is used to obtain the uniformly distributed load acting on the upper surface of the failure zone in the load-bearing area.

[0037] Preferably, a parabolic rupture surface is formed at the upper portion of the destruction zone, and the parabolic shape is consistent with a three-hinged arch with a reasonable arch axis.

[0038] Preferably, a portion of the load acting on the top of a three-hinged arch structure with a reasonable arch axis in the load-bearing area is balanced by the horizontal thrust of the arch foot, and the other portion is transferred to the top of the next three-hinged arch structure with a reasonable arch axis;

[0039] The horizontal thrust of the arch foot of the three-hinged arch structure with a reasonable arch axis in the load-bearing area is obtained by multiplying the load acting on the top of the three-hinged arch structure, the horizontal side pressure coefficient of the arch foot and the length of the arch foot.

[0040] Compared with the prior art, the present invention has the following advantages and technical effects:

[0041] The present invention can calculate the earth pressure at the top of a deep shield tunnel in sand, taking into account overbreak and soil arching effects. The algorithm is relatively simple and applicable to engineering practice. Furthermore, compared with existing algorithms, the proposed algorithm makes more reasonable assumptions, resulting in a deep tunnel top earth pressure that is more consistent with actual conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0043] Figure 1 This is a theoretical model diagram of a deep buried sand shield tunnel according to an embodiment of the present invention;

[0044] Figure 2 A load transfer calculation diagram for the load-bearing area according to an embodiment of the present invention;

[0045] Figure 3 A comparison diagram of the soil pressure on the vault of a deep tunnel according to an embodiment of the present invention and a model experiment;

[0046] Figure 4 A finite element numerical model diagram of an embodiment of the present invention;

[0047] Figure 5 A comparison diagram of the soil pressure on the vault of a deep tunnel and the numerical simulation results according to an embodiment of the present invention;

[0048] In the figure, D is the outer diameter of the tunnel, D m is the outer diameter of the shield machine, C is the buried depth of the top of the shield machine, H1 is the height of the undisturbed area, H2 is the height of the bearing area, H3 is the height of the parabolic damage area, H4 is the height of the rectangular damage area, K0 is the static horizontal side pressure coefficient, which is also the horizontal side pressure coefficient of the top of the bearing area ② and the horizontal side pressure coefficient of the undisturbed area, K l is the horizontal lateral pressure coefficient at the bottom of the bearing zone ② and the horizontal lateral pressure coefficient at the failure zone ①, q0 is the uniformly distributed load acting on the top of the bearing zone, q1 is the uniformly distributed load acting on the top of the parabolic failure zone, q2 is the uniformly distributed load acting on the top of the rectangular failure zone, q3 is the uniformly distributed load acting on the shield tunnel vault, F i is the horizontal thrust of the arch foot of the i-th three-hinged arch, n is the number of three-hinged arch parts that divide the load-bearing area, q iG is the self-weight load of the i-th three-hinged arch, qc(i-1) is the uniformly distributed load acting on the top of the i-th three-hinged arch, q ci is the uniformly distributed load acting on the i+1th three-hinged arch, L i is the length of the arch foot of the i-th three-hinged arch, F i is the horizontal thrust acting on the i-th three-hinged arch. DETAILED DESCRIPTION

[0049] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0050] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0051] like Figure 1-5 As shown, this embodiment provides a method for calculating earth pressure in a deep tunnel considering overbreak effect, comprising the following steps:

[0052] S1. Determine the tunnel over-excavation volume under construction disturbance based on the shield machine design parameters.

[0053] During shield tunnel construction, the outer diameter of the shield machine is slightly larger than the outer diameter of the shield tunnel, that is, the over-excavation volume of the tunnel is:

[0054]

[0055] Where: V L is the tunnel over-excavation volume, D m is the outer diameter of the shield machine, and D is the outer diameter of the tunnel.

[0056] S2. Construct a theoretical analysis model. Determine the parabola height based on the internal friction angle of the soil and the principal stress deflection theory. Combined with the soil volume expansion coefficient and the over-excavation volume, determine the height of the rectangular failure zone above the shield tunnel. Furthermore, the heights of the bearing zone and the undisturbed zone are obtained.

[0057] The soil is assumed to be homogeneous, isotropic, and satisfies the Mohr-Coulomb yield criterion. Subsidence after shield overexcavation results in the formation of two shear zones within the soil above the tunnel. This results in the formation of a failure zone ①, a bearing zone ②, and an undisturbed zone ③ from the tunnel top to the surface, respectively. A corresponding theoretical analysis model was then constructed. Failure zone ① is composed of a rectangular and parabolic shape, while bearing zone ② is an irregular shape with a straight top and a parabolic bottom. The undisturbed zone ③ is rectangular. Compared to the stable soil on either side of the failure zone, the soil within the failure zone undergoes a larger vertical displacement, resulting in frictional stress between the soil and the stable soil on either side. This in turn causes a deflection of the principal stress within the failure zone, manifesting as a maximum principal stress arch effect. The maximum principal stress arch has the same shape as the parabola at the top of the parabolic zone: both are three-hinged arches with a reasonable arch axis.

[0058] The parabola height obtained by the internal friction angle of soil investigation parameters and principal stress deflection theory is:

[0059]

[0060] Where: H3 is the height of the parabola, φ is the internal friction angle of sand, and θ0 is the principal stress deflection angle in the failure zone.

[0061] Combining the soil volume expansion coefficient and the over-excavation volume, the height of the rectangular failure zone above the shield tunnel is determined as:

[0062]

[0063] Where: H4 is the height of the rectangular failure zone, and α is the soil volume expansion coefficient.

[0064] The height of the bearing area can be obtained through numerical simulation, existing literature or experience, and the value is:

[0065] H2=0.4D m

[0066] Wherein: H2 is the height of the bearing area.

[0067] The height of the undisturbed area can be further obtained as:

[0068] H1=C-H2-H3-H4

[0069] Where: C is the burial depth of the top of the shield machine.

[0070] S3. Based on the principle of mechanical equilibrium, theoretical formulas are derived for the undisturbed area, load-bearing area and failure area from top to bottom to obtain the soil pressure on the crown of the deep shield tunnel.

[0071] The theoretical derivation process is as follows:

[0072] Undisturbed zone ③:

[0073] The uniformly distributed load q0 of the undisturbed area ③ acting on the upper surface of the load-bearing area ② is:

[0074] q0=H1γ

[0075] Where: γ is the soil weight per unit volume.

[0076] Loading area ②:

[0077] As the transition area between the undisturbed area ③ and the damaged area ①, the bearing area ② has a bearing arch effect, that is, a soil arch effect. Considering that the bearing area ② connects the damaged area ① and the undisturbed area ③, it has a transitional effect. The horizontal lateral pressure coefficient at the top of the bearing area ② is taken as the static horizontal lateral pressure coefficient K0, and the horizontal lateral pressure coefficient at the bottom of the bearing area ② is taken as the horizontal lateral pressure coefficient K of the failure zone. l .

[0078] Combining the principal stress deflection theory, the horizontal lateral pressure coefficients at the top and bottom of the bearing area ② can be obtained as follows:

[0079]

[0080] Where: K0 is the static horizontal lateral pressure coefficient, which is also the horizontal lateral pressure coefficient of the top of the bearing area ② and the horizontal lateral pressure coefficient of the undisturbed area, K l K is the horizontal lateral pressure coefficient at the bottom of the bearing zone ② and the horizontal lateral pressure coefficient at the failure zone ①, a is the active earth pressure coefficient.

[0081] The load-bearing area ② is divided into n three-hinged arch structures with reasonable arch axes. According to the properties of three-hinged arches with reasonable arch axes, each three-hinged arch is mechanically balanced, and the finite difference method is used to obtain the uniformly distributed load q1 of the load-bearing area ② acting on the upper surface of the failure area ①:

[0082]

[0083] Where: q iG is the deadweight of the i-th three-hinged arch, K i is the horizontal lateral pressure coefficient of the i-th three-hinged arch, θ i is the principal stress deflection angle of the i-th three-hinged arch, L i is the length of the arch foot of the i-th three-hinged arch.

[0084] Destruction Zone ①:

[0085] The parabolic soil in the upper part of the failure zone ① acts on the top of the rectangular soil with its own weight. The load q2 acting on the top of the rectangular soil in the failure zone ① is expressed as:

[0086]

[0087] The friction force generated between the failure zone ① and the stable soil on both sides is as follows:

[0088]

[0089] A parabolic fracture surface is formed at the upper portion of the destruction zone ①, and the parabolic shape is consistent with a three-hinged arch with a reasonable arch axis.

[0090] The undisturbed zone ① does not undergo principal stress deflection, that is, the principal stress deflection angle is 0; the principal stress deflection angle in the damage zone is constant at θ0; the bearing zone ② has a transition effect, and the principal stress deflection angle decreases linearly from θ0 at the bottom to 0 at the top.

[0091] The load-bearing area ① is divided into n three-hinge arch structures with reasonable arch axes. The larger the value of n is, the more accurate the calculation result is. However, when the value of n exceeds 100, the value of n no longer affects the calculation result.

[0092] Part of the load acting on the top of the three-hinged arch structure with a reasonable arch axis in the load-bearing area ② is balanced by the horizontal thrust of the arch foot, and the other part is transferred to the top of the next three-hinged arch structure with a reasonable arch axis.

[0093] The horizontal thrust of the arch foot of the three-hinged arch structure with a reasonable arch axis in the load-bearing area ② can be obtained by multiplying the load acting on the top of the three-hinged arch structure, the horizontal side pressure coefficient of the arch foot and the length of the arch foot.

[0094] The calculation method proposed by the present invention is further described in detail below with reference to the accompanying drawings.

[0095] First, the over-excavation volume of the tunnel under construction disturbance is determined according to the shield machine design parameters. Second, a theoretical analysis model is constructed to determine the parabola height based on the soil internal friction angle and principal stress deflection theory. The height of the rectangular failure zone above the shield tunnel is determined by combining the soil volume expansion coefficient and the over-excavation volume. The heights of the bearing zone and the undisturbed zone are then obtained, as shown in Figure 2. Figure 1 Finally, according to the principle of mechanical equilibrium, theoretical formulas are derived from the undisturbed area, the bearing area and the damaged area from top to bottom to obtain the earth pressure on the crown of the deep buried shield tunnel. Among them, the load transfer model for the bearing area is as follows: Figure 2 As shown in Figure 1, a load-bearing arch with a height of H1 is divided equally into n parts at mid-span height, with each part having a mid-span height of H1 / n. Each part is considered a three-hinged arch structure with a reasonable arch axis. Based on the properties of a three-hinged arch with a reasonable arch axis, the downward load can be calculated from top to bottom, thus obtaining the load q1 acting on the top of the parabolic failure zone.

[0096] (1) Comparison with normalized soil pressure in model tests

[0097] The experimental results of Franza (2018)'s centrifuge model test under different over-excavation conditions were compared with the algorithm proposed in this paper. Figure 3 It can be seen that the calculation results of the algorithm provided by the present invention are relatively close to the model test results, which verifies the accuracy and superiority of the algorithm provided by the present invention.

[0098] (2) Comparison with numerical simulation results

[0099] Establish a two-dimensional finite element numerical model, such as Figure 4 As shown. Finite element calculation is performed on the numerical model to obtain the calculation results of the earth pressure on the deep buried tunnel vault. The calculation results of this algorithm are compared with the numerical simulation results, as shown in Figure 5 As shown in Figure 2, it can be seen that the calculation results provided by this algorithm are in good agreement with the numerical simulation results.

[0100] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for calculating earth pressure in deep tunnels considering overbreak effect, characterized in that: include: Determine the over-excavation volume of the tunnel under construction disturbance based on the shield machine design parameters; A theoretical analysis model was constructed to determine the parabola height based on the soil internal friction angle and principal stress deflection theory. The height of the rectangular failure zone above the shield tunnel was determined by combining the soil volume expansion coefficient and the over-excavation volume. The height of the bearing zone, and thus the height of the undisturbed zone, was obtained through numerical simulation. According to the principle of mechanical equilibrium, the undisturbed area, the bearing area and the damaged area are calculated from top to bottom to obtain the earth pressure of the deep shield tunnel crown; Among them, the damage zone, the bearing zone and the undisturbed zone are formed from the tunnel top to the ground surface; The destruction zone is composed of a rectangle and a parabola; the bearing zone is an irregular shape with a straight line at the top and a parabola at the bottom; the undisturbed zone is a rectangle; According to the principle of mechanical equilibrium, the process of calculating the undisturbed area, the load-bearing area and the damage area from top to bottom includes: Calculating the uniformly distributed load of the undisturbed area acting on the upper surface of the load-bearing area; Calculating the uniformly distributed load of the bearing area acting on the upper surface of the failure area; Calculate the load acting on the top of the rectangular soil mass in the failure zone based on the parabolic soil mass at the upper part of the failure zone acting on the top of the rectangular soil mass with its own weight; Based on the principle of mechanical equilibrium, the load acting on the tunnel top is calculated according to the friction force generated between the failure zone and the stable soil on both sides; The process of calculating the uniformly distributed load of the bearing area acting on the upper surface of the failure area includes: The load-bearing area is divided into n three-hinged arch structures with reasonable arch axes. According to the properties of the three-hinged arch with a reasonable arch axis, each three-hinged arch is mechanically balanced, and the finite difference method is used to obtain the uniformly distributed load acting on the upper surface of the failure zone in the load-bearing area.

2. The method according to claim 1, characterized in that The process of determining the overexcavation volume of the tunnel under construction disturbance based on the shield machine design parameters includes: The over-excavation volume of the tunnel is obtained based on the relationship between the outer diameter of the shield machine and the outer diameter of the shield tunnel during shield tunnel construction. The formula for calculating the over-excavation volume of the tunnel is: Where: V L is the tunnel over-excavation volume, D m is the outer diameter of the shield machine, and D is the outer diameter of the tunnel.

3. The method according to claim 1, characterized in that The process of building a theoretical analysis model includes: Assuming that the soil is homogeneous and isotropic and satisfies the Mohr-Coulomb yield criterion, the soil sinks after the shield machine over-excavates, forming two shear zones within the soil above the tunnel. At this time, a failure zone, a load-bearing zone, and an undisturbed zone are formed from the tunnel top to the surface, respectively. A theoretical analysis model corresponding to these failure zones, load-bearing zones, and undisturbed zones is constructed.

4. The method according to claim 2, characterized in that The formulas for determining the parabola height based on the soil internal friction angle and principal stress deflection theory include: Where: H3 is the height of the parabola, φ is the internal friction angle of sand, and θ0 is the principal stress deflection angle in the failure zone.

5. The method according to claim 4, characterized in that The formula for determining the height of the rectangular failure zone above the shield tunnel by combining the soil volume expansion coefficient and the over-excavation volume is: Where: H4 is the height of the rectangular failure zone, and α is the soil volume expansion coefficient.

6. The method according to claim 5, characterized in that The formula for the height of the bearing area is: H2=0.4D m Where: H2 is the height of the bearing area; The formula for the height of the undisturbed zone is: H1=C-H2-H3-H4 Where: C is the burial depth of the top of the shield machine.

7. The method according to claim 1, characterized in that A parabolic fracture surface is formed at the upper portion of the destruction zone, and the parabolic shape is consistent with a three-hinged arch with a reasonable arch axis.

8. The method according to claim 1, characterized in that A portion of the load acting on the top of a three-hinged arch structure with a reasonable arch axis in the load-bearing area is balanced by the horizontal thrust of the arch foot, and the other portion is transferred to the top of the next three-hinged arch structure with a reasonable arch axis; The horizontal thrust of the arch foot of the three-hinged arch structure with a reasonable arch axis in the load-bearing area is obtained by multiplying the load acting on the top of the three-hinged arch structure, the horizontal side pressure coefficient of the arch foot and the length of the arch foot.

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