A double-line tunnel dynamic ground surface settlement prediction method

Abstract

The application discloses a kind of double-line tunnel dynamic ground surface settlement prediction methods, comprising the following steps: step one, single-line tunnel Peck formula;Step two, the settlement calculation of double-line tunnel excavation in y direction;Step three, the longitudinal ground surface settlement calculation caused by double-line tunnel excavation;Step four, the ground surface settlement calculation when double-line tunnel excavation is completely penetrated;Step five, the longitudinal excavation coefficient calculation of double-line tunnel excavation;Step six, double-line tunnel Peck formula.The prediction method establishes the double-line tunnel dynamic ground surface settlement prediction model considering longitudinal excavation degree parameter, realizes the purpose of double-line tunnel construction ground surface settlement real-time prediction, with rationality and accuracy.

Description

Technical Field

[0001] This invention relates to the field of tunnel excavation technology, specifically to a method for predicting dynamic surface settlement in a dual-track tunnel. Background Technology

[0002] Tunnel excavation inevitably disturbs the surrounding soil, causing deformation and surface subsidence. Subway tunnels are often laid beneath main urban roads, sometimes even passing under buildings and pipelines. Excessive ground and surface subsidence will inevitably impact the safety of road structures, buildings, and pipelines. Therefore, accurately predicting surface subsidence caused by tunnel construction and selecting appropriate construction parameters to minimize it is crucial for ensuring tunnel construction safety.

[0003] Currently, the main methods for predicting surface subsidence both domestically and internationally include the Peck empirical formula method, theoretical analysis method, numerical simulation method, and model test method. Since the Peck empirical formula was proposed in 1969, it has been the most widely used due to its simplicity and rationality. However, the parameter values ​​in the Peck formula are affected by factors such as geological conditions, tunnel depth, construction control level, and time effect, resulting in a certain deviation between the calculated results and the measured values. Many scholars have made applicability modifications to the Peck formula and provided methods for selecting formula parameters.

[0004] Since the spacing between the two parallel subway tunnels does not change significantly and they are symmetrical about the centerline, the construction conditions can be approximated as being the same. Based on the superposition principle, the Peck formulas for the left and right tunnels are added together to obtain the Peck formula for the two-track tunnel. Most surface settlement predictions using the Peck formula are the final surface settlement, but they cannot calculate the real-time surface settlement when the tunnel is excavated to a certain point, nor do they consider the situation of two-track tunnel excavation. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting dynamic surface settlement in twin-track tunnels. This method establishes a modified twin-track Peck formula and introduces a longitudinal excavation degree parameter to solve the problem of real-time prediction of surface settlement during twin-track tunnel construction.

[0006] A method for predicting dynamic surface settlement in a dual-track tunnel includes the following steps:

[0007] Step 1, Peck's formula for single-track tunnels. Peck assumes that the volume of ground loss during the excavation of a single tunnel is equal to the volume of the settlement trough, and that the cross-sectional settlement trough curve follows a normal distribution. The expression for lateral surface settlement is:

[0008]

[0009] In the formula: S(x) is the surface settlement at a distance x from the tunnel's central axis, in meters; S max V represents the maximum surface settlement at the tunnel's central axis, in meters; x represents the horizontal distance from the tunnel's central axis, in meters; i represents the settlement trough width coefficient, i.e., the horizontal distance from the inflection point of the settlement trough curve to the tunnel's central axis, in meters; V l R is the formation loss rate, which is the percentage of formation loss per unit length relative to the volume per unit length; R is the radius of the tunnel, in meters.

[0010] Step two: Calculate the settlement in the y-direction of the excavated double-track tunnel. Treat the soil layer as countless micro-units. The sum of the effects of each excavation unit on surface settlement is the surface settlement caused by tunnel excavation. The settlement Q of the micro-unit δ1 excavated in the y-direction is calculated first. δ1 for:

[0011]

[0012] Settlement Q of micro-unit δ2 in the y direction during subsequent tunnel excavation δ2 It can be expressed by the following formula:

[0013]

[0014] In the formula: y is the distance between the longitudinal excavation micro-unit of the tunnel and the monitoring section, in meters; V δ1 With V δ2 , j1 and j2 are the average formation losses per micro-unit during the excavation of the first and second tunnels, respectively; j1 and j2 are the width factors of the longitudinal influence curves of the first and second tunnels, respectively.

[0015] Step 3: Calculate the longitudinal surface settlement caused by the excavation of the double-track tunnel, including the longitudinal surface settlement G caused by the tunnel in any section. 1(y1，y2) :

[0016]

[0017] Summarized as follows:

[0018]

[0019] The longitudinal surface settlement G caused by the subsequent tunnel in any section 2(y3，y4) :

[0020]

[0021] Summarized as follows:

[0022]

[0023] In the formula: y1 and y2 are the distances from the tunnel face to the monitoring section before and after the excavation of the first tunnel, respectively; y3 and y4 are the distances from the tunnel face to the monitoring section before and after the excavation of the second tunnel, respectively; r is the radial direction of the tunnel; θ is the rotation angle.

[0024] Step 4: Calculate the surface settlement when the double-track tunnel is fully completed. When the first tunnel is fully completed, (y1, y2) is taken as (-∞, +∞), and the corresponding surface settlement G is calculated. T1 for:

[0025]

[0026] When the subsequent tunnel is fully completed, (y3, y4) is taken as (-∞, +∞), and the corresponding surface settlement G T2 for:

[0027]

[0028] Step 5: Calculate the longitudinal excavation coefficient for the double-track tunnel. Define the ratio of the settlement value of a certain excavation section (y1, y2) of the preceding tunnel to the settlement under the condition that the preceding tunnel is completed as the longitudinal excavation coefficient γ1 of the preceding tunnel. γ1 is:

[0029]

[0030] Summarized as follows:

[0031]

[0032] The longitudinal excavation coefficient γ2 of the subsequent tunnel is defined as the ratio of the settlement value of a certain excavated section (y3, y4) of the subsequent tunnel to the settlement value when the subsequent tunnel is completed. γ2 is:

[0033]

[0034] Summarized as follows:

[0035]

[0036] Step Six: Using the Peck formula for dual-track tunnels, we introduce the maximum settlement correction factors α1 and α2, the settlement trough width correction factors β1 and β2, and the longitudinal excavation coefficients γ1 and γ2. Based on the superposition principle, we obtain the expression for the transverse surface settlement:

[0037]

[0038] Summarized as follows:

[0039]

[0040] In the formula: L is the distance between the axes of the preceding tunnel and the following tunnel, in meters; α1 and α2 are the maximum settlement correction coefficients of the preceding tunnel and the following tunnel, respectively; β1 and β2 are the settlement trough width correction coefficients of the preceding tunnel and the following tunnel, respectively; i1 and i2 are the settlement trough width coefficients of the preceding tunnel and the following tunnel, respectively; γ1 and γ2 are the longitudinal excavation coefficients of the preceding tunnel and the following tunnel, respectively.

[0041] Preferably, the longitudinal influence curve width factor j1 of the preliminary tunnel is:

[0042] j1=λ1i1,

[0043] The width factor j2 of the longitudinal influence curve of the subsequent tunnel is:

[0044] j2=λ2i2,

[0045] In the formula: λ1 and λ2 are the longitudinal width ratio coefficients of the first tunnel and the second tunnel, respectively, with values ​​ranging from 0.9 to 3.0. The better the geological conditions, the smaller the value.

[0046] Preferably, the calculation of the settling trough width coefficient i is as follows:

[0047]

[0048] In the formula: m is a coefficient, which can be taken as 0.45 to 0.50, with an average value of 0.475; θ is the internal friction angle of the strata above the tunnel axis. For composite strata, the weighted average value can be taken according to the soil layer thickness, in °; h is the tunnel burial depth, in m; R is the tunnel radius, in m.

[0049] Preferably, when both the preceding and following tunnels are completed, (y1, y2) and (y3, y4) are both taken as (-∞, +∞), then γ1 = γ2 = 1, and the expression for lateral surface settlement is simplified as follows:

[0050]

[0051] This is the double-line modified Peck formula.

[0052] In this invention, a dynamic surface settlement prediction model for a double-track tunnel considering longitudinal excavation parameters was established, achieving the goal of real-time prediction of surface settlement during double-track tunnel construction, and possessing both rationality and accuracy. Attached Figure Description

[0053] Table 1. Values ​​of correction coefficients for Peck's formula;

[0054] Table 2 Peck's Formula V l Range of values;

[0055] Table 3 Formation physical and mechanical parameters;

[0056] Figure 1 This is a schematic diagram of the micro-unit excavation of the present invention;

[0057] Figure 2 This is a schematic diagram of a single-line tunnel modeled using finite element methods according to the present invention.

[0058] Figure 3 This is a schematic diagram of a double-line tunnel modeled using finite element methods according to the present invention.

[0059] Figure 4 This is a comparison chart of the finite element model calculation and the field measured data of the single-line tunnel of this invention;

[0060] Figure 5 This is a comparison chart of the calculations using the Peck formula for a single-track tunnel in this invention and the actual measured data from the field.

[0061] Figure 6 This is a comparison chart of the finite element model calculation and the field measured data of the dual-track tunnel of this invention;

[0062] Figure 7 This is a comparison chart of the calculations using the modified Peck formula for the double-track tunnel of this invention and the actual measured data from the field.

[0063] In the diagram: 1. First tunnel; 2. Second tunnel. Detailed Implementation

[0064] The present invention will be further described below with reference to the accompanying drawings:

[0065] A method for predicting dynamic surface settlement in a dual-track tunnel includes the following steps:

[0066] Step 1, Peck's formula for single-track tunnels. Peck assumes that the volume of ground loss during the excavation of a single tunnel is equal to the volume of the settlement trough, and that the cross-sectional settlement trough curve follows a normal distribution. The expression for lateral surface settlement is:

[0067]

[0068] In the formula: S(x) is the surface settlement at a distance x from the tunnel's central axis, in meters; S max V represents the maximum surface settlement at the tunnel's central axis, in meters; x represents the horizontal distance from the tunnel's central axis, in meters; i represents the settlement trough width coefficient, i.e., the horizontal distance from the inflection point of the settlement trough curve to the tunnel's central axis, in meters; V l The formation loss rate is the percentage of formation loss per unit length relative to the volume per unit length, expressed as %. The actual ground settlement measured 2–3 days after the shield tail passes is used as the settlement value during the construction phase, and the values ​​are shown in Table 2. R is the radius of the tunnel, expressed as m.

[0069] Table 2

[0070]

[0071] Calculation of the settling trough width coefficient i:

[0072]

[0073] In the formula: m is a coefficient, which can be taken as 0.45 to 0.50, with an average value of 0.475; θ is the internal friction angle of the strata above the tunnel axis. For composite strata, the weighted average value can be taken according to the soil layer thickness, in °; h is the tunnel depth, in m; R is the tunnel radius, in m.

[0074] Step two involves calculating the settlement of the double-track tunnel in the y-direction. The soil layers are considered as numerous micro-units. The sum of the effects of each excavation unit on surface settlement is the surface settlement caused by tunnel excavation. For example... Figure 1 As shown, the settlement Q of the micro-unit δ1 excavated in the first tunnel 1 in the y direction is... δ1 for:

[0075]

[0076] Settlement Q of micro-unit δ2 in the y-direction during the excavation of tunnel 2 δ2 It can be expressed by the following formula:

[0077]

[0078] In the formula: y is the distance between the longitudinal excavation micro-unit of the tunnel and the monitoring section, in meters; V δ1 With V δ2 , j1 and j2 are the average formation losses per micro-unit during the excavation of the first tunnel 1 and the second tunnel 2, respectively; j1 and j2 are the longitudinal influence curve width factors of the first tunnel 1 and the second tunnel 2, respectively.

[0079] The longitudinal influence curve width factor j1 of the first tunnel 1 is:

[0080] j1=λ1i1,

[0081] The longitudinal influence curve width factor j2 of the rear tunnel 2 is:

[0082] j2=λ2i2,

[0083] In the formula: λ1 and λ2 are the longitudinal width ratio coefficients of the first tunnel 1 and the second tunnel 2, respectively, with values ​​ranging from 0.9 to 3.0. The better the geological conditions, the smaller the value.

[0084] Step 3: Calculation of longitudinal surface settlement caused by the excavation of the double-track tunnel, including the longitudinal surface settlement G caused by the excavation of tunnel 1 in any section. 1(y1，y2) :

[0085]

[0086] Summarized as follows:

[0087]

[0088] Longitudinal surface settlement G caused by the rear tunnel 2 in any section 2(y3，y4) :

[0089]

[0090] Summarized as follows:

[0091]

[0092] In the formula: y1 and y2 are the distances from the tunnel face to the monitoring section before and after the excavation of the first tunnel 1, respectively; y3 and y4 are the distances from the tunnel face to the monitoring section before and after the excavation of the second tunnel 2, respectively; r is the radial direction of the tunnel; θ is the rotation angle.

[0093] Step 4: Calculation of surface settlement when the double-track tunnel is fully completed. When the first tunnel 1 is fully completed, (y1, y2) is taken as (-∞, +∞), and the corresponding surface settlement G is calculated. T1 for:

[0094]

[0095] When the second tunnel is fully completed, (y3, y4) is taken as (-∞, +∞), and the corresponding surface settlement G T2 for:

[0096]

[0097] Step 5: Calculate the longitudinal excavation coefficient for the double-track tunnel. Define the ratio of the settlement value of a certain excavation section (y1, y2) of the first tunnel 1 to the settlement under the condition that the first tunnel 1 is completed as the longitudinal excavation coefficient γ1 of the first tunnel 1. γ1 is:

[0098]

[0099] Summarized as follows:

[0100]

[0101] The longitudinal excavation coefficient γ2 of the subsequent tunnel 2 is defined as the ratio of the settlement value of a certain excavated section (y3, y4) of the subsequent tunnel 2 to the settlement when the subsequent tunnel 2 is fully completed. γ2 is:

[0102]

[0103] Summarized as follows:

[0104]

[0105] Step Six: Using the Peck formula for dual-track tunnels, we introduce the maximum settlement correction factors α1 and α2, the settlement trough width correction factors β1 and β2, and the longitudinal excavation coefficients γ1 and γ2. Based on the superposition principle, we obtain the expression for the transverse surface settlement:

[0106]

[0107] Summarized as follows:

[0108]

[0109] In the formula: L is the distance between the axes of the first tunnel 1 and the second tunnel 2, in meters; α1 and α2 are the maximum settlement correction coefficients of the first tunnel 1 and the second tunnel 2, respectively, and their values ​​are shown in Table 1; β1 and β2 are the settlement trench width correction coefficients of the first tunnel 1 and the second tunnel 2, respectively, and their values ​​are shown in Table 1; i1 and i2 are the settlement trench width coefficients of the first tunnel 1 and the second tunnel 2, respectively; γ1 and γ2 are the longitudinal excavation coefficients of the first tunnel 1 and the second tunnel 2, respectively.

[0110] Table 1

[0111]

[0112] When both the first tunnel 1 and the second tunnel 2 are completed, and (y1, y2) and (y3, y4) are both taken as (-∞, +∞), then γ1 = γ2 = 1. The expression for lateral surface settlement can be simplified as follows:

[0113]

[0114] This is the double-line modified Peck formula.

[0115] In one embodiment, modeling and calculation are performed using the construction of a shield tunnel in a section of Tianjin Metro Line 7 as an example. The shield tunnel has a burial depth of 13.2m, an inner diameter of 5.9m, an outer diameter of 6.6m, a thickness of 0.35m, and a ring width of 1.5m. C50P10 high-performance concrete is used, and the distance between the two tunnels is 15m. The strata at the construction site, from top to bottom, consist of miscellaneous fill, silty clay, silty clay, and silty clay, etc. The physical and mechanical parameters of the strata are shown in Table 3. The shield machine used is the CRCC Heavy Industry DG541 shield machine, which is 9.5m long, with a cutterhead excavation diameter of 6850mm, a front shield diameter of 6830mm, a middle shield diameter of 6820mm, and a tail shield diameter of 6810mm.

[0116] Table 3

[0117]

[0118] Numerical simulation analysis was performed using finite element method (FEM) software. For the single-track tunnel model, the X-axis represents the horizontal direction of the tunnel cross-section, with coordinates ranging from -40m to 40m, totaling 80m; the Y-axis represents the tunnel excavation direction, with coordinates ranging from -39m to 39m, totaling 78m; and the Z-axis represents the vertical depth direction, with coordinates ranging from -50m to 0m, totaling 50m. The double-track tunnel model has the same dimensions in the Y and Z directions as the single-track model, except that the X-axis is extended by 20m to each side. The dimensions of the double-track tunnel model are 120m × 78m × 50m (X × Y × Z). The established numerical model is shown below. Figure 2 and Figure 3 As shown.

[0119] The following assumptions were made during the construction simulation:

[0120] (1) The soil layer is a homogeneous continuous body, distributed in layers;

[0121] (2) Vertical constraints are applied to the bottom surface of the model, the left and right sides restrict the X-direction displacement, the front and rear sides restrict the Y-direction displacement, and the top surface is a free surface;

[0122] (3) Only the self-weight of the soil is considered, and other loads are not considered;

[0123] (4) The soil conforms to the HHS yield criterion.

[0124] After the finite element model is established, the construction simulation is carried out according to the following steps:

[0125] (1) First step: Apply self-weight load, and reset the formation deformation to zero after the calculation is completed;

[0126] (2) Second step: First, excavate the left tunnel, kill the soil of the tunnel excavation with a length of 1 ring width, and apply the face thrust;

[0127] (3) Third step: Activate the killed segment units and assign material properties to the segments;

[0128] (4) Fourth step: Repeat the operations of the second and third steps, from y = -39m all the way to y = 39m, and the left line is completed;

[0129] (5) After the left tunnel is excavated, the right tunnel is simulated and the right tunnel is constructed in the same way.

[0130] Data comparison and verification

[0131] (1) Single-track tunnel

[0132] Taking a single-track tunnel model as an example, with the y=0 section as the monitoring section, the surface settlement curves were calculated under the conditions of tunnel excavation up to y=-10.5, -4.5, 0, 4.5, and 39m. The results of the tunnel excavation three-dimensional dynamic settlement prediction model, the finite element model calculations, and the field measured data are compared as follows: Figure 4 and Figure 5 As shown.

[0133] (2) Double-track tunnel

[0134] Taking a dual-track tunnel model as an example, the y=0 section is used as the monitoring section. The surface settlement curves are calculated under the following conditions: the left tunnel is completed, and the right tunnel is excavated to y=-39, -10.5, -4.5, 0, 4.5, and 39m. Specifically, when y=-39, γ1=1 and γ2=0; when y=39, γ1=γ2=1. A comparison is shown between the three-dimensional dynamic settlement prediction model for dual-track tunnel excavation, the finite element model calculations, and the field measured data. Figure 6 and Figure 7 As shown.

[0135] Depend on Figure 6 and Figure 7 It can be seen that the surface settlement curve of the three-dimensional dynamic settlement prediction model for tunnel excavation matches well with the surface settlement curve of the numerical simulation, and the error with the actual monitoring value is small. Therefore, the three-dimensional dynamic settlement prediction model for tunnel excavation has good applicability and accuracy.

[0136] The above embodiments are merely illustrative of the concept and implementation of the present invention and are not intended to limit it. Under the concept of the present invention, technical solutions without substantial changes are still within the scope of protection.

Claims

1. A method for predicting dynamic surface settlement in a dual-track tunnel, characterized in that, Includes the following steps: Step 1, Peck's formula for single-track tunnels. Peck assumes that the volume of ground loss during the excavation of a single tunnel is equal to the volume of the settlement trough, and that the cross-sectional settlement trough curve follows a normal distribution. The expression for lateral surface settlement is: In the formula: S(x) is the surface settlement at a distance x from the tunnel's central axis, in meters; S max V represents the maximum surface settlement at the tunnel's central axis, in meters; x represents the horizontal distance from the tunnel's central axis, in meters; i represents the settlement trough width coefficient, i.e., the horizontal distance from the inflection point of the settlement trough curve to the tunnel's central axis, in meters; V l R is the formation loss rate, which is the percentage of formation loss per unit length relative to the volume per unit length; R is the radius of the tunnel, in meters. Step 2: Settlement calculation of the double-track tunnel in the y-direction. The soil layer is regarded as countless micro-units. The superposition of the surface settlement effect of the excavation unit is the surface settlement caused by the tunnel excavation. The settlement Q of the micro-unit δ1 of the tunnel excavation in the y-direction is calculated. δ1 for: Settlement Q of micro-unit δ2 in the y direction during tunnel (2) excavation δ2 It can be expressed as follows: In the formula: y is the distance between the longitudinal excavation micro-unit of the tunnel and the monitoring section, in meters; V δ1 With V δ2 J1 and J2 are the average formation losses per micro-unit during the excavation of the first tunnel (1) and the second tunnel (2), respectively; J1 and J2 are the longitudinal influence curve width factors of the first tunnel (1) and the second tunnel (2), respectively. Step 3: Calculation of longitudinal surface settlement caused by the excavation of the double-track tunnel, and the longitudinal surface settlement G caused by the first tunnel (1) in any section. 1(y1，y2) : Summarized as follows: The longitudinal surface settlement G caused by the rear tunnel (2) in any section 2(y3，y4) : Summarized as follows: In the formula: y1 and y2 are the distances from the tunnel face to the monitoring section before and after the excavation of the first tunnel (1); y3 and y4 are the distances from the tunnel face to the monitoring section before and after the excavation of the second tunnel (2); r is the radial direction of the tunnel; θ is the rotation angle. Step 4: Calculation of surface settlement when the double-track tunnel is fully completed. When the first tunnel (1) is fully completed, the corresponding surface settlement G is calculated. T1 for: When the subsequent tunnel (2) is fully completed, the corresponding surface settlement G T2 for: Step 5: Calculate the longitudinal excavation coefficient for the double-track tunnel. Define the ratio of the settlement value of a certain excavation section (y1, y2) of the preceding tunnel (1) to the settlement when the preceding tunnel (1) is completed as the longitudinal excavation coefficient γ1 of the preceding tunnel (1). γ1 is: Summarized as follows: The longitudinal excavation coefficient γ2 of the subsequent tunnel (2) is defined as the ratio of the settlement value of a certain excavation section (y3, y4) of the subsequent tunnel (2) to the settlement when the subsequent tunnel (2) is completed. γ2 is: Summarized as follows: Step Six: Using the Peck formula for dual-track tunnels, we introduce the maximum settlement correction factors α1 and α2, the settlement trough width correction factors β1 and β2, and the longitudinal excavation coefficients γ1 and γ2. Based on the superposition principle, we obtain the expression for the transverse surface settlement: Summarized as follows: In the formula: L is the distance between the axes of the first tunnel (1) and the second tunnel (2), in meters; α1 and α2 are the maximum settlement correction coefficients of the first tunnel (1) and the second tunnel (2), respectively; β1 and β2 are the correction coefficients for the width of the settlement trough of the first tunnel (1) and the second tunnel, respectively; i1 and i2 are the settlement trough width coefficients of the first tunnel (1) and the second tunnel, respectively. γ1 and γ2 are the longitudinal excavation coefficients of the first tunnel (1) and the second tunnel (2), respectively.

2. The method for predicting dynamic surface settlement of a twin-track tunnel according to claim 1, characterized in that: The longitudinal influence curve width factor j1 of the preliminary tunnel (1) is: j1=λ1i1, The longitudinal influence curve width factor j2 of the rear tunnel (2) is: j2=λ2i2, In the formula: λ1 and λ2 are the longitudinal width ratio coefficients of the first tunnel (1) and the second tunnel (2), respectively, with values ​​ranging from 0.9 to 3.

0. The better the geological conditions, the smaller the value.

3. The method for predicting dynamic surface settlement of a twin-track tunnel according to claim 1 or 2, characterized in that: Calculation of the settling trough width coefficient i: In the formula: m is a coefficient, which can be taken as 0.45 to 0.50, with an average value of 0.475; θ is the internal friction angle of the strata above the tunnel axis. For composite strata, the weighted average value can be taken according to the soil layer thickness, in °; h is the tunnel burial depth, in m; R is the tunnel radius, in m.

4. The method for predicting dynamic surface settlement of a twin-track tunnel according to claim 3, characterized in that: Both (y1, y2) and (y3, y4) are taken as (-∞, +∞), where γ1 = γ2 = 1. The expression for lateral surface settlement is then simplified as follows: This is the double-line modified Peck formula.

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