Method for calculating optimal excavation slope ratio of trench foundation pit

Abstract

The invention provides a calculation method for the optimal excavation slope ratio of a groove foundation pit. The calculation method comprises the steps that physical and mechanical parameters and geometric parameters of the groove foundation pit to be analyzed and the stress state of a sliding body of the groove foundation pit are obtained; establishing a safety stability objective function and an excavation volume objective function of the trench foundation pit, and a slip mass limit equilibrium constraint condition of the trench foundation pit; establishing a multi-objective optimization nonlinear mathematical programming model of the safety and stability of the trench foundation pit and the excavation workload; and solving the multi-objective optimization nonlinear mathematical programming model to obtain a safety stability coefficient and an optimal excavation slope rate when the excavation workload is minimum under the condition of guaranteeing safety. According to the method, an effective calculation method can be provided for the optimal slope ratio of slope excavation of the soil trench foundation pit, and the trench foundation pit slip mass limit equilibrium condition can be combined with the actual workload, so that the actual requirements of foundation pit engineering can be better met, the workload is as small as possible while the safety is ensured, and the construction efficiency is improved. And an effective basis is provided for stability evaluation and actual design construction of the trench foundation pit.

Description

Technical Field

[0001] The present invention relates to the field of slope ratios for trench foundation pit excavation, and more specifically, to a method for calculating the optimal excavation slope ratio of a trench foundation pit. Background Art

[0002] With the continuous advancement of urban modernization construction in China, the number of underground construction projects in urban municipal engineering is increasing day by day. The most common among them is the laying of various water supply and drainage pipelines, power supply lines, or other pipelines. In current construction technologies, the laying of such pipelines often requires trench foundation pits, that is, a construction method of backfilling after trench excavation and pipe laying. Conventional trench foundation pits are generally more than 3 times as long as they are wide, and the depth generally does not exceed 5m. Compared with the deep and large foundation pits during the construction of large buildings, trench foundation pits have the characteristics of small width, shallow depth, and overall long and narrow shape. Due to different dimensions, trench-type foundation pits are more easily affected by the spatial effect.

[0003] At present, industry scholars have carried out a large number of studies on the stability problems of trench foundation pits, including field tests, laboratory tests, and numerical simulations. However, the current research on trench foundation pits is not rich enough, and trench foundation pits are more affected by the spatial dimension effect compared with conventional deep and large foundation pits. There are influencing factors such as high cost and great operation difficulty in field tests and model tests. Among them, numerical simulation can effectively avoid the above problems and ensure the reliability of experimental research to a certain extent, so it is more suitable for the research on the method for calculating the excavation slope ratio of trench foundation pits.

[0004] In actual engineering for foundation pit excavation, the excavation slope ratio of the foundation pit is mainly determined by referring to relevant specifications and combining with the actual situation and engineering experience. For example, the Code for Acceptance of Construction Quality of Foundation Works (GB-50202-2018) gives the recommended slope ratio for temporary excavation works without support measures; the Technical Code for Building Slope Engineering (GB50330-2013) gives the allowable values of slope ratios for soil slopes, etc. However, the excavation slope ratios recommended by general specifications are only empirical values, and the applicable objects are generally conventional deep and large foundation pits. For the excavation slope ratio of narrow trench foundation pits, the existing relevant standard value ranges and safety stabilities are too conservative, and cannot simultaneously make the safety stability coefficient optimal and the excavation volume minimum, that is, cannot ensure safety while minimizing the workload as much as possible. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for calculating the optimal excavation slope ratio of a trench foundation pit to solve the problems existing in the above-mentioned prior art.

[0006] To achieve the above purpose, the present invention provides a method for calculating the optimal excavation slope ratio of a trench foundation pit, including: Obtaining the physical and mechanical parameters and geometric parameters of the trench foundation pit to be analyzed; Conduct a force analysis on the landslide body of the trench foundation pit to be analyzed to obtain the force state of the landslide body of the trench foundation pit to be analyzed; Establish the safety and stability objective function of the trench foundation pit and the excavation volume objective function based on the physical and mechanical parameters and geometric parameters of the trench foundation pit to be analyzed; According to the physical and mechanical parameters, geometric parameters of the trench foundation pit to be analyzed and the force state of the landslide body of the trench foundation pit to be analyzed, establish the limit equilibrium constraint conditions of the landslide body of the trench foundation pit; According to the safety and stability objective function, excavation volume objective function of the trench foundation pit and the limit equilibrium constraint conditions of the landslide body of the trench foundation pit, establish a multi-objective optimization non-linear mathematical programming model for the safety and stability and excavation workload of the trench foundation pit; Solve the multi-objective optimization non-linear mathematical programming model for the safety and stability and excavation workload of the trench foundation pit to obtain the safety stability coefficient and the optimal excavation slope ratio when both the safety and stability and the excavation workload are optimal.

[0007] A method for calculating the optimal excavation slope ratio of a trench foundation pit provided by the present invention can provide an effective calculation method for the optimal slope ratio of slope excavation of a soil trench foundation pit, and can combine the limit equilibrium conditions of the landslide body of the trench foundation pit with the actual workload, so as to better meet the actual requirements of foundation pit engineering, minimize the workload while ensuring safety, and provide an effective basis for the stability evaluation and actual design and construction of the trench foundation pit. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 It is a flow chart of the implementation method of the present invention; Figure 2 It is a regional map of the slope excavation of the trench foundation pit of the present invention; Figure 3 It is a schematic diagram of the slope of the trench foundation pit of the present invention; Figure 4 It is a schematic diagram of the slope of the trench in the implementation case of the present invention; Figure 5 It is a schematic diagram of the force on the landslide body of the trench foundation pit in the implementation case of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0009] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the protection scope of the present invention. Additionally, the technical features in each embodiment or a single embodiment provided by the present invention can be arbitrarily combined with each other to form a feasible technical solution. Such combination is not restricted by the order of steps and / or the structural composition mode, but must be based on what can be achieved by those of ordinary skill in the art. When the combination of technical solutions results in contradictions or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the protection scope required by the present invention.

[0010] As Figures 1 to 5 shown, a method for calculating the optimal excavation slope ratio of a trench foundation pit includes the following steps: Step 1: Obtain the physical and mechanical parameters and geometric parameters of the trench foundation pit to be analyzed.

[0011] Step 2: Conduct a force analysis on the sliding mass of the trench foundation pit to be analyzed to obtain the force state of the sliding mass of the trench foundation pit to be analyzed.

[0012] Step 3: Establish the safety and stability objective function of the trench foundation pit and establish the excavation volume objective function according to the physical and mechanical parameters and geometric parameters of the trench foundation pit to be analyzed.

[0013] Step 4: Establish the limit equilibrium constraint conditions of the sliding mass of the trench foundation pit according to the physical and mechanical parameters, geometric parameters of the trench foundation pit to be analyzed, and the force state of the sliding mass of the trench foundation pit to be analyzed.

[0014] Step 5: Establish a multi-objective optimization non-linear mathematical programming model for the safety and stability and excavation workload of the trench foundation pit according to the safety and stability objective function, excavation volume objective function of the trench foundation pit, and the limit equilibrium constraint conditions of the sliding mass of the trench foundation pit.

[0015] Step 6: Solve the multi-objective optimization non-linear mathematical programming model for the safety and stability and excavation workload of the trench foundation pit to obtain the safety and stability coefficient and the optimal excavation slope ratio when both the safety and stability and the excavation workload are optimal.

[0016] The following will specifically explain each step: Step 1: Obtain the physical and mechanical parameters and geometric parameters of the trench foundation pit to be analyzed.

[0017] As Figure 4For the shown example of a trench foundation pit, the following coordinate system is established: Taking a cross-section perpendicular to the length of the trench foundation pit as the research object, AB is the axis of symmetry of the research cross-section of the foundation pit, where B is the midpoint of the bottom of the foundation pit, A is the intersection point of the axis of symmetry and the extended line of the slope top, the intersection point of the pit wall and the bottom of the pit is O, OC is the free face of the foundation pit excavation, DE is the sliding surface of the landslide, and its extended line intersects the perpendicular line passing through point O and perpendicular to the bottom of the pit at point O 1 , taking the straight line where BO is located as the X-axis and the straight line where OO1 is located as the Y-axis, as shown in Figure 4 the established coordinate system. According to the actual situation of the trench foundation pit, its geometric parameters are determined, specifically including: the excavation depth H of the trench foundation pit is 5 m; the bottom width of the trench foundation pit b is 4 m; the distance from the bottom end of the sliding surface to the X-axis is 0.6 m; the angle between the sliding surface and the horizontal direction is α ; the excavation slope ratio of the trench foundation pit is β .

[0018] According to the actual situation of the trench foundation pit, its physical and mechanical parameters are determined, specifically including: the unit weight of the landslide of the trench foundation pit γ is 19.0 kN / m 3 ; the cohesion c and the internal friction angle φ of the sliding surface are 25 kPa and 15°, respectively.

[0019] Step 2: Analyze the forces acting on the landslide of the trench foundation pit to be analyzed to obtain the force state of the landslide of the trench foundation pit to be analyzed.

[0020] As shown in the schematic diagram of the landslide of the trench foundation pit in Figure 5 , analyze the forces acting on the trench foundation pit to obtain the gravity G acting on the centroid of the trench foundation pit (in the Y-axis direction), the shear force F S acting on the sliding surface of the landslide (negative in the counterclockwise direction) and the normal stress F N (positive for compression).

[0021] Step 3: Establish the safety and stability objective function of the trench foundation pit and the excavation volume objective function according to the physical and mechanical parameters and geometric parameters of the trench foundation pit to be analyzed.

[0022] ① Establish the safety and stability objective function of the trench foundation pit Taking the safety and stability coefficient of the trench foundation pit as the safety and stability objective function, the following objective function is established to determine the maximum value of the safety and stability coefficient of the trench foundation pit. The safety and stability objective function is established as follows: Max: K(1) where Max represents finding the maximum value, and K represents the safety and stability coefficient.

[0023] ② Establish the excavation volume objective function of the trench foundation pit Min: V(2) Where Min represents finding the minimum value, and V represents the excavation volume of the trench foundation pit.

[0024] When calculating the sliding mass of the foundation pit with a unit width: (3) Where: V represents the excavation volume of the trench foundation pit; β represents the excavation slope ratio of the trench foundation pit.

[0025] Step 4: Based on the physical and mechanical parameters, geometric parameters of the trench foundation pit to be analyzed, and the stress state of the sliding mass of the trench foundation pit to be analyzed, establish the limit equilibrium constraint conditions of the sliding mass of the trench foundation pit.

[0026] Among them, the limit equilibrium constraint conditions of the sliding mass of the trench foundation pit specifically include: the equilibrium equation constraint condition and the yield condition of the sliding surface of the sliding mass of the trench foundation pit: ① The equilibrium equation constraint condition of the sliding mass of the trench foundation pit: The sliding mass of the trench foundation pit is subjected to the gravity at the centroid, the shear force and normal stress on the sliding surface, and the above three forces are in balance.

[0027] Establish the horizontal equilibrium equation of the sliding mass of the trench foundation pit as follows: (4) Establish the vertical equilibrium equation of the sliding mass of the trench foundation pit as follows: (5) The gravity G acting at the centroid of the sliding mass of the trench foundation pit is as follows: (6) Where: F S represents the shear force on the sliding surface, with the counterclockwise direction being negative; F N represents the normal stress on the sliding surface, with compression being positive; α represents the angle between the sliding surface and the positive direction of the X-axis, with the counterclockwise direction being positive; β represents the excavation slope ratio of the trench foundation pit.

[0028] ② The yield condition of the sliding surface of the sliding mass of the trench foundation pit: Assume that the sliding mass of the trench foundation pit is a rigid block, and the failure of the trench foundation pit only occurs on the sliding surface and satisfies the Mohr-Coulomb criterion yield condition, specifically: (7) Where: K represents the safety stability coefficient; F S represents the shear force on the sliding surface, with the counterclockwise direction being negative; F NIt represents the normal stress on the sliding surface, with compression being positive; the width of the sliding surface is calculated with a value of 1 m.

[0029] Step 5: Based on the safety stability objective function of the trench foundation pit, the excavation volume objective function, and the limit equilibrium constraint conditions of the sliding mass of the trench foundation pit, establish a multi-objective optimization non-linear mathematical programming model for the safety stability and excavation workload of the trench foundation pit.

[0030] Among them, the multi-objective optimization non-linear mathematical programming model for the optimal safety stability and minimum excavation workload of the trench foundation pit, which takes the safety stability coefficient and excavation workload of the trench foundation pit as the dual objective functions and simultaneously satisfies the constraint conditions of the equilibrium equation of the sliding mass of the trench foundation pit and the yield condition of the sliding surface, is as follows: (8) Among them: K represents the safety stability coefficient; V represents the excavation volume; F S It represents the shear force on the sliding surface, with the counterclockwise direction being negative; F N It represents the normal stress on the sliding surface, with compression being positive; α It represents the angle between the sliding surface and the positive X-axis, with the counterclockwise direction being positive; G It represents the gravity acting at the centroid of the sliding mass of the trench foundation pit; β It represents the excavation slope ratio of the trench foundation pit; l It represents the length of the sliding surface; the width of the sliding surface is calculated with a value of 1 m.

[0031] As a multi-objective non-linear mathematical model, Equation (8) cannot simultaneously obtain the target data such as the safety stability coefficient when the safety stability coefficient and excavation workload are optimal. According to the research of the present invention, first, solve the non-linear mathematical objective function for optimal stability safety to obtain the safety stability coefficient ; further, solve the non-linear mathematical objective function for optimal excavation workload to obtain ; further, based on the solved and construct the objective function when both the stability safety and excavation workload are ideal, so as to obtain the safety stability coefficient , excavation volume and the optimal excavation slope ratio when both the stability safety and excavation workload are ideal. This calculation method solves the problem that the ideal solutions in two aspects cannot be obtained simultaneously. The specific solution process is shown in Step 6.

[0032] Step 6: Solve the multi-objective optimization non-linear mathematical programming model for the safety stability and excavation workload of the trench foundation pit to obtain the stability safety coefficient , excavation volume and the optimal excavation slope ratio .

[0033] ① Solve the non - linear mathematical programming model for the optimal safety and stability of the trench foundation pit.

[0034] According to the objective function (1) and the constraint conditions (3), (4), (5), (7), the non - linear mathematical programming model for the optimal safety and stability of the trench foundation pit excavation is obtained as follows: (9) Where: represents the safety and stability coefficient at the optimal stability; represents the excavation volume at the optimal stability; F S represents the shear force on the slip surface, negative in the counter - clockwise direction; F N represents the normal stress on the slip surface, positive in compression; α represents the angle between the slip surface and the positive x - axis, positive in the counter - clockwise direction; G represents the gravity acting at the centroid of the trench foundation pit slide body; represents the excavation slope ratio at the optimal stability; l represents the length of the slip surface; the width of the slip surface is calculated as 1m.

[0035] ② Solve the non - linear mathematical programming model for the minimum excavation workload of the trench foundation pit.

[0036] According to the objective function (2) and the constraint conditions (3), (4), (5), (7), the non - linear mathematical programming model for the minimum excavation workload of the trench foundation pit is obtained as follows: (10) Where: represents the safety and stability coefficient at the minimum excavation workload; represents the excavation volume at the minimum excavation workload; F S represents the shear force on the slip surface, negative in the counter - clockwise direction; F N represents the normal stress on the slip surface, positive in compression; α represents the angle between the slip surface and the positive x - axis, positive in the counter - clockwise direction; G represents the gravity acting at the centroid of the trench foundation pit slide body; represents the excavation slope ratio at the minimum excavation workload; l represents the length of the slip surface; the width of the slip surface is calculated as 1m.

[0037] ③ Construct the objective function for the optimal safety and stability and the minimum excavation workload.

[0038] The objective function with the optimal safety and stability and the lowest excavation workload is as follows: (11) Where: Z represents the objective function when the safety and stability are optimal and the excavation workload is the lowest; represents the safety and stability coefficient when the stability is optimal; represents the safety and stability coefficient when the safety and stability are optimal and the excavation workload is the lowest; represents the excavation volume when the excavation workload is the lowest; represents the excavation volume when the safety and stability are optimal and the excavation workload is the lowest.

[0039] ④ Establish a nonlinear mathematical programming model for the safety and stability and the excavation workload of the trench foundation pit.

[0040] According to the objective function formula (11) and the constraint conditions (3), (4), (5), and (7), establish the following nonlinear mathematical programming model for the safety and stability and the excavation workload of the trench foundation pit: (12) Where: Z represents the objective function when the safety and stability are optimal and the excavation workload is the lowest; represents the safety and stability coefficient when the stability is optimal; represents the safety and stability coefficient when the safety and stability are optimal and the excavation workload is the lowest; represents the excavation volume when the excavation workload is the lowest; represents the excavation volume when the safety and stability are optimal and the excavation workload is the lowest; F S represents the shear force on the slip surface, negative in the counterclockwise direction; F N represents the normal stress on the slip surface, positive in compression; α represents the angle between the slip surface and the positive X-axis, positive in the counterclockwise direction; G represents the gravity acting at the centroid of the trench foundation pit slide mass; represents the optimal excavation slope ratio when the safety and stability are optimal and the excavation workload is the lowest; the width of the slip surface is calculated as 1 m.

[0041] Solve the nonlinear mathematical programming model for the safety and stability and the excavation workload of the trench foundation pit in formula (12) to obtain the calculation results in the following table.

[0042] Table 1 shows the calculation results obtained when the safety and stability are optimal for different slip surface inclination angles α Specifically:

[0043] Table 2 shows the calculation results obtained when the excavation workload is minimized under different dip angles of the sliding surface, specifically: α

[0044] Table 3 shows the safety stability coefficient, 、 excavation volume and optimal excavation slope ratio calculation results obtained from the research of the present invention, specifically:

[0045] Table 4 shows the comparison between the optimal safety stability results and the calculation results of the present invention under different dip angles of the sliding surface, specifically: α

[0046] Table 5 shows the comparison between the minimum excavation workload results and the calculation results of the present invention under different dip angles of the sliding surface, specifically: α

[0047] As shown in Table 4, when the dip angle of the sliding surface α = 45°, comparing the results obtained by the method of the present invention with the results when the excavation safety stability is the highest, a 6.50% reduction in the safety stability coefficient within the safe range can result in a 1.21% reduction in the excavation workload, achieving the unity of safety stability and excavation workload.

[0048] As shown in Table 5, when the dip angle of the sliding surface α = 60°, comparing the results obtained by the method of the present invention with the results when the excavation workload is the minimum, only a 9.38% increase in the excavation volume can result in a 43.54% increase in the safety factor, achieving the unity of safety stability and excavation workload.

[0049] The above is a detailed description of the specific implementation method of the present invention in combination with the accompanying drawings. However, the calculation method described in the present invention is not limited to the above embodiments. In the relevant field, corresponding adjustments can be made without departing from the purpose of the calculation method described in the present invention.

[0050] The optimal excavation slope ratio calculation method for a trench foundation pit provided by the embodiment of the present invention has the following beneficial effects: ​​​(1) The present invention takes the soil trench foundation pit as the research object, and establishes a multi-objective optimization non-linear mathematical programming model for the safety and stability of the trench foundation pit and the excavation workload. This model takes the maximum value of the safety factor and the minimum value of the excavation volume as the objective functions, and takes the excavation slope ratio, the shear force and the normal stress of the slip surface as the decision variables, and is constrained by the equilibrium equation of the trench foundation pit sliding mass and the yield condition of the slip surface. At the same time, the gravity function constructed in the constraint conditions can change with the change of the excavation slope ratio, and can combine the limit equilibrium condition of the trench foundation pit sliding mass with the actual workload, so as to better meet the actual requirements of the foundation pit project; the calculation method of the present invention combines theory with practice on the basis of traditional engineering construction specifications, professional suggestions and engineering experience, and can minimize the excavation workload as much as possible while ensuring safety and stability, and takes into account the operability of actual excavation and the safety and stability of the trench foundation pit.

[0051] (2) The present invention provides a calculation method for the optimal excavation slope ratio of a trench foundation pit, which is applicable to the calculation of the optimal excavation slope ratio of a soil trench foundation pit considering the excavation workload and the safety stability coefficient comprehensively. This calculation method has the advantages of clear logic, clear concept and strong practicability.

[0052] It should be noted that in the above embodiments, the descriptions of each embodiment have their own emphases. For the parts not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0053] Although the preferred embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications to these embodiments once they know the basic creative concept. Therefore, the appended claims are intended to be construed as including the preferred embodiments and all changes and modifications falling within the scope of the present invention.

[0054] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. A method for calculating the optimal excavation slope of a trench foundation pit, characterized in that: include: Obtain the physical and mechanical parameters and geometric parameters of the trench foundation pit to be analyzed; Perform stress analysis on the groove foundation pit sliding body to be analyzed, and obtain the stress state of the groove foundation pit sliding body to be analyzed; Establish the safety and stability objective function of the trench foundation pit and establish the excavation volume objective function according to the physical and mechanical parameters and geometric parameters of the trench foundation pit to be analyzed; According to the physical and mechanical parameters of the trench foundation pit to be analyzed, the geometric parameters and the stress state of the trench foundation pit sliding body to be analyzed, establishing the limit equilibrium constraint condition of the trench foundation pit sliding body; A multi-objective optimization nonlinear mathematical programming model for trench foundation pit safety stability and excavation workload is established according to the safety stability objective function of the trench foundation pit, the excavation volume objective function and the limit equilibrium constraint condition of the trench foundation pit sliding body; A multi-objective optimization nonlinear mathematical programming model for the trench foundation pit safety stability and excavation workload is solved to obtain the safety stability coefficient and the optimal excavation slope when both the safety stability and excavation workload are optimal.

2. The method for calculating the optimal excavation slope of a trench foundation pit according to claim 1, characterized in that: The physical and mechanical parameters of the trench foundation pit to be analyzed include the bulk density of the foundation pit sliding body. γ , the inclination angle of the sliding surface α、 Cohesion of sliding surface c and the internal friction angle of the sliding surface φ , the geometric parameters include the foundation pit height H , the distance from the bottom of the sliding surface to the X axis H 1 and excavation slope of trench foundation pit β ; The force vector of the groove foundation pit sliding body to be analyzed obtained by the force analysis of the groove foundation pit sliding body to be analyzed includes the gravity acting at the centroid of the groove foundation pit sliding body. G、 Shear force acting on sliding surface of sliding body in trench foundation pit F S and normal stress F N ,in F S Counterclockwise rotation is negative. F N Pressure is positive.

3. The method for calculating the optimal excavation slope of a trench foundation pit according to claim 1, characterized in that: The method of establishing the safety and stability objective function of the trench foundation pit and establishing the excavation volume objective function according to the physical and mechanical parameters and geometric parameters of the trench foundation pit to be analyzed includes: The safety stability coefficient of the trench foundation pit to be analyzed is taken as the safety stability control index, and an extreme value function is established to seek the maximum value of the safety stability coefficient of the trench foundation pit, that is, the safety stability objective function of the trench foundation pit: Max:K Among them, Max - find the maximum value; K——safety stability coefficient; Taking the trench foundation pit excavation volume as the excavation workload control index, an extreme value function for seeking the minimum value of the trench foundation pit excavation volume is established, that is, the trench foundation pit excavation workload objective function: Min:V Among them: Min——find the minimum value; V – excavation volume; When the unit width foundation pit sliding body is taken for calculation, the excavation volume of the trench foundation pit sliding body is: in: H ——trench foundation pit height; b ——Width of trench foundation pit base; β ——Slope of trench foundation pit excavation; H and b are the geometric parameters of the trench foundation pit.

4. The method for calculating the optimal excavation slope of a trench foundation pit according to claim 1, characterized in that: The method of establishing the limit equilibrium constraint condition of the groove foundation pit sliding body according to the physical and mechanical parameters of the groove foundation pit to be analyzed, the geometric parameters and the stress state of the groove foundation pit sliding body to be analyzed includes: According to the physical and mechanical parameters of the trench foundation pit and the stress state of the trench foundation pit sliding body, the horizontal equilibrium equation of the trench foundation pit sliding body, the vertical equilibrium equation of the trench foundation pit sliding body and the yield condition of the sliding surface of the trench foundation pit sliding body are established respectively; Among them, the horizontal equilibrium equation of the trench foundation pit sliding body and the vertical equilibrium equation of the trench foundation pit sliding body constitute the equilibrium equation constraint conditions of the trench foundation pit sliding body, and the equilibrium equation constraint conditions of the trench foundation pit sliding body and the yield conditions of the sliding surface constitute the ultimate equilibrium constraint conditions of the trench foundation pit sliding body.

5. The method for calculating the optimal excavation slope of a trench foundation pit according to claim 4 is characterized in that: The method of establishing a horizontal equilibrium equation of the groove foundation pit sliding body, a vertical equilibrium equation of the groove foundation pit sliding body and a yield condition of the sliding surface of the groove foundation pit sliding body respectively according to the physical and mechanical parameters of the groove foundation pit and the stress state of the groove foundation pit sliding body comprises: The horizontal equilibrium equation of the sliding body of the trench foundation pit is established as follows: The vertical equilibrium equation of the sliding body of the trench foundation pit is established as follows: Gravity acting at the centroid of the sliding body in the trench foundation pit G as follows: in: F S ——The shear force on the sliding surface is negative in the counterclockwise direction; F N ——normal stress on the sliding surface, with compression as positive; α ——The angle between the sliding surface and the positive direction of the X-axis, with the counterclockwise direction being positive; H —— Excavation depth of trench foundation pit; H 1——The distance from the bottom of the sliding surface to the X axis; β —— excavation slope of trench foundation pit; γ ——Bulk density of the sliding body of the trench foundation pit; The yield condition of the sliding surface of the groove foundation pit sliding body is established as follows: Where: K——safety stability coefficient; F S ——The shear force on the sliding surface is negative in the counterclockwise direction; F N ——normal stress on the sliding surface, with compression as positive; c , φ — cohesion and internal friction angle of sliding surface; l ——The length of the sliding surface.

6. The method for calculating the optimal excavation slope of a trench foundation pit according to claim 5, characterized in that: The multi-objective optimization nonlinear mathematical programming model for trench foundation pit safety stability and excavation workload is established according to the safety stability objective function of the trench foundation pit, the excavation volume objective function and the limit equilibrium constraint condition of the trench foundation pit sliding body, including: A dual objective function with the trench pit safety stability coefficient and excavation workload as indicators is established. The multi-objective optimization nonlinear mathematical programming model for the optimal trench pit safety stability and the minimum excavation workload that satisfies the constraint conditions of the trench pit sliding body equilibrium equation and the yield condition of the sliding surface is: Where: K——safety stability coefficient; V – excavation volume; F S ——The shear force on the sliding surface is negative in the counterclockwise direction; F N ——normal stress on the sliding surface, with compression as positive; α ——The angle between the sliding surface and the positive direction of the X-axis, with the counterclockwise direction being positive; G ——Gravity acting at the centroid of the sliding body in the trench foundation pit; H —— Excavation depth of trench foundation pit; H 1——The distance from the bottom of the sliding surface to the X axis; β —— excavation slope of trench foundation pit; γ ——Bulk density of the sliding body of the trench foundation pit; b ——Width of trench foundation pit base.

7. The method for calculating the optimal excavation slope of a trench foundation pit according to claim 6, characterized in that: Solve the multi-objective optimization nonlinear mathematical programming model of the trench foundation pit safety stability and excavation workload, and obtain the safety stability coefficient and the optimal excavation slope when both the safety stability and excavation workload are optimal, including: Based on the multi-objective optimization nonlinear mathematical programming model of trench foundation pit safety stability and excavation workload, solve the nonlinear mathematical programming model with the best trench foundation pit safety stability and the nonlinear mathematical programming model with the lowest trench foundation pit excavation workload; According to the nonlinear mathematical programming model with the best safety and stability of the trench foundation pit and the nonlinear mathematical programming model with the lowest excavation workload of the trench foundation pit, an objective function with the best safety and stability and the lowest excavation workload is constructed; The nonlinear mathematical programming model with the best safety and stability of trench foundation pit and the lowest excavation workload is solved, and the optimal excavation slope with the best safety and stability and the lowest excavation workload is obtained.

8. The method for calculating the optimal excavation slope of a trench foundation pit according to claim 7, characterized in that: The nonlinear mathematical programming model for the optimal safety and stability of the trench foundation pit is as follows: in: ——Safety stability coefficient when stability is optimal; —— excavation volume for optimal stability; F S ——The shear force on the sliding surface is negative in the counterclockwise direction; F N ——normal stress on the sliding surface, with compression as positive; α ——The angle between the sliding surface and the positive direction of the X-axis, with the counterclockwise direction being positive; G ——Gravity acting at the centroid of the sliding body in the trench foundation pit; H —— Excavation depth of trench foundation pit; —— Excavation slope for optimal stability; b ——Width of trench foundation pit base; The nonlinear mathematical programming model with the lowest trench foundation pit excavation workload is as follows: in: ——Safety stability coefficient when the excavation workload is minimum; ——the excavation volume when the excavation workload is minimum; ——The excavation slope when the excavation workload is minimum; The objective function with optimal safety and stability and minimum excavation workload is as follows: Where: Z is the objective function when safety and stability are optimal and excavation workload is minimum; ——Safety and stability coefficient when safety and stability are optimal and excavation workload is minimum; ——The excavation volume with optimal safety and stability and minimum excavation workload; The nonlinear mathematical programming model for the safety stability and excavation workload of the trench foundation pit is as follows: in: ——The optimal excavation slope with optimal safety and stability and minimum excavation workload.

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