A method for compensating design of bearing capacity of rock-socketed foundation considering rock mass constraint

Abstract

The present application relates to a kind of rock-socketed foundation bearing capacity compensation design method considering rock mass constraint, comprising: establishing rock-socketed foundation calculation model, determine its consolidation boundary condition in rock layer;Calculate the horizontal soil resistance of triangle distribution produced when foundation rotates;Solve the resisting moment of horizontal rock resistance to base center;The deformation of base is decomposed into integral subsidence and rotating component;Determine the calculation formula of base zero stress point position, and establish base vertical pressure distribution model;Establish the overall balance equation group, and solve the foundation rotation angle and zero stress point position by iteration calculation;Calculate the maximum compressive stress of base and evaluate the bearing capacity compensation effect;Finally, section internal force analysis and reinforcement design are carried out.The present application provides additional resisting moment by quantifying rock mass constraint, effectively reduces the maximum compressive stress of base, provides theoretical basis and technical support for improving foundation bearing capacity and optimizing foundation size, and is especially suitable for rock-socketed foundation design in high intensity seismic region.

Description

Technical Field

[0001] This invention belongs to the field of bridge foundation engineering technology, specifically relating to a design method for compensating the bearing capacity of rock-socketed foundations that takes into account rock mass constraints. Background Technology

[0002] In existing design theories of rock-socketed foundations, simplified calculation methods are typically employed, treating the foundation's embedment in the rock strata as a fully consolidated boundary and assuming a linear distribution of base pressure. These methods, based on the assumption of complete contact between the foundation bottom and the rock mass, fail to adequately consider the stress redistribution that may occur during actual stress loading. However, engineering practice and experimental studies show that under high-intensity earthquakes, rock-socketed foundations undergo rotational deformation. Due to the limited tensile strength of the rock mass, voids will form at the base edge, leading to a significant change in the base stress state. Traditional design methods cannot accurately reflect this complex stress redistribution process, and their calculation results often deviate from the actual stress state. To meet the design requirements of full-section compression, engineers are forced to use excessively large safety factors, resulting in oversized foundations and significant material waste. Although modern finite element methods can simulate base voiding, their complex modeling and high computational costs make them difficult to widely apply in conventional engineering design. Therefore, there is an urgent need to develop a practical design method that accurately reflects the stress redistribution characteristics of rock-socketed foundations and is easy to apply in engineering, thereby achieving precision and economy in foundation design. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a design method for compensating the bearing capacity of embedded rock foundations that considers rock mass constraints. By establishing a reasonable stress redistribution model, the stress state after the foundation is detached is accurately calculated, providing a theoretical basis for the optimized design of embedded rock foundations.

[0004] The technical solution of the present invention is as follows: A design method for bearing capacity compensation of rock-socketed foundations considering rock mass constraints includes the following steps: A. Establish a calculation model for the rock-embedded foundation and determine its consolidation boundary conditions in the rock strata; B. Calculate the triangularly distributed horizontal soil resistance generated by the soil layer segment during foundation rotation; C. Solve for the resistive moment of the horizontal soil layer about the center of the foundation; D. Decompose the base deformation into overall subsidence and rotation components; E. Determine the calculation formula for the location of the zero stress point of the base and establish a vertical pressure distribution model for the base; F. Establish a system of overall equilibrium equations and solve for the foundation rotation angle and the location of the zero-stress point through iterative calculations; G. Calculate the maximum compressive stress at the base and evaluate the bearing capacity compensation effect of the rock mass constraint; H. Perform cross-sectional internal force analysis and reinforcement design.

[0005] Furthermore, in step A, the specific calculation model for the rock-embedded foundation is as follows: the foundation is considered as a rigid foundation embedded in the rock strata, and the portion of the foundation embedded in the rock strata is considered to be at the center of the basement. C The point is solidified at a depth of [missing information] from the ground. h Vertical force at the top of the foundation F y Horizontal force F x Bending moment M z Under the action, around C The point rotates.

[0006] Furthermore, in step B, the burial depth y Horizontal earth pressure stress at the foundation t x It can be calculated using the following formula: t x =( h - y )· my (1) In the formula, m It is the soil foundation ratio coefficient, with units of kPa / m. 2 ; i It is the basic winding C The vertical rotation angle of a point, measured in rad.

[0007] Along depth t x By integration, the horizontal soil resistance of the foundation can be obtained. T x The calculation formula is as follows:

[0008] In the formula, t It is based on a force perpendicular to the horizontal. F x The length of the direction, in meters (m).

[0009] Furthermore, in step C, the horizontal soil resistance at the base center... C Point resistance torque M 1. Calculate using the following formula:

[0010] Furthermore, in step D, the distance from the centroid of the base is... x Vertical stress at the point t y Calculate using the following formula: t y =C 0( d + θx (4) In the formula, C 0 is the vertical foundation coefficient of the basement rock mass, with units of kPa / m; d It represents the overall subsidence displacement of the foundation, in meters (m). d + θx Used to represent base deformation.

[0011] Furthermore, in step E, let t y =0, thus obtaining the formula for calculating the location of the zero-stress point: x 0=- d / i ; The vertical pressure distribution model of the base is the vertical pressure on the base center. C resistance torque M 2. Calculate using the following formula:

[0012] In the formula, q It is based on horizontal force F x The length in the direction, in meters (m).

[0013] Furthermore, in step F, at the consolidation point C Establish a system of equilibrium equations at this point:

[0014] In the formula, T p It is the concentrated horizontal resistance generated at the substrate embedding point. T y The resultant vertical reaction force at the base is expressed in kN.

[0015] Resultant vertical reaction force of the base T y By analyzing the effective pressure zone ( x 0 to the base edge) t y The integral yields:

[0016] The basic rotation angle is obtained by solving the system of equations (7) using an iterative method. i and the location of the zero stress point x The value of 0.

[0017] Furthermore, in step G, the maximum compressive stress of the base... t max Calculate using the following formula:

[0018] In the formula, A 0 represents the area of ​​the base, measured in m². 2 .

[0019] The bearing capacity compensation effect is quantitatively evaluated by comparing the maximum compressive stress at the base under two scenarios: one that takes into account the rock mass stress redistribution and the other that does not.

[0020] Furthermore, in step H, the base depth y Bending moment at section M y and horizontal stress V x Calculate using the following formula:

[0021] Compared with the prior art, the beneficial effects of this invention are as follows: By establishing a stress redistribution model that considers base voids, the actual working state of the rock-embedded foundation is accurately reflected; by using an iterative algorithm to solve the equilibrium equations, the location of the zero-stress point and the stress distribution of the base can be accurately determined; by quantifying the rock mass constraint effect, a theoretical basis is provided for optimizing the bearing capacity of the rock-embedded foundation; the calculation method is simple and practical, ensuring both calculation accuracy and meeting the efficiency requirements of engineering design; under the premise of ensuring structural safety, the foundation size can be effectively reduced, saving engineering costs. Attached Figure Description

[0022] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram of the rock-embedded foundation calculation model of the present invention; Figure 3 This is a comparison diagram of the load-bearing capacity compensation effect of the present invention. Detailed Implementation

[0023] Exemplary embodiments of the present invention will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present invention and to fully convey the scope of the invention to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0024] This invention discloses an embodiment of a design method for compensating the bearing capacity of a rock-socketed foundation considering rock mass constraints, the details of which are as follows: I. Project Overview This embodiment takes a bridge pier rock-socketed foundation located at a design seismic acceleration of 0.2g and a characteristic period of 0.35s as an example. The foundation is a rectangular excavated well foundation, such as... Figure 2 As shown, the specific parameters are as follows: Basic dimensions: length q =10m, horizontal length t =20m Rock embedding depth: 3m basal center C Burial depth: h =5m Upper load: Vertical force F y =203166 kN; Horizontal force F x =15869 kN; bending moment M z =320590 kN·m Soil and rock parameters: horizontal subgrade coefficient m =42188kPa / m²; Vertical foundation coefficient of the basement rock mass C 0 = 5812500 kPa / m, allowable stress of the base [ t =2425kPa.

[0025] II. Specific Implementation Process according to Figure 1 The flowchart shown below details the specific steps: 1. Establish a calculation model for rock-socketed foundations The foundation is considered as a rigid foundation embedded in the rock strata, with the consolidation point located at the center of the basement. C At this point, the depth from the ground h =5m. The foundation is wrapped around the top load. C The point rotates.

[0026] 2. Calculate the resistance of the horizontal soil layer Calculate the depth of the rock-socketed section according to formula (1) y Horizontal earth pressure stress at: t x =( h - y )· i · my =(5- y )· i ·42188 y (kPa) The resultant force of horizontal soil resistance is obtained by integration:

[0027] 3. Solve for the resisting torque Horizontal rock resistance to the center of the basement C The resisting torque is:

[0028] 4. Decompose the base deformation Distance from the centroid of the base is x The vertical displacement at the point is decomposed into overall subsidence. d and rotational components θx Then the vertical stress of the base is: t y = C 0( d + θx )=5812500( d + θx ) 5. Determine the zero stress point t y =0, thus obtaining the formula for calculating the location of the zero-stress point: x 0=- d / i 6. Establish a vertical pressure distribution model for the base. Vertical pressure on the base center C The resisting torque is:

[0029] 7. Establish the equilibrium equations and solve them iteratively. At the solidification point C Establish a system of equilibrium equations at this point:

[0030] The resultant vertical reaction force Ty at the base can be obtained by equation (7).

[0031] The above system of equations was obtained through iterative calculation: Base corner i =0.000042 rad Zero stress point location x 0 = -4.115 m 8. Calculate the base stress and evaluate the compensation effect. Calculate the maximum compressive stress on the base according to formula (8):

[0032] To evaluate the bearing capacity compensation effect, and comparing it with the case where rock mass stress redistribution is not taken into account, to ensure that no tensile stress occurs at the base, the longitudinal length of the base needs to be increased to 12m. At this point, the maximum compressive stress... t max=1678.1 kPa, which is much smaller than the allowable stress of the substrate. t The initial pressure is 2425 kPa, indicating significant design redundancy. However, this invention not only reduces the foundation size but also compensates for the load-bearing capacity, resulting in an improvement of (2236.2 - 1678.1) / 1678.1 × 100% = 33.3%. 9. Cross-sectional internal force analysis and reinforcement design Calculate the internal forces of each section of the foundation according to formulas (9) and (10), and design the reinforcement according to the "Code for Design of Concrete Structures".

[0033] Implementation effect

[0034] like Figure 3 As shown, the method of this invention quantitatively evaluated the compensation effect of rock mass constraint on foundation bearing capacity, reaching 33.3%. Under the same load conditions, the foundation size can be optimized by (12-10) / 12=16.7%, or the safety reserve of the structure's bearing capacity can be significantly improved under the same foundation size.

[0035] The present invention has been described in detail above through embodiments, but the content described is only an exemplary embodiment of the present invention and should not be considered as limiting the scope of the present invention. The scope of protection of the present invention is defined by the claims. Any technical solutions designed by those skilled in the art using the technical solutions described in the present invention, or similar technical solutions designed by those skilled in the art under the inspiration of the technical solutions of the present invention, within the substance and scope of protection of the present invention, to achieve the above-mentioned technical effects, or equivalent changes and improvements made to the scope of the application, should still fall within the patent protection scope of the present invention. It should be noted that, for clarity, descriptions of some components and processes that are not directly and obviously related to the scope of protection of the present invention but are known to those skilled in the art have been omitted in the description of the present invention.

Claims

1. A design method for compensating the bearing capacity of a rock-socketed foundation considering rock mass constraints, characterized in that, Includes the following steps: A. Establish a calculation model for the rock-embedded foundation and determine its consolidation boundary conditions in the rock strata; B. Calculate the triangularly distributed horizontal soil resistance generated by the soil layer segment during foundation rotation; C. Solve for the resistive moment of the horizontal soil layer about the center of the foundation; D. Decompose the base deformation into overall subsidence and rotation components; E. Determine the calculation formula for the location of the zero stress point of the base and establish a vertical pressure distribution model for the base; F. Establish a system of overall equilibrium equations and solve for the foundation rotation angle and the location of the zero-stress point through iterative calculations; G. Calculate the maximum compressive stress at the base and evaluate the bearing capacity compensation effect of the rock mass constraint; H. Perform cross-sectional internal force analysis and reinforcement design.

2. The method according to claim 1, characterized in that, In step A, the specific calculation model for the rock-embedded foundation is as follows: the foundation is considered as a rigid foundation embedded in the rock strata, and the portion of the foundation embedded in the rock strata is considered to be at the center of the basement. C The point is solidified at a depth of [missing information] from the ground. h Vertical force on the foundation at the top F y Horizontal force F x Bending moment M z Under the action, around C The point rotates.

3. The method according to claim 2, characterized in that, In step B, the horizontal soil resistance of the foundation T x The calculation formula is as follows: ； In the formula, t It is based on a force perpendicular to the horizontal. F x Length in the direction, in meters; m It is the soil foundation ratio coefficient, with units of kPa / m. 2 ; θ It is the basic winding C The vertical rotation angle of a point, measured in rad.

4. The method according to claim 3, characterized in that, In step C, the horizontal soil resistance relative to the center of the base... C Point resistance torque M 1. Calculate using the following formula: 。 5. The method according to claim 4, characterized in that, In step D, the distance from the centroid of the base is x Vertical stress at the point τ y Calculate using the following formula: τ y = C 0( d + θx )； In the formula, C 0 is the vertical foundation coefficient of the basement rock mass, with units of kPa / m; d It represents the overall subsidence displacement of the foundation, in meters (m). d + θx Used to represent base deformation.

6. The method according to claim 5, characterized in that, In step E, let τ y =0, solve for the location of the zero stress point. x 0=- d / θ ; Establish a vertical pressure distribution model for the base: the vertical pressure on the base relative to the center of the base. C resistance torque M 2. The calculation formula is as follows: ； In the formula, q It is based on horizontal force F x The length in the direction, in meters.

7. The method according to claim 6, characterized in that, In step F, at the solidification point C Establish a system of equilibrium equations at the point: ； In the formula, T p It is the concentrated horizontal resistance generated at the substrate embedding point. T y The resultant vertical reaction force at the base is expressed in kN. The basic rotation angle is obtained by solving the equilibrium equations using an iterative method. θ and the location of the zero stress point x 0.

8. The method according to claim 7, characterized in that, Resultant vertical reaction force of the base T y By analyzing the effective pressure zone τ y The integral yields: 。 9. The method according to claim 8, characterized in that, In step G, the maximum compressive stress of the base τ max Calculate using the following formula: ； In the formula, A 0 represents the area of ​​the base, measured in m². 2 ; The bearing capacity compensation effect is quantitatively evaluated by comparing the maximum compressive stress at the base under two scenarios: one that takes into account the rock mass stress redistribution and the other that does not.

10. The method according to claim 9, characterized in that, In step H, the base depth y Bending moment at section M y and horizontal stress V x Calculate using the following formula: 。

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