Calculation method for lateral displacement of soil retaining structure with pre - applied bending moment

Abstract

The present invention discloses a method for calculating the lateral displacement of a soil retaining structure with pre-applied bending moment, including: a soil retaining structure, pre-stressed high-strength steel strands, elastic supports for calculating soil reaction forces, a fixed end at the bottom, a pre-stressed anchorage end at the top, determining the calculation mechanical model of the soil retaining structure, arranging the soil and water lateral pressures on the side of the soil retaining structure, converting the surface overload into a formation horizontal load, and the load borne by the soil retaining structure is mainly in the horizontal direction. The method for calculating the lateral displacement of the soil retaining structure with pre-applied bending moment proposes a structural calculation model and a displacement calculation formula for the soil retaining structure with pre-applied bending moment, optimizing the deficiency that the existing design method cannot calculate the displacement of the soil retaining structure with pre-applied bending moment, providing theoretical support for the design of the soil retaining structure with pre-applied bending moment, contributing to the engineering application of the soil retaining structure with pre-applied bending moment, and providing a more reasonable, economical and effective support measure for underground projects with strict deformation requirements.

Description

Technical Field

[0001] The present invention belongs to the technical fields of underground engineering, foundation pit engineering, and slope engineering, and relates to a method for calculating the lateral displacement of a soil retaining structure with pre-applied bending moment. Background Technique

[0002] Existing foundation pit support methods mainly rely on the self-stiffness of the retaining structure and the supporting and anchoring structure to resist earth pressure and control the deformation impact on the surrounding environment caused by foundation pit excavation. For deep and large foundation pits or foundation pit projects in deformation-sensitive areas, the required support system is huge, with disadvantages such as high engineering costs, long construction periods, and a large amount of construction waste generated.

[0003] By applying prestress to pre-apply bending moment to the soil retaining structure, the internal force distribution under the working state of the soil retaining structure can be improved, the structural size of the soil retaining structure can be reduced, and the ability of the soil retaining structure to resist deformation can be increased. In the current "Technical Code for Building Foundation Pit Support" JGJ120-2012, the elastic fulcrum method of plane bar system structure is used for the analysis of the retaining structure. This calculation method is based on the Winkler elastic foundation beam theory, and the soil reaction force is deduced from the horizontal displacement of the retaining member and the soil at the calculation point, without considering the support force and deformation conditions during the pre-deformation caused by pre-applying bending moment to the retaining structure, and cannot accurately calculate the displacement and internal force distribution of the soil retaining structure with pre-applied bending moment, and there is room for improvement. Summary of the Invention

[0004] (1) Technical Problems to be Solved

[0005] The purpose of the present invention is to provide a method for calculating the lateral displacement of a soil retaining structure with pre-applied bending moment, so as to solve the problem that in the above background technique, this calculation method is based on the Winkler elastic foundation beam theory, and the soil reaction force is deduced from the horizontal displacement of the retaining member and the soil at the calculation point, without considering the support force and deformation conditions during the pre-deformation caused by pre-applying bending moment to the retaining structure, and cannot accurately calculate the displacement and internal force distribution of the soil retaining structure with pre-applied bending moment, and there is room for improvement.

[0006] (2) Technical Solutions

[0007] To achieve the above purpose, the present invention provides the following technical solutions: A method for calculating the lateral displacement of a soil retaining structure with pre-applied bending moment, including a soil retaining structure, prestressed high-strength steel strands, an elastic support for calculating soil reaction force, a bottom fixed end, and a top pre-stress anchoring end: including the following steps:

[0008] Step 1: Determine the calculation mechanical model of the soil retaining structure, arrange the soil and water lateral pressures on the side of the soil retaining structure, convert the surface overload into a stratum horizontal load, and the load borne by the soil retaining structure is mainly in the horizontal direction;

[0009] Step 2: Determine the basic parameters required for the calculation, including soil unit weight, groundwater level, formation physical and mechanical parameters, formation lateral pressure coefficient, retaining height, retaining structure material, retaining structure size, and surface overload magnitude, and reasonably determine them according to the specification requirements and geological exploration results;

[0010] Step 3: Approximately calculate the relationship formula between the prestressing force and the prestressed moment in the retaining structure;

[0011]

[0012] In the formula: \(M_P\) is the prestressed moment of the retaining structure, with the unit of N·m; \(d\) is the thickness of the retaining structure, with the unit of m; \(L\) is the length of the prestressing force anchorage end, with the unit of m; \(N\) P is the prestressing force, with the unit of N;

[0013] Step 4: Establish a structural calculation model;

[0014] Step 5: Calculate the lateral displacement of the retaining structure caused by rigid body rotation after excavation:

[0015]

[0016] In the formula: \(v\) r is the lateral displacement of the retaining structure caused by rigid body rotation, with the unit of m; \(E\) ak is the standard value of the active earth pressure per unit length on the outside of the retaining structure, with the unit of N·m; \(b\) a is the calculated width of the retaining structure, with the unit of m; \(p\) s0 is the initial distributed soil reaction force in the embedded section, with the unit of kPa; \(b_0\) is the calculated width of the soil reaction force, with the unit of m; \(l\) d is the length of the embedded section of the retaining structure, with the unit of m; \(l\) is the length of the retaining structure, with the unit of m; \(z\) is the calculation depth, with the unit of m; \(m\) is the proportional coefficient of the soil horizontal reaction coefficient, with the unit of MN / m 4 ;

[0017] Step 6: Calculate the bending moment function of the cantilever section of the retaining structure caused by earth pressure after excavation:

[0018]

[0019] In the formula: \(p\) ak,i is the standard value of the active earth pressure intensity at the calculation point in the \(i\)-th layer of soil outside the retaining structure, with the unit of kPa; \(z\) is the calculation depth, with the unit of m;

[0020] Step 7: Obtain the distribution formula of the lateral displacement of the cantilever section of the retaining structure with the prestressed moment along the depth \(z\):

[0021]

[0022] In the formula: \(v\)s is the horizontal displacement of the retaining structure, with the unit of m; E ak is the standard value of the active earth pressure on the outside of the retaining structure per unit length, with the unit of N·m; b a is the calculated width of the retaining structure, with the unit of m; p s0 is the initial distributed soil reaction force of the embedded section, with the unit of kPa; b0 is the calculated width of the soil reaction force, with the unit of m; l d is the length of the embedded section of the retaining structure, with the unit of m; l is the length of the retaining structure, with the unit of m; z is the calculated depth, with the unit of m; m is the proportional coefficient of the horizontal soil reaction coefficient, with the unit of MN / m 4 ; E is the elastic modulus of the retaining structure, with the unit of MPa; I is the moment of inertia of the cross-section of the retaining structure, with the unit of m 4 .

[0023] Preferably, the loads that the retaining structure may be subjected to are analyzed and simplified for easy calculation. The retaining structure mainly bears the lateral horizontal soil and water pressure. The surface overload is converted into a stratum horizontal load for calculation. The deformations of the retaining structure and the soil caused by the external bending moment and soil pressure conditions are all tiny. Therefore, it can be calculated according to the elastic theory. By applying prestress, a pre-bending moment is applied to the retaining structure to improve the internal force distribution under the working state of the retaining structure, reduce the structural size of the retaining structure, and increase the ability of the retaining structure to resist deformation.

[0024] Preferably, the external bending moment of the retaining structure is realized by installing high-strength steel strands on the retaining structure and stretching and anchoring the steel strands to generate prestress. For the application and transmission of prestress, a certain distance and angle are set between the steel strands and the retaining structure. This angle is tiny compared with the self-size of the retaining structure. Therefore, it is approximately considered that the direction of the prestressing force N P is parallel to the retaining structure, and thus the eccentricity e of the prestressing force is obtained as e = (d + L) / 2, providing a theoretical support for the design of the retaining structure with pre-bending moment.

[0025] Preferably, the structural calculation is carried out using the elastic support point method of the plane bar system structure specified in the Technical Specification for Building Foundation Pit Support JGJ120 - 2012. To apply the prestressing force, measures need to be taken to partially fix the bottom of the retaining structure. Therefore, the end of the retaining structure entering the soil is simplified as a hinge support. The entire retaining structure with pre-bending moment is regarded as a rigid body. Under the action of the external active earth pressure, it rotates slightly around the support, pushing the inner soil to generate a reaction force until static equilibrium. The active earth pressure is calculated layer by layer using the Rankine theory, and the soil reaction force is calculated using the m method, providing a theoretical support for the design of the retaining structure with pre-bending moment.

[0026] Preferably, the value of m is determined by the horizontal load test of the support structure and regional experience. When there is a lack of data, it is calculated according to Formula 4.1.6 in the Technical Specification for Building Foundation Pit Support JGJ120-2012. Both b0 and b a are calculated according to the relevant requirements in the Technical Specification for Building Foundation Pit Support JGJ120-2012, which helps the retaining structure with pre-added moment to be put into engineering application.

[0027] Preferably, only the rigid body rotation displacement of the structure is considered in the embedded section of the retaining structure with pre-added moment. The lateral displacement of the cantilever section is composed of the superposition of the rigid body rotation displacement and the structural bending deformation of the structure. The bending deformation of the retaining structure is generated by the combined action of the moment generated by the active earth pressure and the pre-added moment, providing a more reasonable, economical and effective support measure for underground projects with strict deformation requirements.

[0028] Compared with the prior art, the beneficial effects of the present invention are as follows: a structural calculation model and displacement calculation formula for a retaining structure with pre-added moment are proposed, optimizing the deficiency that the existing design method cannot calculate the displacement of the retaining structure with pre-added moment, providing theoretical support for the design of the retaining structure with pre-added moment, helping the retaining structure with pre-added moment to be put into engineering application, and providing a more reasonable, economical and effective support measure for underground projects with strict deformation requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is a schematic diagram of the installation process of the pre-stressing device;

[0030] In the figure, 1. retaining structure, 2. high-strength steel strand for pre-added force, 3. elastic support for calculating soil reaction force, 4. bottom fixed end, 5. top pre-added force anchorage end;

[0031] Figure 2 is a schematic diagram of the structural calculation model of the device;

[0032] Figure 3 is a schematic diagram of the working mechanism after the installation of the device;

[0033] Figure 4 is a schematic diagram of the bending moment in the working state of the device. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0034] 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. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0035] Please refer to Figure 1, the present invention provides a technical solution: a method for calculating the lateral displacement of a soil retaining structure with pre - applied bending moment, including a soil retaining structure, pre - stressed high - strength steel strands, elastic supports for calculating soil reaction forces, a fixed end at the bottom, and a prestressed section at the top, comprising the following steps:

[0036] Step 1: Determine the computational mechanical model of the soil retaining structure, arrange the soil and water lateral pressures on the side of the soil retaining structure, convert the surface surcharge into a stratum horizontal load, and the loads borne by the soil retaining structure are mainly in the horizontal direction;

[0037] Step 2: Determine the basic parameters required for the calculation, including soil unit weight, groundwater level, stratum physical and mechanical parameters, stratum lateral pressure coefficient, soil retaining height, soil retaining structure material, soil retaining structure size, and surface surcharge magnitude, and reasonably determine them according to the specification requirements and geological exploration results;

[0038] Step 3: Approximately calculate the relationship formula between the pre - applied force and the pre - applied bending moment in the soil retaining structure;

[0039]

[0040] In the formula: \(M_P\) is the pre - applied bending moment of the soil retaining structure, in N·m; \(d\) is the thickness of the soil retaining structure, in m; \(L\) is the length of the pre - applied force anchorage end, in m; \(N\) P is the pre - applied force, in N;

[0041] Step 4: Establish a structural calculation model;

[0042] Step 5: Calculate the lateral displacement of the soil retaining structure caused by rigid body rotation after excavation:

[0043]

[0044] Step 6: Calculate the bending moment function of the cantilever section of the soil retaining structure caused by soil pressure after excavation:

[0045]

[0046] Step 7: Obtain the distribution formula of the lateral displacement of the cantilever section of the soil retaining structure with pre - applied bending moment along the depth \(z\):

[0047]

[0048] Furthermore, analyze and simplify the possible loads on the soil retaining structure for easy calculation. The soil retaining structure mainly bears the lateral soil and water pressures in the horizontal direction on the side, and the surface surcharge is converted into a stratum horizontal load for calculation. The deformations of the soil retaining structure and the soil caused by the external bending moment and soil pressure conditions are all negligible compared to the size of the support structure, so the calculation is carried out according to the elastic theory.

[0049] Furthermore, the additional bending moment of the retaining structure is achieved by installing high-strength steel strands on the retaining structure and applying tensile anchorage to the steel strands to generate prestress. To facilitate the application and transmission of prestress, a certain distance and angle are set between the steel strands and the retaining structure. This angle is negligible compared to the dimensions of the retaining structure itself. Therefore, it is approximately considered that the direction of the prestressing force N P is parallel to the retaining structure, and thus the eccentricity e of the prestressing force is obtained as e = (d + L) / 2.

[0050] Furthermore, the structural calculation is carried out using the elastic support method for plane frame structures specified in the Technical Specification for Building Foundation Pit Support JGJ120 - 2012. To apply the prestressing force, measures need to be taken to partially fix the bottom of the retaining structure. Therefore, the embedded end of the retaining structure is simplified as a hinge support, and the entire retaining structure with the pre - applied bending moment is regarded as a rigid body. Under the action of the active earth pressure on the outside, it undergoes a small rotation around the support, pushing the soil on the inside to generate a reaction force until static equilibrium is reached. The active earth pressure is calculated layer - by - layer using the Rankine theory, and the soil reaction force is calculated using the m - method.

[0051] Furthermore, m is determined based on the horizontal load test of the retaining structure and local experience. When there is a lack of data, it is calculated according to formula 4.1.6 in the Technical Specification for Building Foundation Pit Support JGJ120 - 2012, and both b0 and ba are calculated according to the relevant requirements in the Technical Specification for Building Foundation Pit Support JGJ120 - 2012.

[0052] Furthermore, for the embedded section of the retaining structure with the pre - applied bending moment, only the rigid - body rotation displacement of the structure is considered. The lateral displacement of the cantilever section is composed of the superposition of the rigid - body rotation displacement and the bending deformation of the structure. The bending deformation of the retaining structure is generated by the combined action of the bending moment caused by the active earth pressure and the pre - applied bending moment.

[0053] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, rather than to limit the protection scope of the present invention. Any simple modification or equivalent replacement of the technical solution of the present invention by those of ordinary skill in the art shall not depart from the essence and scope of the technical solution of the present invention.

Claims

1. Lateral displacement calculation method for a retaining structure with pre - applied bending moment, including a retaining structure, high - strength steel strands with pre - applied force, elastic supports for calculating soil reaction forces, a fixed end at the bottom, and a pre - applied force anchoring end at the top: It is characterized in that: It includes the following steps: Step 1: Determine the computational mechanical model of the retaining structure, arrange the soil and water lateral pressures on the side of the retaining structure, convert the surface surcharge into a stratum horizontal load, and the main load borne by the retaining structure is in the horizontal direction; Step 2: Determine the basic parameters required for the calculation, including soil unit weight, groundwater level, stratum physical and mechanical parameters, stratum lateral pressure coefficient, retaining height, retaining structure material, retaining structure size, and surface surcharge magnitude, and reasonably determine them according to the specification requirements and geological exploration results; Step 3: Approximately calculate the relationship formula between the prestress and the prestressed moment in the retaining structure; Where: M P is the pre-added bending moment of the retaining structure, in N·m; d is the thickness of the retaining structure, in m; L is the length of the pre-added force anchoring end, in m; N P is the prestress, unit N; Step 4: Establish a structural calculation model; Step 5: Calculate the lateral displacement of the retaining structure caused by rigid body rotation after excavation; Where: v r is the lateral displacement caused by the rigid body rotation of the retaining structure, with the unit of m; E ak is the standard value of the active earth pressure acting on the outside of the retaining structure per unit length, with the unit of N·m; b a is the calculated width of the retaining structure, with the unit of m; p s0 is the initial distributed soil reaction force of the fixed section, with the unit of kPa; b0 is the calculation width of the soil reaction force, with the unit of m; l d is the length of the fixed section of the retaining structure, with the unit of m; l is the length of the retaining structure, with the unit of m; z is the calculation depth, with the unit of m; m is the proportional coefficient of the horizontal soil reaction coefficient, with the unit of MN / m 4 ; Step 6: Calculate the moment function of the cantilever section of the retaining structure caused by soil pressure after excavation; Where: p ak,i is the standard value of the active earth pressure intensity at the calculation point in the i-th layer of soil outside the retaining structure, with the unit of kPa; z is the calculation depth, with the unit of m; Step 7: Obtain the distribution formula of the lateral displacement of the cantilever section of the retaining structure with prestressed moment along the depth z; where: v s is the horizontal displacement of the retaining structure, with the unit of m; E ak is the standard value of the active earth pressure acting on the outside of the retaining structure per unit length, with the unit of N·m; b a is the calculated width of the retaining structure, with the unit of m; p s0 is the initial distributed soil reaction force of the fixed section, in kPa; b0 is the calculated width of the soil reaction force, in m; l d is the length of the fixed section of the retaining structure, in m; l is the length of the retaining structure, in m; z is the calculated depth, with the unit of m; m is the proportionality coefficient of the horizontal soil reaction coefficient, with the unit of MN / m 4 ; E is the elastic modulus of the retaining structure, with the unit of MPa; I is the moment of inertia of the cross-section of the retaining structure, with the unit of m 4 .

2. The calculation method for the lateral displacement of the pre-bending moment retaining structure according to claim 1, characterized in that: Analyze and simplify the possible loads on the retaining structure for easy calculation. The retaining structure mainly bears the soil and water lateral pressures in the horizontal direction on the side, and the surface surcharge is converted into a stratum horizontal load for calculation. The deformations of the retaining structure and the soil caused by the applied moment and soil pressure conditions are all negligible compared to the size of the supporting structure, so the calculation is carried out according to the elastic theory.

3. The method for calculating the lateral displacement of the pre-bending moment retaining structure according to claim 2, characterized in that: The additional bending moment of the retaining structure is achieved by installing high-strength steel strands on the retaining structure and generating prestress through tension anchoring of the steel strands. In order to apply and transfer the prestress, a certain distance and angle are set between the steel strands and the retaining structure. This angle is small compared to the size of the retaining structure itself. Therefore, it is approximately considered that the direction of the prestressing force N P P is parallel to the retaining structure, and thus the eccentricity e of the prestressing force is obtained as e = (d + L) / 2.

4. The method for calculating the lateral displacement of the preloaded moment retaining structure according to claim 3, characterized in that: The structural calculation is carried out using the elastic support method of the plane bar system specified in the Technical Specification for Building Foundation Pit Support JGJ120 - 2012. To apply the prestress, measures need to be taken to partially fix the bottom of the retaining structure. Therefore, the embedded end of the retaining structure is simplified as a hinge support, and the entire retaining structure with prestressed moment is regarded as a rigid body. Under the action of the active earth pressure on the outside, it rotates slightly around the support, pushing the soil on the inside to generate a reaction force until static equilibrium. The active earth pressure is calculated layer by layer using the Rankine theory, and the soil reaction force is calculated using the m method.

5. The calculation method for the lateral displacement of the preloaded moment retaining structure according to claim 4, characterized in that: The value of m is determined by the horizontal load test of the support structure and local experience. When there is a lack of data, it is calculated according to Formula 4.1.6 in Technical Specification for Building Foundation Pit Support JGJ120 - 2012, and b0 and b a are both calculated according to the relevant requirements in Technical Specification for Building Foundation Pit Support JGJ120 - 2012.

6. The calculation method for the lateral displacement of the preloaded moment retaining structure according to claim 5, characterized in that: For the embedded section of the retaining structure with prestressed moment, only the rigid body rotation displacement of the structure is considered. The lateral displacement of the cantilever section is composed of the superposition of the rigid body rotation displacement and the structural bending deformation of the structure. The structural bending deformation is caused by the combined action of the moment generated by the active earth pressure and the prestressed moment.

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