Method for determining surrounding rock pressure distribution of shield tunnel with cavity behind lining wall

Abstract

This invention discloses a method for determining the surrounding rock pressure distribution of a shield tunnel with cavities behind its lining, relating to the field of tunnel construction technology. The method includes: acquiring the geometric characteristic parameters of the cavities behind the lining of the shield tunnel to be tested; inputting the geometric characteristic parameters into a surrounding rock pressure correction model, fitting a relationship using correction coefficients corresponding to the circumferential positions, and performing quantitative calculations based on radial height and circumferential angles to obtain surrounding rock pressure correction coefficients; correcting the baseline surrounding rock pressure under cavity-free conditions using the surrounding rock pressure correction coefficients to obtain the corrected equivalent uniformly distributed surrounding rock pressure value; and determining the actual surrounding rock pressure distribution of the shield tunnel under the cavity defect condition based on the corrected equivalent uniformly distributed surrounding rock pressure value. This invention enables the load distribution characteristics to adaptively adjust with changes in the cavity location, significantly improving the efficiency of determining the surrounding rock pressure distribution.

Description

Technical Field

[0001] This invention relates to the field of tunnel construction technology, and in particular to a method for determining the pressure distribution of surrounding rock in shield tunnels with cavities behind the lining wall. Background Technology

[0002] Voids behind tunnel lining walls are one of the most common defects in tunnel engineering. Their presence alters the interaction mechanism between the surrounding rock and the lining structure, leading to pressure redistribution in the surrounding rock and deterioration of the lining's stress state. Studying the impact of voids behind the tunnel lining structure on its stress characteristics and internal force distribution, and understanding the distribution and evolution of cracks in the lining structure, not only helps elucidate the disaster mechanism of tunnels but also facilitates prevention and repair, laying the foundation for assessing the safety and health status of tunnels.

[0003] In existing technologies, some scholars have used theoretical analysis to refine the pressure load of the surrounding rock when cavities exist, and then used it to modify the lining structure model. The implementation process includes: first, based on physical model tests, revealing the redistribution law of the surrounding rock pressure load when cavities exist, that is, stress concentration occurs on both sides of the cavity, and the load first increases and then decreases; then, based on this, the traditional load-structure model is modified, changing the originally uniformly distributed surrounding rock pressure to a non-uniform loading mode that reflects the characteristics of the load increase on both sides of the cavity; finally, the reliability of the modified model is verified by comparing numerical examples and indoor tests, and a lining safety influence coefficient is introduced for tunnel structure safety assessment.

[0004] When the location of the cavity changes continuously, the non-uniform distribution characteristics of the surrounding rock pressure will change significantly. However, the existing correction model lacks an adaptive mechanism that can dynamically adjust the load distribution function or boundary conditions according to the location of the cavity. The same set of correction parameters cannot be applied to working conditions at different cavity locations, and its versatility in engineering applications is significantly restricted. It is necessary to recalibrate the model for each new location, which reduces the efficiency of determining the distribution of surrounding rock pressure. Summary of the Invention

[0005] Therefore, it is necessary to provide a method for determining the surrounding rock pressure distribution of shield tunnels with cavities behind the lining wall, in order to address the above-mentioned technical problems.

[0006] This invention provides a method for determining the pressure distribution of surrounding rock in a shield tunnel with cavities behind the lining wall, comprising: Obtain the geometric characteristic parameters of the shield tunnel under test with cavities behind the lining wall. The geometric characteristic parameters include the circumferential position, radial height and circumferential angle of the cavity. The geometric characteristic parameters are input into the surrounding rock pressure correction model. The relationship is fitted by the correction coefficient corresponding to the circumferential position and quantitatively calculated based on the radial height and circumferential angle to obtain the surrounding rock pressure correction coefficient. The surrounding rock pressure correction model is obtained by regression analysis based on the numerical simulation results under different combinations of circumferential position, radial height and circumferential angle of the cavity. The reference surrounding rock pressure under the condition of no voids is corrected by the surrounding rock pressure correction coefficient to determine the actual load value borne by each circumferential position of the shield tunnel lining to be tested, and the corrected equivalent uniformly distributed surrounding rock pressure value is obtained. Based on the corrected equivalent uniformly distributed surrounding rock pressure value, the actual surrounding rock pressure distribution of the shield tunnel under the condition of void defects is determined.

[0007] Optionally, the circumferential location of the cavity includes at least one of the vault, shoulder, or waist; When the circumferential position is the crown, the surrounding rock pressure correction factor includes: the vertical surrounding rock pressure correction factor. β y and horizontal surrounding rock pressure correction factor β x ; When the circumferential location is the shoulder or waist of an arch, the surrounding rock pressure correction factor includes: the vertical surrounding rock pressure correction factor. β y Correction coefficient for horizontal surrounding rock pressure on the cavity side β lx Correction factor for horizontal surrounding rock pressure on non-cavitary side β rx .

[0008] Optionally, geometric feature parameters are input into the surrounding rock pressure correction model to fit the relationship through correction coefficients corresponding to the circumferential positions and to perform quantitative calculations based on radial height and circumferential angle, thereby obtaining the surrounding rock pressure correction coefficients, including: The fitting equation for the correction coefficient is a polynomial function with circumferential angle as the independent variable, or a polynomial function with radial height as the independent variable. The fitting accuracy of the polynomial function is verified by the coefficient of determination, and the coefficient of determination is not less than the preset accuracy threshold. By processing the geometric characteristic parameters using polynomial functions, the surrounding rock pressure correction coefficient is obtained.

[0009] Optionally, the numerical simulation results based on different circumferential cavity locations and different combinations of radial height and circumferential angle are obtained through the following methods: A refined two-dimensional finite element model containing the strata, grouting layer, lining, and voids was constructed using finite element simulation software. For the three circumferential positions of the arch crown, arch shoulder, and arch waist, as well as the combined working conditions with radial heights of 0.1m, 0.3m, 0.6m, and 0.9m and circumferential angles of 15°, 30°, 45°, and 60° at each circumferential position, a full-condition combined simulation analysis was performed on the two-dimensional refined finite element model, and numerical simulation results were obtained.

[0010] Optionally, the baseline surrounding rock pressure under void-free conditions is corrected using a surrounding rock pressure correction factor to determine the actual load values ​​borne by the shield tunnel lining at each circumferential position, including: When the radial height is greater than or equal to the set threshold, the surrounding rock pressure at the circumferential position corresponding to the cavity area is determined to be zero, and the surrounding rock pressure at the circumferential positions on both sides of the cavity is increased according to the surrounding rock pressure correction coefficient. When the radial height is less than the set threshold, it is determined that the surrounding rock pressure at the circumferential position corresponding to the cavity area is not zero, and the surrounding rock pressure at the circumferential positions on both sides of the cavity increases gradually according to the surrounding rock pressure correction coefficient. The degree of gradual increase is lower than the degree when the radial height is greater than or equal to the set threshold.

[0011] Optionally, the surrounding rock pressure at the circumferential locations immediately adjacent to the cavity can be determined based on the following formula: ; ; in, q For vertical surrounding rock pressure, e For horizontal surrounding rock pressure, γ The bulk density of soil, R Where is the radius of the tunnel. φ It is the internal friction angle. f k The surrounding rock firmness coefficient, β y This is the correction factor for vertical surrounding rock pressure. β x This is the correction factor for horizontal surrounding rock pressure.

[0012] The method for determining the surrounding rock pressure distribution of a shield tunnel with cavities behind the lining wall provided in this embodiment of the invention has the following advantages compared with the prior art: This invention establishes a surrounding rock pressure correction model through numerical simulation covering different combinations of circumferential positions, radial heights, and circumferential angles. This model includes a fitting formula for correction coefficients that dynamically adjust with the circumferential position of the cavity. After inputting arbitrary cavity position parameters, the corresponding correction coefficients are automatically calculated and quantified to obtain the surrounding rock pressure correction coefficients. This technique enables the load distribution characteristics to adaptively adjust with changes in cavity position, eliminating the need for re-calibration at each new location and significantly improving the efficiency of determining the surrounding rock pressure distribution. Attached Figure Description

[0013] Figure 1 This is a diagram illustrating the pressure distribution pattern of surrounding rock without cavities in a shield tunnel with cavities behind the lining wall, provided in one embodiment. Figure 2 This is a characteristic map of the surrounding rock pressure redistribution in a method for determining the surrounding rock pressure distribution of a shield tunnel with cavities behind the lining wall, provided in one embodiment. Figure 3 This embodiment provides a method for determining the surrounding rock pressure distribution in a shield tunnel with cavities behind the lining wall. β y Fitting curve with the circumferential angle α of the cavity; Figure 4 This embodiment provides a method for determining the surrounding rock pressure distribution in a shield tunnel with cavities behind the lining wall. β x Fitting curve with the circumferential angle α of the cavity; Figure 5 This embodiment provides a method for determining the surrounding rock pressure distribution in a shield tunnel with cavities behind the lining wall. β y Fitting curve of the cavity radial height H; Figure 6 This embodiment provides a method for determining the surrounding rock pressure distribution in a shield tunnel with cavities behind the lining wall. β x Fitting curve of the cavity radial height H; Figure 7 This embodiment provides a method for determining the surrounding rock pressure distribution in a shield tunnel with cavities behind the lining wall. β y Fitting curve with the circumferential angle α of the cavity; Figure 8 This embodiment provides a method for determining the surrounding rock pressure distribution in a shield tunnel with cavities behind the lining wall. β lx Fitting curve with the circumferential angle α of the cavity; Figure 9 This embodiment provides a method for determining the surrounding rock pressure distribution in a shield tunnel with cavities behind the lining wall. β rx Fitting curve with the circumferential angle α of the cavity; Figure 10 This embodiment provides a method for determining the surrounding rock pressure distribution in a shield tunnel with cavities behind the lining wall. β y Fitting curve with the circumferential angle α of the cavity; Figure 11 This embodiment provides a method for determining the surrounding rock pressure distribution in a shield tunnel with cavities behind the lining wall. β lx Fitting curve with the circumferential angle α of the cavity; Figure 12 This embodiment provides a method for determining the surrounding rock pressure distribution in a shield tunnel with cavities behind the lining wall. β rx Fitting curve with the circumferential angle α of the cavity; Figure 13 This embodiment provides a method for determining the surrounding rock pressure distribution in a shield tunnel with cavities behind the lining wall. β y Fitting curve of the cavity radial height H; Figure 14 This is a technical roadmap for a method to determine the pressure distribution of surrounding rock in a shield tunnel with cavities behind the lining wall, as provided in one embodiment. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0015] This invention provides a method for determining the pressure distribution of surrounding rock in shield tunnels with cavities behind the lining wall, such as... Figure 14 As shown, the method includes: Obtain the geometric characteristic parameters of the shield tunnel under test with cavities behind the lining wall. The geometric characteristic parameters include the circumferential position, radial height and circumferential angle of the cavity.

[0016] Geometric characteristic parameters are input into the surrounding rock pressure correction model. The relationship is fitted using correction coefficients corresponding to the circumferential position, and quantitative calculations are performed based on radial height and circumferential angle to obtain the surrounding rock pressure correction coefficients. The surrounding rock pressure correction model is obtained by regression analysis of numerical simulation results based on combinations of circumferential position, radial height, and circumferential angle of different cavities.

[0017] The reference surrounding rock pressure under the condition of no voids is corrected by the surrounding rock pressure correction coefficient to determine the actual load value borne by each circumferential position of the shield tunnel lining to be tested, and the corrected equivalent uniformly distributed surrounding rock pressure value is obtained. Based on the corrected equivalent uniformly distributed surrounding rock pressure value, the actual surrounding rock pressure distribution of the shield tunnel under the condition of void defects is determined.

[0018] Preferably, the circumferential location of the cavity includes at least one of the vault, shoulder, or waist.

[0019] When the circumferential position is the crown, the surrounding rock pressure correction factor includes: the vertical surrounding rock pressure correction factor. β y and horizontal surrounding rock pressure correction factor β x .

[0020] When the circumferential location is the shoulder or waist of an arch, the surrounding rock pressure correction factor includes: the vertical surrounding rock pressure correction factor. β y Correction coefficient for horizontal surrounding rock pressure on the cavity side β lx Correction factor for horizontal surrounding rock pressure on non-cavitary side β rx .

[0021] Preferably, geometric feature parameters are input into the surrounding rock pressure correction model, and the relationship is fitted through correction coefficients corresponding to the circumferential positions and quantitatively calculated based on radial height and circumferential angle to obtain the surrounding rock pressure correction coefficients, including: The fitting equation for the correction coefficients is a polynomial function with either the circumferential angle or the radial height as the independent variable. The fitting accuracy of the polynomial function is verified by the coefficient of determination, and the coefficient of determination is not less than a preset accuracy threshold. The surrounding rock pressure correction coefficients are obtained by processing the geometric feature parameters using the polynomial function.

[0022] Preferably, the numerical simulation results based on different circumferential cavity locations and different combinations of radial height and circumferential angle are obtained through the following methods: A refined two-dimensional finite element model, including the strata, grouting layer, lining, and voids, was constructed using finite element simulation software. A full-condition combined simulation analysis was performed on the refined two-dimensional finite element model for three circumferential positions: the arch crown, arch shoulder, and arch waist, with radial heights of 0.1m, 0.3m, 0.6m, and 0.9m at each position, and circumferential angles of 15°, 30°, 45°, and 60° at each position. Numerical simulation results were obtained.

[0023] Preferably, the reference surrounding rock pressure under void-free conditions is corrected using a surrounding rock pressure correction coefficient to determine the actual load-bearing values ​​at each circumferential position of the shield tunnel lining to be tested, including: When the radial height is greater than or equal to the set threshold, the surrounding rock pressure at the circumferential position corresponding to the cavity area is determined to be zero, and the surrounding rock pressure at the circumferential positions immediately adjacent to the cavity is increased according to the surrounding rock pressure correction coefficient.

[0024] When the radial height is less than the set threshold, it is determined that the surrounding rock pressure at the circumferential position corresponding to the cavity area is not zero, and the surrounding rock pressure at the circumferential positions on both sides of the cavity increases gradually according to the surrounding rock pressure correction coefficient. The degree of gradual increase is lower than the degree when the radial height is greater than or equal to the set threshold.

[0025] A specific embodiment of the present invention is provided: Step 1: Establish a numerical simulation model and obtain the baseline surrounding rock pressure.

[0026] Taking a section of loess strata in a subway system in a certain region as an example, a refined two-dimensional finite element numerical model was established, including the strata, grouting layer, lining, and cavities. The baseline value of vertical surrounding rock pressure under cavity-free conditions was obtained. q Compared with the horizontal surrounding rock pressure benchmark value e Its distribution pattern is as follows Figure 1 As shown.

[0027] The physical and mechanical parameters of the soil (new loess, old loess, and silty clay) and the lining (C50 concrete, with a modulus reduced by 70%) were determined. A weakened element was used to simulate cavities, and a complete construction phase was established (ground stress equilibrium → tunnel excavation → support grouting → cavity formation). The accuracy of the model was verified by comparing the calculation results under a cavity-free condition with Protodyakonov's theoretical values.

[0028] Step 2: Systematically reveal the redistribution pattern of surrounding rock pressure.

[0029] Vertical pressure benchmark value under void-free working conditions q and horizontal pressure reference value e For reference, based on the numerical model, a full-condition combined simulation analysis was conducted for three typical locations of the cavity: the arch crown, the arch shoulder, and the arch waist, and for the radial height H (0.1m, 0.3m, 0.6m, and 0.9m) and circumferential angle α (15°, 30°, 45°, and 60°) of the cavity at each location. The following three characteristic redistribution patterns were obtained:

[0030] Void top pattern: Vertical surrounding rock pressure accumulates on both sides of the void, forming a gradient distribution of "zero pressure in the void area and high pressure in the adjacent area".

[0031] Arch-shoulder cavity mode: Horizontal surrounding rock pressure is explosively concentrated at the close proximity of the cavity, and vertical pressure rises significantly in sync.

[0032] Arched waist cavity mode: The original core bearing area is completely depressurized, the vertical pressure is transferred to both sides of the cavity, and the horizontal pressure is transferred to the arch foot.

[0033] Meanwhile, the abrupt change characteristics of the critical radial height H=0.3m were clarified: when H≥0.3m, due to the isolation effect of the grouting layer, the vertical and horizontal surrounding rock pressure in the cavity area are both reduced to zero, and the stress concentration effect is significantly enhanced.

[0034] Step 3: Propose and derive the surrounding rock pressure correction formula based on the void parameters.

[0035] Introducing correction coefficients β Define the correction factor β It is the ratio of the equivalent uniformly distributed surrounding rock pressure when cavities exist to the equivalent uniformly distributed surrounding rock pressure when there are no cavities.

[0036] Derivation of the Area Equivalence Method: Initial surrounding rock pressure is calculated based on Protodyakonov's theory for cases without cavities. For cases with cavities, the area equivalence method is used to equate the redistributed pressure curve around the cavity's influence area to a uniformly distributed load, leading to the following derivation: β The mathematical expression for the initial surrounding rock pressure without cavities is given. The modified Protodyakonov theory formula is used to calculate this initial pressure.

[0037] ; ; in: q For vertical surrounding rock pressure, e For horizontal surrounding rock pressure, γ The bulk density of soil, R Where is the radius of the tunnel. φ It is the internal friction angle. f k The surrounding rock firmness coefficient, β y This is the correction factor for vertical surrounding rock pressure. β x This is the correction factor for horizontal surrounding rock pressure.

[0038] High-precision formula fitting: Using a large number of data samples obtained from numerical simulation, correction coefficients are established through regression analysis. β The fitting relationship between the radial height H and the circumferential angle α of the cavity is as follows: Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 , Figure 9 , Figure 10 , Figure 11 and Figure 12 As shown, and as detailed calculation formulas listed in Tables 1 to 6.

[0039] in, Figure 3 The vertical surrounding rock pressure correction factor at different radial heights H under the condition of voids in the arch crown. βy A fitted curve of the cavity circumferential angle α is used to show the effect of α increasing. β y The non-linear growth trend. Figure 4 The correction factor for horizontal surrounding rock pressure at different radial heights H under the condition of voids in the arch crown. β x The fitted curve of the cavity circumferential angle α shows... β x It fluctuates within the range of 1.0 to 1.3. Figure 5 The vertical surrounding rock pressure correction factor for different circumferential angles α under the condition of voids in the arch crown. β y The fitted curve of H = 0.3m with the radial height H of the cavity reveals that H = 0.3m is... β y The critical point of abrupt change. Figure 6 The correction factor for horizontal surrounding rock pressure at different circumferential angles α under the condition of voids in the arch crown. β x The fitted curve of the cavity radial height H reflects the result after H ≥ 0.3m. β x The changing pattern as H increases.

[0040] Figure 7 The vertical surrounding rock pressure correction factor for different radial heights H under the arch shoulder cavity condition. β y The fitted curve of the cavity circumferential angle α is used to characterize the redistribution of vertical pressure. Figure 8 The correction factor for the horizontal surrounding rock pressure on the left side at different radial heights H under the condition of arch shoulder cavity. β lx The fitted curve of the cavity circumferential angle α reflects the explosive concentration effect of horizontal pressure on the cavity side. Figure 9 The correction factor for the horizontal surrounding rock pressure on the right side at different radial heights H under the condition of arch shoulder void. β rx The fitted curve of the cavity circumferential angle α shows the variation of the horizontal pressure on the non-cavitary side.

[0041] Figure 10 The vertical surrounding rock pressure correction factor for different radial heights H under the arch-waist cavity condition. β y The fitted curve of the cavity circumferential angle α is used to describe the steep increase trend of vertical load transfer to both sides of the cavity. Figure 11 The correction factor for the horizontal surrounding rock pressure on the left side at different radial heights H under the arch-waist cavity condition. β lx The fitting curve of the cavity circumferential angle α reflects the degree of pressure relief and edge stress concentration in the cavity area. Figure 12 The correction factor for the horizontal surrounding rock pressure on the right side at different radial heights H under the arch-waist cavity condition. β rx The fitted curve of the cavity circumferential angle α shows the response characteristics of the horizontal pressure on the non-cavitary side.

[0042] Table 1. When α increases under the arch cavity β Calculation formula Table 2 When H increases under the arch cavity β Calculation formula Table 3. When α increases under the arch shoulder cavity β Calculation formula Table 4. When H increases under the arch shoulder cavity β Calculation formula Table 5. When α increases under the arched cavity β Calculation formula Table 6 When H increases under the arched cavity β Calculation formula Furthermore, taking the calculation of surrounding rock pressure when there are cavities in the arch as an example, an application embodiment of the present invention is provided: Taking a tunnel section of Metro Line 9 in a certain area as an example, the tunnel radius R = 3.0m, and the average density of the stratum... γ =18.9kN / m³, internal friction angle φ =19.7°. On-site non-destructive testing revealed a cavity behind the lining arch, with a measured radial height H=0.6m and a circumferential angle α=45°.

[0043] 1. Determination of the reference surrounding rock pressure.

[0044] First, the initial vertical surrounding rock pressure under void-free conditions is calculated using the modified Protodyakonov theory formula. q and horizontal pressure e According to calculations, q =232.93 kPa, e =140.15 kPa. The ideal pressure distribution pattern without cavities is as follows: Figure 1 As shown in the figure, the equilibrium state is achieved when the lining and surrounding rock are in complete contact and share the load. The peak values ​​of both vertical and horizontal pressures are concentrated at the arch waist.

[0045] 2. Analysis of pressure redistribution patterns.

[0046] For the arch cavity condition in this embodiment (H=0.6m≥0.3m, α=45°), its surrounding rock pressure redistribution characteristics are as follows: Figure 2 .like Figure 2 As shown, under the condition of H≥0.3m, due to the isolation effect of the 0.3m thick grouting layer, the vertical and horizontal surrounding rock pressure in the cavity area (corresponding to the center of the arch crown) both return to zero. At the same time, significant vertical pressure concentration occurs in the areas immediately adjacent to the cavity, forming a "double cat's ear" type stress peak, while the horizontal pressure in the area from the arch waist to the arch foot remains basically stable. This phenomenon indicates that the cavity in the arch crown cuts off the transmission path of the vertical load, forcing the load to transfer to the intact surrounding rock areas on both sides.

[0047] 3. Selection and calculation of correction coefficients.

[0048] To quantify the aforementioned pressure concentration effect, a correction factor β needs to be introduced. Referring to Table 1, for the arch cavity, when the radial height H = 0.6 m, the high-precision fitting relationship between the correction factor and the circumferential angle α is as follows (see table for fitting curve). Figure 3 and Figure 4 ):

[0049] β y = 0.0012α² - 0.045α + 1.88; β x = 0.0008α² - 0.030α + 1.62; Figure 3 This intuitively reflects the different values ​​under different H values. β y The nonlinear growth trend that occurs as α increases; Figure 4 This shows that the impact of the voids in the vault on horizontal pressure is relatively limited. β x It fluctuates only within the range of 1.0 to 1.3.

[0050] Substituting α=45° from this embodiment into the above formula, we obtain: β y = 0.0012×(45)² - 0.045×45 + 1.88 = 2.28; β x = 0.0008×(45)² - 0.030×45 + 1.62 = 1.89; Alternatively, a correction formula based on the radial height H can be obtained from Table 2, and combined with... Figure 5 and Figure 6 Perform cross-validation. Figure 5 This reveals that H=0.3m is the critical mutation point: when H<0.3m... β y The change is gradual; when H ≥ 0.3m, β y It increases rapidly as H increases.

[0051] 4. Calculation of the corrected surrounding rock pressure.

[0052] The correction factor is applied to the reference pressure to obtain the equivalent surrounding rock pressure actually borne by the lining when void defects exist.

[0053] 5. Engineering applications.

[0054] 5.1 Grouting pressure design.

[0055] Based on the calculated vertical loosening pressure of 531.08 kPa, in order to prevent the formation of voids again after the grouting body consolidates and shrinks, it is recommended that the final grouting pressure on site should not be less than 0.5 MPa.

[0056] 5.2 Segment reinforcement design.

[0057] The above-mentioned modified pressure value was applied to the load-structure model for load-bearing capacity verification. The results showed that the segment bending moment within a 30° range on both sides of the arch exceeded the limit, and carbon fiber cloth needed to be pasted within a 100° range of the tunnel arch for reinforcement.

[0058] Furthermore, taking the calculation of surrounding rock pressure when there are cavities in the arch as an example, an application embodiment of the present invention is provided: This paper describes a common tunnel arch cavity defect in operating tunnels. Detection revealed a cavity behind the left arch of a certain tunnel section, with a measured radial height H = 0.2m and a circumferential angle α = 35°.

[0059] 1. Analysis of pressure redistribution patterns.

[0060] Although H=0.2m in this embodiment did not reach the critical value of 0.3m for "pressure zeroing", the void in the arch waist had already begun to change the distribution pattern of the surrounding rock pressure. As the core load-bearing area under void-free conditions, the presence of voids in the arch waist causes local pressure relief. When H<0.3m, the pressure in the void area of ​​the arch waist has begun to decrease, while the pressure on both sides of the void is increasing, showing a trend of transitioning from a pressure relief zone to a stress accumulation zone.

[0061] 2. Calculation of correction coefficient and safety early warning.

[0062] Referring to Table 5, for the arched cavity, when H=0.3m (in this embodiment, H=0.2m needs to be predicted according to the most unfavorable case with reference to the formula for H=0.3m), the relationship between the correction coefficient and α is as follows: β y = 0.0009α² - 0.021α + 1.21; Substituting α=35° into the calculation β y = 0.0009×1225 - 0.735 + 1.21 ≈ 1.58.

[0063] This means that even with a small cavity height, the vertical pressure at its edge is still 1.58 times the initial pressure due to the circumferential angle reaching 35°.

[0064] Based on the early warning threshold system of this invention (arched cavities α>30° or H>0.1m are prone to entering an unsafe state), α=35° in this embodiment has exceeded the 30° warning line. According to this calculation result, the pressure on the surrounding rock at the cavity edge has begun to concentrate rapidly. Further refer to... Figure 10 ( β y (fit curve with α) and Figure 13 ( β y The two figures (fitting curves with H) respectively illustrate the steep increase trend of the vertical correction coefficient under the arched cavity condition: Figure 10 The nonlinear growth relationship of βy from 2.76 to 4.48 as α increases from 15° to 60° is clearly shown when H is fixed at 0.9m; when α increases from 15° to 60°, β y The value increased from 2.76 to 4.48; when α was fixed at 60°, H increased from 0.3m to 0.9m. β y The value increased from 1.43 to 4.48. This demonstrates that the voids in the arched waist significantly reduce the safety factor, necessitating early intervention.

[0065] 3. Project handling.

[0066] Based on the early warning and quantitative assessment of the method of this invention, temporary steel support and micro-disturbance grouting filling measures were immediately taken on site, which effectively controlled the further redistribution of the surrounding rock pressure and avoided deformation and cracking of the lining structure.

[0067] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for determining the pressure distribution of surrounding rock in a shield tunnel with cavities behind the lining wall, characterized in that, include: Obtain the geometric characteristic parameters of the shield tunnel under test with cavities behind the lining wall. The geometric characteristic parameters include the circumferential position, radial height and circumferential angle of the cavity. The geometric feature parameters are input into the surrounding rock pressure correction model. The relationship is fitted by the correction coefficient corresponding to the circumferential position and quantitatively calculated based on the radial height and the circumferential angle to obtain the surrounding rock pressure correction coefficient. The surrounding rock pressure correction model is obtained by regression analysis of numerical simulation results based on the combination of circumferential position, radial height and circumferential angle of different cavities. The reference surrounding rock pressure under the condition of no voids is corrected by the surrounding rock pressure correction coefficient to determine the actual load value borne by each circumferential position of the lining of the shield tunnel to be tested, and the corrected equivalent uniformly distributed surrounding rock pressure value is obtained. The actual surrounding rock pressure distribution of the shield tunnel to be tested under the condition of void defects is determined based on the corrected equivalent uniformly distributed surrounding rock pressure value.

2. The method for determining the surrounding rock pressure distribution of a shield tunnel with cavities behind the lining wall as described in claim 1, characterized in that, The circumferential location of the cavity includes at least one of the vault, shoulder, or waist; When the circumferential position is the arch crown, the surrounding rock pressure correction factor includes: vertical surrounding rock pressure correction factor. β y and horizontal surrounding rock pressure correction factor β x ; When the circumferential position is an arch shoulder or arch waist, the surrounding rock pressure correction factor includes: a vertical surrounding rock pressure correction factor. β y Correction coefficient for horizontal surrounding rock pressure on the cavity side β lx Correction factor for horizontal surrounding rock pressure on non-cavitary side β rx .

3. The method for determining the surrounding rock pressure distribution of a shield tunnel with cavities behind the lining wall as described in claim 1, characterized in that, The step of inputting the geometric feature parameters into the surrounding rock pressure correction model, fitting the relationship through the correction coefficient corresponding to the circumferential position, and performing quantitative calculation based on the radial height and the circumferential angle to obtain the surrounding rock pressure correction coefficient includes: The fitting formula for the correction coefficient is a polynomial function with the circumferential angle as the independent variable or a polynomial function with the radial height as the independent variable. The polynomial function is fitted with a coefficient of determination, and the coefficient of determination is not less than a preset accuracy threshold. The surrounding rock pressure correction coefficient is obtained by processing the geometric characteristic parameters using the polynomial function.

4. The method for determining the surrounding rock pressure distribution of a shield tunnel with cavities behind the lining wall as described in claim 1, characterized in that, The numerical simulation results based on different combinations of cavity circumferential position, radial height, and circumferential angle were obtained through the following methods: A refined two-dimensional finite element model containing the strata, grouting layer, lining, and voids was constructed using finite element simulation software. For the three circumferential positions of the arch crown, arch shoulder, and arch waist, as well as the combined working conditions where the radial heights at each circumferential position are 0.1m, 0.3m, 0.6m, and 0.9m, and the circumferential angles at each circumferential position are 15°, 30°, 45°, and 60°, a full-condition combined simulation analysis was performed on the two-dimensional refined finite element model to obtain numerical simulation results.

5. The method for determining the surrounding rock pressure distribution of a shield tunnel with cavities behind the lining wall as described in claim 1, characterized in that, The process of correcting the baseline surrounding rock pressure under void-free conditions using the surrounding rock pressure correction coefficient to determine the actual load values ​​borne by the lining of the shield tunnel under test at each circumferential position includes: When the radial height is greater than or equal to a set threshold, the surrounding rock pressure at the circumferential position corresponding to the cavity area is determined to be zero, and the surrounding rock pressure at the circumferential positions adjacent to both sides of the cavity is increased according to the surrounding rock pressure correction coefficient. When the radial height is less than the set threshold, it is determined that the surrounding rock pressure at the circumferential position corresponding to the cavity area is not zero, and the surrounding rock pressure at the circumferential positions adjacent to both sides of the cavity increases gradually according to the surrounding rock pressure correction coefficient. The degree of the gradual increase is lower than the degree when the radial height is greater than or equal to the set threshold.

6. The method for determining the surrounding rock pressure distribution of a shield tunnel with cavities behind the lining wall as described in claim 5, characterized in that, The surrounding rock pressure at the circumferential positions immediately adjacent to the cavity is determined based on the following formula: ； ； in, q For vertical surrounding rock pressure, e For horizontal surrounding rock pressure, γ The bulk density of soil, R Where is the radius of the tunnel. φ It is the internal friction angle. f k The surrounding rock firmness coefficient, β y This is the correction factor for vertical surrounding rock pressure. β x This is the correction factor for horizontal surrounding rock pressure.

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