Deep tunnel soil pressure calculation method considering overexcavation effect

Abstract

The invention discloses a deep tunnel soil pressure calculation method considering an over-excavation effect. The method comprises the following steps that the over-excavation volume of a tunnel under construction disturbance is determined according to design parameters of a shield tunneling machine; a theoretical analysis model is constructed, the parabola height is determined according to the soil internal friction angle and the principal stress deflection theory, the height of a rectangular damage area above the shield tunnel is determined by combining the soil volume expansion coefficient and the overexcavation volume, and then the height of a bearing area and the height of an undisturbed area are obtained; according to the mechanical equilibrium principle, the undisturbed area, the bearing area and the damaged area are sequentially calculated from top to bottom, and the vault soil pressure of the deeply-buried shield tunnel is obtained. The method can be applied to calculation and analysis of the vault soil pressure of the deeply-buried shield tunnel, and reference is provided for design of segments of the deeply-buried shield tunnel.

Description

Technical Field

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

[0002] With the rapid development of my country's economy and the acceleration of urbanization, major cities are building a large number of urban rail transit lines to alleviate ground traffic congestion. As the depth of shield tunnels gradually increases, the sliding shear zone of the soil formed by the over-excavation of the shield machine cannot extend to the surface and remains inside the stratum, thus showing a strong soil arch effect, resulting in the soil pressure acting on the crown of the shield tunnel being much smaller than the self-weight stress of the overlying soil. Therefore, how to reasonably predict the vertical soil pressure acting on the crown of a deep-buried shield tunnel and optimize the structural design is a huge challenge facing geotechnical engineering designers today.

[0003] At present, most of the calculation methods for the soil pressure on the crown of shield tunnels are still for shallow tunnels, and the research on the soil pressure on the crown of deep buried tunnels considering the over-excavation and soil arching effect 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 buried tunnels. Chen and Peng (2018) pointed out that the height of the failure zone can be regarded as 0.75 times the diameter of the tunnel for soft soil strata, and believed that the soil pressure acting on the crown of the tunnel 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 a deep buried tunnel.

[0004] In the above models, it is assumed that the soil above the damage zone is still in an undisturbed state and the self-weight stress acts directly on the damage zone. However, based on the discrete element simulation of the sliding door test, Lai (2018) pointed out that the soil in a certain range above the damage zone is not in a self-weight stress state, but also undergoes stress redistribution. It can be seen that it is unreasonable to ignore the transition zone between the damage zone and the undisturbed zone in the current theoretical calculation method. Summary of the invention

[0005] In order to overcome the above-mentioned deficiencies of the prior art, the present invention provides a method for calculating the earth pressure of the arch of a deep buried shield tunnel in sand soil, taking into account the over-excavation and soil arching effect during construction. The calculation method can calculate the destruction area, bearing area and undisturbed area of ​​the soil above the tunnel according to the over-excavation volume of the shield machine. When calculating the load transfer in the bearing area and the destruction area, the soil arching effect of the sand soil is taken into account.

[0006] To achieve the above object, the present invention provides a method for calculating earth pressure of a deep buried 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 is constructed to determine the height of the parabola according to the internal friction angle of the soil and the principal stress deflection theory, and the height of the rectangular damage zone above the shield tunnel is determined by combining the soil volume expansion coefficient and the over-excavation volume, thereby obtaining the height of the bearing zone and the undisturbed zone;

[0009] According to the principle of mechanical balance, the undisturbed area, the bearing area and the damaged area are calculated in sequence from top to bottom to obtain the soil 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] According to the relationship between the outer diameter of the shield machine and the outer diameter of the shield tunnel during the shield tunnel construction process, the over-excavation volume of the tunnel is obtained;

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

[0013]

[0014] Where: V L is the tunnel overcut 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 that the soil is homogeneous, isotropic, and satisfies the Mohr-Coulomb yield criterion, the soil sinks after the shield machine over-excavates, and two shear zones are formed inside the soil above the tunnel. At this time, a damage zone, a load-bearing zone, and an undisturbed zone are formed from the top of the tunnel to the surface, respectively. The theoretical analysis models corresponding to the damage zone, the load-bearing zone, and the undisturbed zone are 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:

[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 buried depth of the top of the shield machine.

[0030] Preferably, according to the principle of mechanical balance, 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] According to the parabolic soil in the upper part of the damage zone acting on the top of the rectangular soil with its own weight, the load acting on the top of the rectangular soil in the damage zone is calculated;

[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 damage area includes:

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

[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, part of the load acting on the top of the 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 part 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 soil pressure of the arch of a deep buried shield tunnel in sand soil considering the over-excavation and soil arching effect during construction. The algorithm is relatively simple and can be applied to engineering practice. At the same time, compared with the existing algorithms, the algorithm has more reasonable assumptions, and the obtained soil pressure of the arch of the deep buried tunnel is more in line with the actual situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0043] Figure 1 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 of a 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 buried 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 result 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 load-bearing zone ② and the horizontal lateral pressure coefficient at the damage zone ①, q0 is the uniformly distributed load acting on the top of the load-bearing zone, q1 is the uniformly distributed load acting on the top of the parabolic damage zone, q2 is the uniformly distributed load acting on the top of the rectangular damage 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 arches 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 in the embodiments of the present 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, in this embodiment, a method for calculating earth pressure of a deep buried tunnel considering overbreak effect is provided, comprising the following steps:

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

[0053] During the shield tunnel construction process, 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 overcut 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 soil internal friction angle and principal stress deflection theory, and determine the height of the rectangular damage zone above the shield tunnel by combining the soil volume expansion coefficient and the over-excavation volume, and then obtain the height of the bearing area and the undisturbed area.

[0057] The soil is assumed to be homogeneous, isotropic, and meets the Mohr-Coulomb yield criterion. The subsidence of the soil after the shield machine over-excavates will form two shear zones inside the soil above the tunnel. At this time, the damage zone ①, the bearing zone ②, and the undisturbed zone ③ are formed from the top of the tunnel to the surface, and then the corresponding theoretical analysis model is constructed. The damage zone ① is composed of a rectangle and a parabola, the bearing zone ② is an irregular shape with a straight line at the top and a parabola at the bottom, and the undisturbed zone ③ is a rectangle. Compared with the stable soil on both sides of the damage zone, the soil in the damage zone undergoes a larger vertical displacement, and there is friction stress between the soil and the stable soil on both sides, which leads to the deflection of the principal stress in the failure zone, showing the maximum principal stress arch effect. The shape of the maximum principal stress arch is the same as the parabola at the top of the parabola zone, both of which are three-hinged arches with a reasonable arch axis.

[0058] The parabola height obtained by the internal friction angle of soil investigation parameters and the 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 damage 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] Further, the height of the undisturbed area can be obtained as:

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

[0069] Where: C is the buried 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, bearing area and damaged area from top to bottom to obtain the soil pressure on the crown of the deep buried shield tunnel.

[0071] The theoretical derivation process is as follows:

[0072] Undisturbed zone③:

[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 transition effect. The horizontal side pressure coefficient at the top of the bearing area ② is taken as the static horizontal side pressure coefficient K0, and the horizontal side pressure coefficient at the bottom of the bearing area ② is taken as the horizontal side 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 are:

[0079]

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

[0081] The bearing area ② is divided into n three-hinged arch structures with reasonable arch axes. According to the properties of the three-hinged arch 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 bearing area ② acting on the upper surface of the failure area ①:

[0082]

[0083] Where: q iG is the self-weight 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 damage 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 damage zone ① is expressed as:

[0086]

[0087] The friction force is generated between the damage zone ① and the stable soil on both sides. According to the principle of mechanical equilibrium, the load q3 acting on the top of the tunnel is:

[0088]

[0089] A parabolic rupture 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 the bottom θ0 to the top 0.

[0091] The load-bearing area ① is divided into n three-hinged 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 transmitted 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 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 in conjunction with the accompanying drawings.

[0095] Firstly, the over-excavation volume of the tunnel under construction disturbance is determined according to the design parameters of the shield machine. Secondly, a theoretical analysis model is constructed to determine the parabola height according to the internal friction angle of the soil and the principal stress deflection theory, and the height of the rectangular damage zone above the shield tunnel is determined by combining the soil volume expansion coefficient and the over-excavation volume, and then the height of the bearing zone and the undisturbed zone is obtained, such as Figure 1 As shown; Finally, according to the principle of mechanical equilibrium, the 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. The load-bearing arch with a height of H1 is divided into n parts at the mid-span height, and the mid-span height of each load-bearing arch is H1 / n. Each load-bearing arch is considered to be a three-hinged arch structure with a reasonable arch axis. According to the properties of the three-hinged arch with a reasonable arch axis, the load transferred downward can be obtained from top to bottom, and the load q1 acting on the top of the parabolic failure zone can be obtained.

[0096] (1) Comparison with normalized earth 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 soil pressure on the deep tunnel vault. The calculation results of this algorithm are compared with the numerical simulation results, as shown in Figure 5 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 only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A method for calculating earth pressure of a deep tunnel 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 is constructed to determine the height of the parabola according to the internal friction angle of the soil and the principal stress deflection theory, and the height of the rectangular damage zone above the shield tunnel is determined by combining the soil volume expansion coefficient and the over-excavation volume, thereby obtaining the height of the bearing zone and the undisturbed zone; According to the principle of mechanical balance, the undisturbed area, the bearing area and the damaged area are calculated in sequence from top to bottom to obtain the soil pressure on the crown of the deep shield tunnel.

2. The method according to claim 1, characterized in that The process of determining the over-excavation volume of the tunnel under construction disturbance based on the shield machine design parameters includes: According to the relationship between the outer diameter of the shield machine and the outer diameter of the shield tunnel during the shield tunnel construction process, the over-excavation volume of the tunnel is obtained; The formula for calculating the over-excavation volume of the tunnel is: Where: V L is the tunnel overcut 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, isotropic, and satisfies the Mohr-Coulomb yield criterion, the soil sinks after the shield machine over-excavates, and two shear zones are formed inside the soil above the tunnel. At this time, a damage zone, a load-bearing zone, and an undisturbed zone are formed from the top of the tunnel to the surface, respectively. The theoretical analysis models corresponding to the damage zone, the load-bearing zone, and the undisturbed zone are constructed. 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.

4. The method according to claim 1, 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 1, characterized in that: 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: Where: H4 is the height of the rectangular failure zone, and α is the soil volume expansion coefficient.

6. The method according to claim 1, 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 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; According to the parabolic soil in the upper part of the damage zone acting on the top of the rectangular soil with its own weight, the load acting on the top of the rectangular soil in the damage zone is calculated; 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.

8. The method according to claim 7, characterized in that The process of calculating the uniformly distributed load of the bearing area acting on the upper surface of the failure area includes: The bearing area is divided into n three-hinged arch structures with reasonable arch axes. According to the properties of the three-hinged arch with reasonable arch axes, each three-hinged arch is mechanically balanced, and the uniformly distributed load of the bearing area acting on the upper surface of the failure area is obtained by using the finite difference method.

9. The method according to claim 8, characterized in that 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.

10. The method according to claim 8, characterized in that A part of the load acting on the top of the 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 part is transmitted 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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