Method for predicting land subsidence caused by ultra-shallow-buried excavation pilot tunnel construction based on random medium

Abstract

The invention discloses a method for predicting land subsidence caused by ultra-shallow-buried excavation pilot tunnel construction based on a random medium, and relates to the technical field of urban rail transit engineering. The method is mainly used for predicting the problem of land subsidence caused by shallow burial depth of the subway station, which is crucial for safe and efficient construction and operation of rail transit systems such as urban subways and light rails. In urban rail transit construction, the ultra-shallow-buried underground excavation technology can be used in complex environments without blocking traffic, damaging road surfaces, changing and moving pipelines, influencing residents and the like, and has the advantages of being safe, reliable, rapid, environmentally friendly, capable of saving resources and the like, so that the ultra-shallow-buried underground excavation technology is widely applied. The invention provides a novel land subsidence prediction method by combining a random medium theory and an optimization algorithm so as to improve the prediction accuracy and the construction safety.

Description

Technical Field

[0001] The present invention relates to the field of urban rail transit engineering technology, and in particular to a settlement prediction technology for ultra-shallow buried underground excavation pilot tunnel construction used in subway construction. This technology is mainly used to predict ground subsidence problems caused by shallow buried depths of subway stations, which is crucial for the safe and efficient construction and operation of rail transit systems such as urban subways and light rails. In urban rail transit construction, ultra-shallow buried underground excavation technology is widely used because it can be used in complex environments without blocking traffic, damaging road surfaces, changing pipelines, or affecting residents, and has the advantages of safety, reliability, speed, environmental protection, and cost-saving. The present invention provides a new ground subsidence prediction method by combining random medium theory and optimization algorithms to improve the accuracy of prediction and the safety of construction. Background Art

[0002] Currently, random media are often used in theoretical formulas for predicting surface deformation caused by subway tunnel construction. In ultra-shallow tunnel construction, because the construction cross-section is often horseshoe-shaped, calculations of construction-induced lateral ground settlement are based on plane strain. When predicting surface deformation based on random media theory, the horseshoe-shaped cross-section is typically converted to a circular shape, assuming uniform cross-section convergence. However, in actual projects, the construction cross-section is not circular, and due to the influence of construction conditions and initial stratum stress, the cross-section convergence is also non-uniform, resulting in inaccurate prediction results. In particular, in ultra-shallow cases, the errors are large. Therefore, a new prediction method is needed to improve prediction accuracy. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for predicting ground subsidence caused by ultra-shallow buried underground pilot tunnel construction based on random medium theory. This method is based on the actual shape and convergence mode of the construction section, takes into account the influence of multiple factors in actual engineering, and can more accurately predict ground subsidence.

[0004] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0005] The present invention provides a method for predicting ground subsidence caused by ultra-shallow buried underground excavation pilot tunnel construction based on random medium theory, comprising the following steps:

[0006] Step 1: Determine the initial horseshoe cross-section shape parameters

[0007] like Figure 1 The initial horseshoe cross section shown is composed of two parts, the upper arched part is a circle with a radius of R and a height of C, and the lower rectangle has a height of B and a width of A.

[0008]

[0009] Step 2: Determine the cross-sectional non-uniform shrinkage process and parameters

[0010] The final deformed convergent shape is formed by the combination of two deformations, such as Figure 2 As shown. The blue dashed line is the initial horseshoe section, as shown Figure 2 As shown in a), the soil shrinks uniformly during the first deformation. The green dotted line is the horseshoe cross-section outline after the first deformation. During uniform shrinkage, the center of the initial cross-section is the shrinkage center, which is located at (B+C) / 2. Assume that the uniform shrinkage displacement of the cross-section is ΔR. The arched part after shrinkage is still circular, and the radius of the arc after shrinkage is R1. The height of the arched part after shrinkage is C1, C1=C-ΔR. The height of the rectangular part below after shrinkage is B1, B1=B-ΔR, and the width of the rectangular part is A1, A1=A-2*ΔR. The second non-uniform deformation that occurred afterwards is shown in Figure 1. Figure 2 As shown in b), the green dotted line is the cross-sectional profile of the horseshoe after the first deformation, and the black solid line is the cross-sectional profile of the horseshoe after the second deformation. The center of the cross-section after the first deformation is the shrinkage center, and non-uniform convergence deformation occurs. After the second deformation, the arched part changes from a circle to an ellipse, and the shrinkage value of the arched top is positive δ. The height of the rectangle becomes shorter, and the width of the rectangle becomes larger. When the second shrinkage value δ is negative, it means that the top of the arch bulges upward, and the height of the rectangle becomes larger and the width becomes narrower. The cross-sectional parameters after deformation are determined based on the equal cross-sectional area before and after the second deformation. The height of the arched part after shrinkage is C2, C2 = C1-δ, the radius of the arc is R2, the height of the lower rectangular part after shrinkage is B2 = A1*B1 / A2, and the width of the rectangular part is A2. A2 is solved by the following equation:

[0011]

[0012] in:

[0013]

[0014] Step 3: Establish a ground settlement prediction model caused by ultra-shallow buried pilot tunnel construction based on random media. According to Axiom 3 of random medium theory, the surface settlement value W(x) caused by ultra-shallow buried pilot tunnel excavation under the two-stage non-uniform convergence model is calculated as follows:

[0015] W(x)=W1(x)+W2(x)

[0016] Where x is the horizontal distance from the pilot tunnel axis. Figure 3 As shown in the figure, W1(x) and W2(x) are the surface displacements caused by the two deformations of the section, respectively. The calculation formula is as follows:

[0017]

[0018]

[0019] Each double integral of W1(x) and W2(x) should be superimposed after the corresponding integral limits are calculated according to the arch part and the rectangular part respectively. The double integral limits a, b, c, d, e, f, g, h, e', f', g', h' of W1(x) and W2(x) are shown in Table 1. tanβ is the tangent value of the main influence angle of the upper surrounding rock of the pilot tunnel, and the specific value is obtained by inverse analysis according to the measured data. Details are shown in step four. η is the depth coordinate of the micro-soil unit of excavation, ξ is the horizontal axis coordinate of the micro-soil unit of excavation, the section center is buried at a depth of H from the ground surface, and π is the circular constant.

[0020] Table 1: Integral limits of horse-shoe-shaped section area

[0021]

[0022] The meanings of the remaining symbols are the same as above

[0023] Step four: solve the three key parameters in step two by establishing a target function, convert the parameter solving problem into a minimum optimization problem of the target function, and the optimal solution of the target function is the best estimate value of the three parameters. Establish a target function about the three parameters to be solved, and take the three key parameters in step two as unknown quantities v: the tangent value tanβ of the main influence angle of the surrounding rock, the uniform shrinkage displacement ΔR of the section, and the second shrinkage displacement δ. The target function F(v) is established as:

[0024]

[0025] In the formula: W 0 i is the i-th measured value of ground settlement; W i (v) is the i-th theoretical calculation value of ground settlement,

[0026] Each W i (v) is obtained according to W(x) = W1(x) + W2(x); m is the total number of measured data; v is the parameter to be determined, where v = {tanβ, ΔR, δ}. λ is the coefficient of the penalty function, which is taken as 0.0001 in this case.

[0027] Step five: according to the measured values of ground surface deformation of the characteristic section of the ultra-shallow pilot tunnel, such as Figure 4As shown in the figure, the n-dimensional optimized Powell algorithm is used to minimize the objective function F(v). The resulting solution is the optimal parameter combination. Using MATLAB, the backAnalyse.m file is created. Inputs include an initial trial step of 1 for the extrapolation method, 0 initial trial points for the extrapolation method, 0 golden section accuracy, 0.001 precision for the n-dimensional optimized Powell algorithm, initial estimated values ​​for the undetermined parameters (DR = 40; tanb = 0.4; sigma = 150), the central buried depth H of the pilot tunnel section (different for each case), the height C of the arched portion of the horseshoe section (different for each case), the height B of the rectangular portion of the horseshoe section (different for each case), the width A of the rectangular portion of the horseshoe section (different for each case), the measured settlement value, and the horizontal distance corresponding to the measured settlement value. The n-dimensional optimized Powell algorithm first obtains the number of parameters to be determined and calculates the value of the objective function under the initial conditions. The objective function calculation is divided into two parts: a ground settlement prediction model caused by ultra-shallow buried pilot tunnel construction based on random medium theory and a penalty function. After that, iterative calculations are performed based on the specified output accuracy. First, the golden section single search interval is determined by extrapolation, and then the step size of this search is determined. The new coordinates are obtained based on the initial direction. The function change value corresponding to this forward direction is recorded, and the direction with the largest change is found before the end of this round of search. At the end of this round of search, a reflection point is made to determine whether it meets the optimized Powell condition. If it does, an accelerated search is performed and the direction with the largest change is replaced. Otherwise, this step is skipped and only the starting point of the next search is updated. Finally, it is determined whether it meets the target accuracy. If it is output data, three key parameters are finally obtained: the tangent value tanβ of the main influencing angle of the surrounding rock, the specific values ​​of the uniform shrinkage displacement ΔR of the section, and the second shrinkage displacement δ.

[0028] Step 6:

[0029] Based on the tangent value of the main influencing angle of the surrounding rock tanβ, the uniform shrinkage displacement ΔR of the section and the second shrinkage displacement δ obtained in step 5, the initial parameters of the predicted section are input into the settlement prediction model proposed in step 3 to obtain the predicted surface settlement curve.

[0030] Beneficial effects:

[0031] The above formula, compiled using Matlab, can be used to easily calculate ground subsidence caused by ultra-shallow buried pilot tunnel construction. Compared with existing technologies, this method can more accurately predict ground subsidence caused by ultra-shallow buried pilot tunnel construction, reducing misjudgments and losses during construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 Schematic diagram of the initial horseshoe cross section

[0033] Figure 2 Horseshoe-shaped cross-section contraction form

[0034] Figure 3 Schematic diagram of pilot tunnel excavation calculation model

[0035] Figure 4 Flowchart of parameter determination using back analysis method

[0036] Figure 5 Comparison of calculation results of Kunming Tunnel

[0037] Figure 6 Comparison of calculation results of ultra-shallow buried pilot tunnels in Beijing DETAILED DESCRIPTION

[0038] Example 1

[0039] The section between the East Passenger Station and Dabanqiao Station on the Kunming Metro Line was constructed using the shallow-buried, underground excavation method. This single-track, single-hole tunnel features significantly varying hydrological and engineering geological conditions. The tunnel primarily traverses silty clay and fully weathered argillaceous siltstone formations. The silty clay has an elastic modulus of 7.24 MPa, a Poisson's ratio of 0.28, a cohesion of 12.8 kPa, and an internal friction angle of 15.6°. The fully weathered argillaceous siltstone has an elastic modulus of 8.55 MPa, a Poisson's ratio of 0.3, a cohesion of 14.6 kPa, and an internal friction angle of 18.7°. Both have a bulk density of 18.8 kN / m³, and crosses the expressway. The tunnel depth varies from 2 to 50 meters. The selected cross-section has a vault approximately 10 meters above the ground surface. The tunnel cross-section is horseshoe-shaped, 6.7 meters wide, with a rectangular section 3.5 meters high and a circular section 3.1 meters high. The tunnel center is buried at a depth of 14.5 meters. The tunnel vault is pre-reinforced with Φ42 advanced small guide tubes within 120°, and Φ89 long pipe shed grouting reinforcement is used within 150°; the primary lining is about 0.3m thick and consists of C25 concrete, Φ8 full-ring steel mesh with a spacing of 150×150mm, and 200 grid steel frame. The excavation adopts a combination of circular excavation with core soil retention and step method.

[0040] The calculation parameters are as follows: H = 14.5, A = 6.7m, B = 3.5m, C = 3.1m, ΔR = 30.26mm, tanβ = 0.7, δ = 228.96mm.

[0041] Example 2

[0042] Beijing Metro Line 13 Xueyuan South Road Station is located on the south side of the intersection of Xueyuan South Road and Jiaoda East Road. The pilot tunnel has a horseshoe-shaped tunnel section, 4 meters wide, 3.4 meters high in the rectangular part, 1.7 meters high in the circular part, and a center burial depth of 5.5 meters. The calculation parameters are as follows: H = 5.5m, A = 4m, B = 3.4m, C = 1.7m, ΔR = -7.75mm, tanβ = 0.17, δ = 350.89mm. The calculation results are shown in Figure 6 , the central axis of the tunnel is at a horizontal distance of 0m.

[0043] From Figure 6 It can be seen that the theoretical calculation results in this paper have the same overall trend as the measured data, but there is no stage of small increase in the uplift value again. The settlement value calculated by the random medium theory is the largest above the axis, which is -4.23 mm. The settlement decreases rapidly along the direction away from the axis and turns to uplift. The uplift speed is 1.41 mm / m. The surface inclination direction points to the axis. The uplift reaches the extreme value of 10.19 mm at a horizontal distance of 10.2 m. The uplift decreases rapidly along the direction away from the axis. The uplift value decreases to 1.04 mm at a horizontal distance of 23.7 m. The decreasing rate is 0.67 mm / m, and the surface inclination direction is away from the axis. The correlation between the random medium theoretical calculation results and the measured data is the highest within a range of 5 m from the axis. At the same time, this is also the decreasing stage of the surface settlement, which has a similar rule to the measurement. The surface uplift value increases at a rate of about twice that of the decreasing stage. The surface inclination degree in the uplift decreasing stage has a high correlation with the measurement.

Claims

1. A method for predicting ground subsidence caused by ultra-shallow buried pilot tunnel construction based on random media, characterized by: Step 1: Determine the initial horseshoe cross-section shape parameters The initial horseshoe cross section consists of two parts, the upper arched part is a circle with a radius of R and a height of C, and the lower rectangle has a height of B and a width of A. Step 2: Determine the cross-sectional non-uniform shrinkage process and parameters The final deformation convergence shape is formed by the combination of two deformations. During the first deformation, the soil shrinks uniformly. During the uniform shrinkage, the center of the initial section is the shrinkage center. The center of the initial section is located at (B+C) / 2. Assume that the uniform shrinkage displacement of the section is ΔR. The arched part after shrinkage is still circular. The radius of the arc after shrinkage is R1. The height of the arched part after shrinkage is C1, C1=C-ΔR. The height of the rectangular part below after shrinkage is B1, B1=B-ΔR, and the width of the rectangular part is A1, A1=A-2*ΔR. The second inhomogeneous deformation occurred afterwards; The center of the cross section after the first deformation is used as the shrinkage center, and non-uniform convergent deformation occurs. After the second deformation, the arched part changes from a circle to an ellipse. The shrinkage value of the arch top is positive δ, and the height of the rectangle becomes shorter while the width of the rectangle increases. When the second shrinkage value δ is negative, it means that the arch top bulges upward, and the height of the rectangle increases while the width becomes narrower. The cross-sectional parameters after deformation are determined based on the fact that the cross-sectional areas before and after the second deformation are equal. The height of the arched part after contraction is C2, C2 = C1-δ, the radius of the arc is R2, the height of the rectangular part below after contraction is B2 = A1*B1 / A2, and the width of the rectangular part is A2. A2 is solved by the following equation: in: Step 3: Establish a ground settlement prediction model caused by ultra-shallow buried pilot tunnel construction based on random media; Step 4: Solve the three key parameters in step 2 by establishing the objective function. Convert the parameter solving problem into the minimum value optimization problem of the objective function. The optimal solution of the objective function is the best estimated value of the three parameters. Establish an objective function for the three parameters to be determined, with the three key parameters in step 2 as unknown quantities v: the tangent value tanβ of the main influencing angle of the surrounding rock, the uniform shrinkage displacement ΔR of the cross section, and the second shrinkage displacement δ; establish its objective function F(v) as: Where: W 0 i is the measured value of the i-th surface settlement; W i (v) is the theoretical calculated value of the i-th surface settlement, Each W i (v) is obtained according to W(x) = W1(x) + W2(x); m is the total number of measured data; v is the unknown parameter, where v = {tanβ, ΔR, δ}; λ is the coefficient of the penalty function; Step 5: Based on the measured surface deformation values ​​of the characteristic section of the ultra-shallow buried pilot tunnel, the n-dimensional optimization Powell algorithm is used to find the minimum value of the objective function F(v). The obtained solution is the optimal parameter combination. Step 6: Based on the tangent value of the main influencing angle of the surrounding rock tanβ, the uniform shrinkage displacement ΔR of the section and the second shrinkage displacement δ obtained in step 5, the initial parameters of the predicted section are input into the settlement prediction model proposed in step 3 to obtain the predicted surface settlement curve.

2. The method according to claim 1, characterized in that Step 3 is as follows: The calculation formula for the surface settlement value W(x) caused by ultra-shallow buried pilot tunnel excavation under the two-stage non-uniform convergence mode is as follows: W(x)=W1(x)+W2(x) Where x is the horizontal distance from the pilot tunnel axis, W1(x) and W2(x) are the surface displacements caused by the two deformations of the section, respectively. The calculation formula is as follows: For each double integral in W1(x) and W2(x), the corresponding integral limits should be calculated according to the arch part and the rectangular part respectively and then superimposed. The double integral limits a, b, c, d, e, f, g, h, e', f', g', h' of W1(x) and W2(x) are as follows; tanβ is the tangent value of the main influencing angle of the surrounding rock above the pilot tunnel, and the specific value is obtained by back analysis based on the measured data; η is the depth coordinate of the excavated micro-soil unit, ξ is the horizontal axis coordinate of the excavated micro-soil unit, the buried depth of the section center from the ground surface is H, and π is the pi; 3. The method according to claim 1, characterized in that Step 5 is as follows: Through MATLAB implementation, first create the backAnalyse.m file, input the extrapolation method initial trial step 1, the extrapolation method initial trial point 0, the golden section method accuracy 0.001, the n-dimensional optimization Powell algorithm accuracy 0.001, the initial estimated value of the undetermined parameters, the buried depth H of the center of the pilot tunnel section, the height C of the arch part of the horseshoe section, the height B of the rectangular part of the horseshoe section, the width A of the rectangular part of the horseshoe section, the measured settlement value, and the horizontal distance corresponding to the measured settlement value; the n-dimensional optimization Powell algorithm first obtains the number of parameters to be determined, and calculates the function value of the objective function under the initial conditions. The calculation of the objective function is divided into a ground settlement prediction model caused by ultra-shallow buried dark excavation pilot tunnel construction based on random medium theory and a penalty The function consists of two parts; then, iterative calculations are performed based on the specified output accuracy. First, the extrapolation method is used to determine the single search interval of the golden section, and then the step size of this search is determined. The new coordinates are obtained according to the initial direction, and the function change value corresponding to this forward direction is recorded. Before the end of this round of search, the direction with the largest change is found; at the end of this round of search, a reflection point is made to determine whether it meets the optimized Powell condition. If so, an accelerated search is performed and the direction with the largest change is replaced. Otherwise, this step is skipped and only the starting point of the next search is updated; finally, it is determined whether it meets the target accuracy. If so, the output data is obtained, and finally three key parameters are obtained: the tangent value tanβ of the surrounding rock influence angle, the specific values ​​of the uniform shrinkage displacement ΔR of the section, and the second shrinkage displacement δ.

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