A method for predicting ground surface settlement outside a soft clay foundation pit considering space-time effect

Abstract

The present application relates to the field of ground settlement prediction, and provides a soft clay foundation pit outside ground settlement prediction method considering time and space effects, comprising: establishing a three-dimensional numerical model of foundation pit excavation induced ground settlement outside the pit; correcting the parameters of the three-dimensional numerical model, taking the corrected three-dimensional numerical model as a reference example; obtaining a fitting function one of excavation depth H and ground maximum settlement δ vm based on the reference example; giving fitting functions two to six considering different time and space factors; obtaining a fitting function seven of A based on the three-dimensional numerical model; collecting engineering data of a foundation pit to be predicted in the same region, substituting the parameters of the foundation pit to be predicted into the fitting functions one to six to obtain the ground maximum settlement δ vm outside the pit of the foundation pit to be predicted; obtaining A by using the fitting function seven, substituting A into the complementary error function, combining δ vm to give the ground maximum settlement δ vm outside the pit of any profile perpendicular to the retaining wall; substituting the ground maximum settlement δ vm outside the pit into a three-fold line model to obtain the ground settlement δ v at any point of the corresponding profile.

Description

Technical Field

[0001] This invention relates to the field of surface settlement prediction, and in particular to a method for predicting surface settlement outside soft clay foundation pits that takes into account spatiotemporal effects. Background Technology

[0002] With the vigorous development of urban construction activities, the demand for land resources in cities is increasing daily, and more and more foundation pit projects are located adjacent to buildings, subway stations, underground pipelines, etc. Foundation pit construction along subway tunnels is unavoidable. Excavation of foundation pits in soft soil areas with dense buildings and pipelines will inevitably disturb the surrounding environment, causing uneven road surface settlement, deformation of underground pipelines, and in severe cases, even structural cracking and damage. Therefore, accurate, rapid, and simple prediction of surface settlement induced throughout the entire foundation pit excavation process is crucial.

[0003] The characteristics of surface settlement outside the excavation pit are influenced by various factors such as geological conditions, pit size, and retaining structure type, making accurate assessment of surface settlement outside the pit generally difficult. However, deep excavations in soft soil with complex surrounding environments often share many similarities in retaining structure design, earthwork excavation, and construction. Modeling a typical deep excavation case under specific geological conditions in a certain region to provide an analytical method for surface settlement caused by excavation in that region is feasible. On the other hand, the deformation of soft clay pits exhibits significant spatiotemporal effects, as first observed during the construction of Shanghai Metro Line 1. However, the analysis of surface settlement outside soft soil pits rarely considers the influence of time effects, leading to inaccurate surface settlement predictions. Summary of the Invention

[0004] To address the above problems, the present invention provides the following technical solution:

[0005] This invention provides a method for predicting surface settlement outside soft clay foundation pits considering spatiotemporal effects, the method comprising:

[0006] (1) Based on the engineering data of typical foundation pits in soft clay areas, a three-dimensional numerical model of surface settlement induced by foundation pit excavation was established.

[0007] (2) Correct the parameters of the three-dimensional numerical model until the simulated calculated values ​​match the measured values ​​well, and use the corrected three-dimensional numerical model as a reference example.

[0008] (3) Based on the reference example, the excavation depth H and the maximum surface settlement δ are obtained. vm Fitting function one;

[0009] (4) The effect of different spatiotemporal factors on the maximum surface subsidence δ based on the reference case vmThe influence of different spatiotemporal factors is considered, and fitting functions two to six are given to calculate the maximum surface subsidence δ for the reference example. vm Make corrections;

[0010] (5) Based on the three-dimensional numerical model, obtain the fitting function of the distance A from the corner point to the inflection point of the enclosure wall;

[0011] (6) Collect engineering data of the foundation pits to be predicted in the same area, substitute the parameters of the foundation pits to be predicted into fitting functions one through six, and obtain the maximum surface settlement δ outside the foundation pit. vm ';

[0012] (7) Obtain A using the fitting function 7, substitute A into the complementary error function, and combine this with the maximum surface settlement δ outside the foundation pit to be predicted. vm 'Give the maximum surface settlement δ outside the pit for any cross-section perpendicular to the retaining wall.' vm ”;

[0013] (8) The maximum surface settlement δ outside the pit vm Substituting the values ​​into the three-segment model, the surface subsidence δ at any point on the corresponding profile is obtained. v .

[0014] Furthermore, in step (1), the engineering data for a typical foundation pit in a soft clay area includes the physical and mechanical parameters of the soil layer, the length, width, and depth of the foundation pit excavation, the retaining structure system, and the construction log.

[0015] Furthermore, in step (3), the specific expression of fitting function one is as follows:

[0016]

[0017] Let the length and width of the foundation pit be L1 and L2, respectively, and δ vm The sample was taken from the ground surface outside the retaining wall pit of length L1.

[0018] Furthermore, the spatiotemporal factors include: the excavation rate v (the volume of soil excavated per unit time) and the thickness l of the soft soil layer. s Soft soil creep, excavation area S, and length-to-width ratio L1 / L2 of the excavation pit (without changing the excavation area);

[0019] Furthermore, the specific process of step (4) is as follows:

[0020] The signs of the correction coefficients are defined as ξ. v ξ ls ξ c ξ S ξ L1 / L2 Then the fitting functions two through six are as follows:

[0021]

[0022] Where v0 is the unit excavation rate (1m). 3 / d);l s0 S0 represents the unit soft soil layer thickness (1m); S0 represents the unit excavation area (1m²). 2 ).

[0023] Furthermore, in step (5), the specific expression of the fitting function 7 is:

[0024] 2A / L1 = -0.21ln(H / L1) + 0.06;

[0025] Where L1 is the length of the foundation pit.

[0026] Furthermore, in step (6), the engineering data of the foundation pit that needs to be predicted includes the physical and mechanical parameters of the soil layer, the length, width, and depth of the foundation pit excavation, and the construction plan.

[0027] Furthermore, in step (6), it is necessary to predict the maximum surface settlement δ outside the foundation pit. vm The specific calculation formula for ' is:

[0028] The maximum surface settlement δ outside the foundation pit is obtained by considering various correction coefficients for spatiotemporal factors. vm 'for

[0029]

[0030] Furthermore, the specific process of step (7) is as follows:

[0031] Define the direction parallel to the retaining wall as the y-direction, the corner of the foundation pit as the origin, and the direction towards the middle of the retaining wall as positive. At this time, the coordinates of the cross section at the middle of the retaining wall are y = L1 / 2; the inflection point refers to the point on the cross section parallel to the retaining wall where the ground settlement is 1 / 2 of the maximum settlement.

[0032] Substituting the excavation depth H and the length L1 of the foundation pit into the fitting function 7, we obtain the distance A from the corner point to the inflection point of the retaining wall:

[0033]

[0034] Substituting the distance A from the corner point to the inflection point of the retaining wall into the complementary error function, based on the maximum surface settlement δ outside the foundation pit that needs to be predicted. vm The complementary error function gives the maximum surface settlement δ outside the pit for any cross-section perpendicular to the retaining wall. vm The specific expression is as follows:

[0035]

[0036] Furthermore, the specific process of step (8) is as follows:

[0037] Define the direction perpendicular to the retaining wall as the x-direction, with the outer wall of the retaining wall as the origin and the direction outward from the pit as positive.

[0038] δ vm Substituting the values ​​into the three-segment model, the surface subsidence δ at any point on the corresponding profile is obtained. v The specific expression is:

[0039]

[0040] The present invention has the following beneficial effects:

[0041] (1) The present invention provides a method for predicting the settlement of the ground surface outside the soft clay foundation pit considering the spatiotemporal effect. It overcomes the disadvantage of traditional methods that require prior assessment of the lateral displacement of the retaining wall, and also overcomes the disadvantage of existing analysis methods that cannot consider the creep effect of soil. It provides a new method for deep foundation pit engineering practice in soft clay areas, and has engineering significance and good promotion and application value.

[0042] (2) The present invention can predict the settlement of any surface outside the pit in advance without the need for excavation of the foundation pit, and at the same time, it can help to take corresponding engineering measures in advance according to the size of the settlement. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the prediction method of the present invention.

[0044] Figure 2 These are two inclination measurement points of the retaining wall and two surface settlement monitoring profiles of the B2 foundation pit in this embodiment of the invention.

[0045] Figure 3 This is a schematic diagram of a three-dimensional numerical model in an embodiment of the present invention.

[0046] Figure 4 This is a comparison chart of the simulation results of the three-dimensional numerical model and the measured values ​​under the condition of 5cm inclination measurement of the retaining wall in an embodiment of the present invention.

[0047] Figure 5 This is a comparison chart of the simulation results of the three-dimensional numerical model and the measured values ​​under the condition of 7cm inclination measurement of the retaining wall in an embodiment of the present invention.

[0048] Figure 6 This is a comparison chart of the simulation results of the three-dimensional numerical model and the measured values ​​under the condition of 2cm surface subsidence in an embodiment of the present invention.

[0049] Figure 7 This is a comparison chart of the simulation results of the three-dimensional numerical model and the measured values ​​under the condition of 4cm surface subsidence in an embodiment of the present invention.

[0050] Figure 8 This is a schematic diagram of ground settlement parallel to the direction of the retaining wall according to the present invention.

[0051] Figure 9 This is a schematic diagram of the surface settlement monitoring point outside the B1 foundation pit in an embodiment of the present invention.

[0052] Figure 10 This is a schematic diagram of the complementary error function in an embodiment of the present invention.

[0053] Figure 11 This is a comparison chart of the calculated and measured values ​​of surface settlement under the condition that the distance between the monitoring profile and the corner of the foundation pit is 11.2m in an embodiment of the present invention.

[0054] Figure 12 This is a comparison chart of the calculated and measured values ​​of surface settlement when the distance from the monitoring profile to the corner of the foundation pit is 17.3m in an embodiment of the present invention.

[0055] Figure 13 This is a comparison chart of the calculated and measured values ​​of surface settlement when the distance from the monitoring profile to the corner of the foundation pit is 29.0m in an embodiment of the present invention. Detailed Implementation

[0056] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be noted that the embodiments are only specific illustrations of the invention and should not be regarded as limitations on the invention. The purpose of the embodiments is to enable those skilled in the art to better understand and reproduce the technical solution of the present invention. The scope of protection of the present invention should still be determined by the scope defined in the claims.

[0057] like Figure 1 As shown, this invention provides a method for predicting surface settlement outside a soft clay foundation pit, considering spatiotemporal effects. The method includes:

[0058] S1. Based on the engineering data of typical foundation pits in soft clay areas, establish a three-dimensional numerical model of the surface settlement induced by foundation pit excavation. The engineering data includes the physical and mechanical parameters of the site soil, the length, width, and depth of the foundation pit excavation, the retaining structure system, and the construction log.

[0059] S2, correct the parameters of the 3D numerical model until the simulated calculated values ​​match the measured values ​​well, and use the corrected 3D numerical model as a reference case; compare the simulation results of the 3D numerical model with the measured values. If the simulated calculated values ​​match the measured values ​​well, it indicates that the accuracy of the 3D numerical model is high, and it is used as a reference case; otherwise, find the cause of the error, and further correct the input parameters according to the cause until the simulated calculated values ​​of the 3D numerical model match the measured values ​​well.

[0060] S3, based on the reference example, obtain the excavation depth H and the maximum surface settlement δ. vm The fitting function is one;

[0061] The specific expression for fitting function one is as follows:

[0062]

[0063] Let the length and width of the foundation pit be L1 and L2, respectively, and δ vm The sample was taken from the ground surface outside the retaining wall pit of length L1.

[0064] S4, The effect of different spatiotemporal factors on maximum surface subsidence δ based on the reference case vm The influence of different spatiotemporal factors is considered, and fitting functions two to six are given to calculate the maximum surface subsidence δ for the reference example. vm Corrections are made; the spatiotemporal factors include: the excavation rate v (the volume of soil excavated per unit time), and the thickness l of the soft soil layer. s Soft soil creep, excavation area S, and length-to-width ratio L1 / L2 of the excavation pit (without changing the excavation area);

[0065] The signs of the correction coefficients are defined as ξ. v ξ ls ξ c ξ S ξ L1 / L2 Then the fitting functions two through six are respectively:

[0066]

[0067] Where v0 is the unit excavation rate (1m). 3 / d);l s0 S0 represents the unit soft soil layer thickness (1m); S0 represents the unit excavation area (1m²). 2 ).

[0068] S5, The fitting function for the distance A from the corner point to the inflection point of the enclosure wall is obtained based on the three-dimensional numerical model;

[0069] The specific expression for the fitting function seven is as follows:

[0070] 2A / L1 = -0.21ln(H / L1) + 0.06;

[0071] Where L1 is the length of the foundation pit.

[0072] S6. Collect engineering data for the foundation pits to be predicted in the same area. The engineering data includes the physical and mechanical parameters of the site soil, the length, width, and depth of the foundation pit excavation, and the construction plan. Substitute the parameters of the foundation pits to be predicted into fitting functions one through six to obtain the maximum surface settlement δ outside the foundation pits. vm ';

[0073] The maximum surface settlement δ outside the foundation pit is obtained by considering various correction coefficients for spatiotemporal factors. vm 'for

[0074]

[0075] S7, using the fitting function seven to obtain A, substitute A into the complementary error function, and combine it with the maximum surface settlement δ outside the foundation pit to be predicted. vm 'Give the maximum surface settlement δ outside the pit for any cross-section perpendicular to the retaining wall.' vm ”;

[0076] Define the direction parallel to the retaining wall as the y-direction, the corner of the foundation pit as the origin, and the direction towards the middle of the retaining wall as positive. At this time, the coordinates of the cross section at the middle of the retaining wall are y = L1 / 2; the inflection point refers to the point on the cross section parallel to the retaining wall where the ground settlement is 1 / 2 of the maximum settlement.

[0077] Substituting the excavation depth H and the length L1 of the foundation pit into the fitting function 7, we obtain the distance A from the corner point to the inflection point of the retaining wall:

[0078]

[0079] Substituting the distance A from the corner point to the inflection point of the retaining wall into the complementary error function, based on the maximum surface settlement δ outside the foundation pit that needs to be predicted. vm The complementary error function gives the maximum surface settlement δ outside the pit for any cross-section perpendicular to the retaining wall. vm The specific expression is as follows:

[0080]

[0081] S8 will determine the maximum surface settlement δ outside the pit. vm Substituting the values ​​into the three-segment model, the surface settlement δ at any point on the corresponding profile is obtained. v .

[0082] Define the direction perpendicular to the retaining wall as the x-direction, with the outer wall of the retaining wall as the origin and the direction outward from the pit as positive.

[0083] δ vm Substituting the values ​​into the three-segment model, the surface settlement δ at any point on the corresponding profile is obtained. v The specific expression is:

[0084]

[0085] Example

[0086] This embodiment uses the B2 foundation pit of an ultra-deep foundation pit group in a certain central project as an example. Figure 2-3As shown, the main strata from top to bottom are ① fill, ② soft clay, ③ silty clay, ④ gravel, ⑤ strongly weathered and ⑥ moderately weathered sandstone; the excavation depth of the foundation pit is 30.2m, and the plan dimensions are approximately 98m × 92m; the retaining structure adopts a 1.2m thick and 50m deep diaphragm wall combined with six layers of concrete full-span bracing and passive zone skirt reinforcement with strip reinforcement, and the soil reinforcement range is from 7.6m to 33m below the ground surface; the construction of the foundation pit took a total of 230 days;

[0087] S1, based on the engineering data of typical foundation pits in soft clay areas, PLAXIS 3D software was used to create a model as follows: Figure 3 The figure shows a three-dimensional numerical model of the ground surface settlement induced by the excavation of the foundation pit.

[0088] The soil creep constitutive model in PLAXIS 3D software is the SSC model. The formula for calculating the corrected creep index in the model is as follows:

[0089]

[0090] Among them, C α e0 is the creep index, which can be obtained from laboratory tests; e0 is the initial void ratio of the soil.

[0091] S2, as Figure 4-7 The figure shows a comparison between the simulation results of the three-dimensional numerical model and the measured values. δ h The calculation results showed good agreement between the calculated and measured values, indicating that the accuracy of the three-dimensional finite element calculation model was high. This model was then used as a reference example.

[0092] S3, based on the reference example, obtain the excavation depth H and the maximum surface settlement δ. vm The fitting function is one;

[0093] The specific expression for fitting function one is as follows:

[0094]

[0095] Let the length and width of the foundation pit be L1 and L2, respectively, and δ vm The sample was taken from the ground surface outside the retaining wall pit of length L1.

[0096] S4, in the reference example, v = 1000m 3 l s =20.4m, u*=0.003, S=9016m 2 L1 / L2 = 1.06; Based on the reference example, different spatiotemporal factors are discussed, and fitting functions two to six considering different spatiotemporal factors are given using the calculation results of parametric analysis. The specific expressions are as follows:

[0097]

[0098] Where v0 is the unit excavation rate (1m). 3 / d);l s0 S0 represents the unit soft soil layer thickness (1m); S0 represents the unit excavation area (1m²). 2 ).

[0099] S5, such as Figure 8 As shown, the fitting function seven for the distance A from the corner point to the inflection point of the enclosure wall, obtained based on the three-dimensional numerical model, is specifically expressed as follows:

[0100] 2A / L1 = -0.21ln(H / L1) + 0.06;

[0101] S6, Collect engineering data for foundation pits that need to be predicted in the same area. Figure 9 This is a schematic diagram of the surface settlement monitoring points outside the B1 foundation pit of a certain central project. The surface settlement needs to be predicted at excavation depths of 22.1m, 26.3m, and 30.2m. The foundation pit has a plan dimension of 75m × 64m, with the analysis object located on the shorter side, and L1 / L2 = 0.85. The total excavation time is approximately 137 days, with an excavation rate of approximately 1050m / s. 3 / d; In terms of soil conditions, foundation pits B1 and B2 are the same; such as Figure 9 As shown, 3×4 surface settlement monitoring points were buried outside the pit. The monitoring points perpendicular to the retaining wall were 2.0m, 7.0m, 17.0m, and 45.5m away from the retaining wall from near to far. The settlement observation sections d1 to d3 parallel to the retaining wall were 17.3m, 29.0m, and 11.2m away from the nearest corner, respectively.

[0102] Substituting the parameters of the excavation pit to be predicted into fitting functions one through six, we obtain the δ values ​​for H = 22.1m, 26.3m, and 30.2m. vm The thicknesses are 69.1 mm, 94.2 mm, and 119.3 mm, respectively, with correction factors ξ. v =0.98、ξ ls =1、ξ c =1、ξ S =0.62, ξ L1 / L2 =0.85, δ vm Multiplying the result by the correction factor yields the maximum surface settlement δ outside the foundation pit for prediction when H = 22.1m, 26.3m, and 30.2m. vm The lengths are 35.9mm, 49.0mm, and 62.0mm respectively. S7, Substituting H and L1 = 64m into the fitting function, we obtain the parameter A for H = 22.1m, 26.3m, and 30.2m as 9.1m, 7.9m, and 7.0m respectively. Substituting parameter A into the complementary error function;

[0103] like Figure 10The diagram shown is a schematic of the complementary error function provided in an embodiment of the present invention. The complementary error function erfc() is defined as follows:

[0104]

[0105] Where u is the normalization variable of the normalized Gaussian function, erf(0)=0, erf(∞)=1.

[0106] The general formula for the deformed curve based on the complementary error function is: y = C·erfc[(xA) / B] + D.

[0107] Based on the need to predict the maximum surface settlement δ outside the foundation pit. vm The complementary error function gives the maximum surface settlement δ outside the pit for the cross-sections perpendicular to the retaining wall (y = 11.2m, 17.3m, 29.0m). vm The specific expression is as follows:

[0108]

[0109] S8 will determine the maximum surface settlement δ outside the pit. vm Substituting the values ​​into the three-segment model, the surface settlement δ at any point on the corresponding profile is obtained. v Specifically:

[0110]

[0111] Figure 11-13 The comparison between the calculated and measured values ​​of surface settlement at the distance from the monitoring profile to the corner of the foundation pit in the embodiments is presented. It can be seen that the calculated and measured values ​​are in good agreement, indicating that the method presented in this paper can accurately predict the surface settlement outside the deep foundation pit in soft clay areas. Furthermore, the method is simple and practical, and has significant practical implications for evaluating the environmental effects of foundation pit engineering.

[0112] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0113] It should be noted that any technical features not described in detail in this invention can be implemented using any existing technology.

Claims

1. A method for predicting surface settlement outside a soft clay foundation pit considering spatiotemporal effects, characterized in that, The method includes: (1) Based on the engineering data of typical foundation pits in soft clay areas, a three-dimensional numerical model of surface settlement induced by foundation pit excavation was established. (2) Correct the parameters of the three-dimensional numerical model until the simulated calculated values ​​match the measured values ​​well, and use the corrected three-dimensional numerical model as a reference example; (3) Based on the reference example, the excavation depth H and the maximum surface settlement δ are obtained. vm The fitting function is one; The specific expression for fitting function one is as follows: ； Let the length and width of the foundation pit be L1 and L2, respectively, and δ vm Taken from the ground surface outside the retaining wall pit of length L1; (4) The effect of different spatiotemporal factors on the maximum surface subsidence δ based on the reference case vm The influence of different spatiotemporal factors is considered, and fitting functions two to six are given. The spatiotemporal factors include: excavation rate v of the foundation pit and thickness of the soft soil layer l. s Soft soil creep, excavation area S of the foundation pit, length-to-width ratio L1 / L2 of the foundation pit; The signs of the correction coefficients are defined as ξ. v ξ ls ξ c ξ S ξ L1 / L2 Then the fitting functions two through six are as follows: ； Where v0 is the unit excavation rate; l s0 S0 represents the unit thickness of the soft soil layer; S0 represents the unit excavation area; μ * It is the corrected creep index in the model; (5) Based on the three-dimensional numerical model, obtain the fitting function of the distance A from the corner point to the inflection point of the enclosure wall; The specific expression for the fitting function seven is as follows: ； Where L1 is the length of the foundation pit; (6) Collect engineering data of the foundation pits to be predicted in the same area, substitute the parameters of the foundation pits to be predicted into fitting functions one to six, and obtain the maximum surface settlement δ outside the foundation pits to be predicted. vm '; (7) Obtain A using the fitting function 7, substitute A into the complementary error function, and combine it with the maximum surface settlement δ outside the foundation pit to be predicted. vm 'Give the maximum surface settlement δ outside the pit for any cross-section perpendicular to the retaining wall.' vm ''; (8) The maximum surface settlement δ outside the pit vm Substituting the values ​​into the three-segment model, the surface settlement δ at any point on the corresponding profile is obtained. v .

2. The method for predicting surface settlement outside a soft clay foundation pit considering spatiotemporal effects according to claim 1, characterized in that, In step (1), the engineering data for a typical foundation pit in a soft clay area includes the physical and mechanical parameters of the soil layer, the length, width, and depth of the foundation pit excavation, the retaining structure system, and the construction log.

3. The method for predicting surface settlement outside soft clay foundation pits considering spatiotemporal effects according to claim 1, characterized in that, In step (6), the engineering data to be predicted for the foundation pit includes the physical and mechanical parameters of the soil layer, the length, width, and depth of the foundation pit excavation, and the construction plan.

4. The method for predicting surface settlement outside a soft clay foundation pit considering spatiotemporal effects according to claim 1, characterized in that, The specific process of step (7) is as follows: Define the direction parallel to the retaining wall as the y-direction, the corner of the foundation pit as the origin, and the direction towards the middle of the retaining wall as positive. At this time, the coordinates of the cross section at the middle of the retaining wall are y=L1 / 2; the inflection point refers to the point on the cross section parallel to the retaining wall where the ground settlement is 1 / 2 of the maximum settlement. Substituting the excavation depth H and the length L1 of the foundation pit into the fitting function 7, we obtain the distance A from the corner point to the inflection point of the retaining wall: A= -0.105 ； Substituting the distance A from the corner point to the inflection point of the retaining wall into the complementary error function, based on the maximum surface settlement δ outside the foundation pit that needs to be predicted. vm The complementary error function gives the maximum surface settlement δ outside the pit for any cross-section perpendicular to the retaining wall. vm The specific expression is as follows: 。 5. The method for predicting surface settlement outside a soft clay foundation pit considering spatiotemporal effects according to claim 1, characterized in that, The specific process of step (8) is as follows: Define the direction perpendicular to the retaining wall as the x-direction, with the outer wall of the retaining wall as the origin and the direction outward from the pit as positive. δ vm Substituting the values ​​into the three-segment model, the surface settlement δ at any point on the corresponding profile is obtained. v The specific expression is: 。

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