Variable cross-section group anchor horizontal bearing capacity design method considering anchor rod exerting coefficient

Abstract

The invention discloses a variable cross-section group anchor horizontal bearing capacity design method considering an anchor rod exerting coefficient. The group anchor foundation horizontal bearing capacity is the sum of anchor rod group horizontal resistance and bearing platform stand column horizontal resistance. Assuming a foundation soil horizontal resistance distribution function f (x) in a horizontal influence depth range; according to the foundation soil horizontal resistance distribution function f (x), calculating the ultimate horizontal bearing capacity # imgabs0 # of the bearing platform stand column; the variable cross-section anchor rod is regarded as a socketed pile, and the ultimate horizontal bearing capacity # imgabs1 # of a variable cross-section single anchor is calculated through an m method; calculating a horizontal bearing capacity exerting coefficient zeta of the anchor rod according to the buried depth of the bearing platform; according to the method, the effect of the horizontal resistance of the anchor rod is considered, the horizontal load distribution proportion of the bearing platform stand column and the anchor rod is quantified, and the problem that a traditional design method is too conservative is solved. According to the method, redundant design can be reduced, the structure economy is optimized, the engineering cost is reduced, and the method has remarkable engineering significance on environmental protection, water and soil conservation and terrain condition adaptation.

Description

Technical Field

[0001] The present invention relates to the technical field of transmission line foundation design, and specifically refers to a design method for the horizontal bearing capacity of a variable-section group anchor considering the anchor rod utilization coefficient. Background Art

[0002] Rock anchor rod foundations can make full use of the anti-pulling bearing capacity of rock foundations, have a high degree of construction mechanization, small construction equipment volume, and little environmental damage. They are a "resource-saving and environment-friendly" foundation type and have been favored in the selection of overhead transmission line foundations in recent years.

[0003] However, transmission lines have the characteristics of a large number of points and wide areas. Transmission lines inevitably pass through areas with steep terrain and thick overburden layers. In the traditional anchor rod foundation design process, only the horizontal resistance of the pile cap column is considered. When the overburden layer is thick, the soil resistance on the side of the pile cap is not enough to resist the horizontal external force, resulting in the need for rock embedding treatment of the anchor rod foundation pile cap to meet the requirements of horizontal bearing capacity. The depth and excavation volume of the pile cap increase significantly, making its environmental protection advantages no longer exist and restricting the application of anchor rod foundations in areas with thick overburden layers.

[0004] To solve the above problems, engineering and technical personnel have proposed a solution for a new type of variable-section anchor rod. The variable-section anchor rod foundation increases the diameter of the anchor rod section in the upper overburden layer to improve the horizontal resistance of the anchor rod and jointly resist the horizontal load with the pile cap, thereby canceling the requirement for rock embedding of the pile cap, reducing the buried depth and excavation volume of the pile cap, and can be used in geological conditions with an overburden thickness of 3 - 5m, greatly expanding the application range of anchor rod foundations.

[0005] However, there is little research on the calculation method of the horizontal bearing capacity of variable-section anchor rod foundations at present. The existing calculation and evaluation methods mainly simply add the horizontal resistance of the variable-section anchor rod and the horizontal resistance of the pile cap column. This method overestimates the contribution of the variable-section anchor rod to the horizontal resistance, making the foundation design unsafe. It is necessary to propose a more accurate and reliable design method for variable-section group anchor foundations. Summary of the Invention

[0006] In view of the deficiencies of the prior art, the present invention proposes a design method for the horizontal bearing capacity of a variable-section group anchor considering the anchor rod utilization coefficient. The present invention considers the contributions of the pile cap and the anchor rod to the horizontal bearing capacity and analyzes the synergistic effect between the pile cap and the anchor rod for the first time, with good calculation accuracy and practicability.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows: S1) The design method for the horizontal bearing capacity of a variable-section group anchor considering the anchor rod utilization coefficient consists of two parts: the horizontal bearing capacity of the foundation pile cap column and the horizontal bearing capacity of the variable-section group anchor. The calculation formula is as follows: ; In the formula: represents the ultimate horizontal bearing capacity of the group anchor foundation (kN); represents the ultimate horizontal bearing capacity of the single anchor with variable cross-section (kN); represents the ultimate horizontal bearing capacity of the pile cap column (kN); ζ represents the coefficient of the horizontal bearing capacity of the anchor rod, which is related to the buried depth of the pile cap; n represents the number of anchor rods.

[0008] S2) When calculating the ultimate horizontal bearing capacity of the single anchor with variable cross-section, only consider the contribution of the variable cross-section section of the anchor rod to the horizontal bearing capacity, and regard the anchor rod in the variable cross-section section as a rock-socketed pile, and use the m method to calculate its ultimate horizontal bearing capacity. The calculation method is as follows: ; In the formula: represents the ultimate horizontal bearing capacity of the single anchor with variable cross-section (kN); represents the characteristic value of the horizontal bearing capacity of the single anchor with variable cross-section (kN); γ represents the horizontal deformation coefficient of the anchor rod in the variable cross-section section; EI represents the flexural rigidity of the anchor rod in the variable cross-section section; represents the elastic modulus of concrete; represents the moment of inertia of the anchor rod section, including the moment of inertia of the anchor reinforcement and the grouting body; represents the allowable displacement of the top of the anchor rod (m). For the anchor rod foundation with variable cross-section, take 6 mm; represents the horizontal displacement coefficient of the top of the anchor rod, which can be determined by referring to Article 5.7.2 of the "Code for Building Pile Foundations" (JGJ94-2008), that is, assuming that the restraint at the top of the anchor rod is fixed, and the buried depth h takes the length of the variable cross-section section of the anchor rod; m represents the proportional coefficient of the horizontal soil resistance coefficient of the anchor rod side, which can be determined by referring to Article 5.7.5 of the "Technical Code for Building Pile Foundations" (JGJ94-2008); represents the calculated width of the anchor rod (m), which is obtained by calculating the diameter of the anchor rod; represents the diameter of the anchor rod (m).

[0009] S3) The calculation method of the ultimate horizontal bearing capacity of the pile cap column is as follows: ; In the formula: Indicates the horizontal ultimate bearing capacity of the pedestal column (kN); Indicates the buried depth of the foundation (m); f(x) It represents the theoretical distribution function of the horizontal resistance of the foundation soil on the side of the cap column; w Indicates the width of the platform or column (m); dx Represents differential.

[0010] S4) The theoretical distribution function of the horizontal resistance of the foundation soil on the side of the foundation column is as follows: ; Where: f(x) It represents the theoretical distribution function of the horizontal resistance of the foundation soil on the side of the cap column; It represents the saturated undrained shear strength of foundation soil (kPa); Indicates the thickness of the foundation soil affected by the horizontal force on the side of the cap column (m); Indicates the buried depth of the foundation (m); x Indicates the distance from the calculation point to the ground (m).

[0011] S5) The values of the anchor horizontal bearing capacity coefficient are shown in Table 1: Table 1 Anchor bolt horizontal bearing capacity utilization coefficient

[0012] The beneficial effects of the present invention are: 1. The proposed method considers the horizontal resistance of anchor bolts and quantifies the distribution ratio of horizontal load between the cap columns and anchor bolts, addressing the overly conservative nature of traditional design methods. This method reduces redundant design, optimizes structural economics, and reduces project costs, with significant engineering significance for environmental protection, soil and water conservation, and adaptation to terrain conditions.

[0013] 2. The method of the present invention supports the design of variable-section anchor foundations, promotes the engineering application of new anchor foundations, and can expand the application scenarios of anchor foundations under complex terrain and soil conditions.

[0014] 3. The present invention proposes a method for designing the horizontal bearing capacity of a variable-section group anchor that takes into account the anchor rod utilization coefficient. This method can relatively accurately evaluate and determine the horizontal bearing capacity of the group anchor foundation. Compared with the on-site actual test, the total error does not exceed 8%, and it has excellent calculation accuracy and consistency. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is the flow chart of the calculation method of the present invention.

[0016] Figure 2 This is the schematic diagram of the variable cross-section group anchor foundation structure of the present invention.

[0017] Figure 3 This is the cross-sectional view of the variable cross-section group anchor foundation of the present invention; Figure 4 This is the finite element simulation model diagram of the variable cross-section group anchor foundation.

[0018] Figure 5 This is the finite element simulation result diagram of the load distribution of the variable cross-section group anchor foundation under different embedment depths of the bearing platform.

[0019] Figure 6 This is the schematic diagram of the horizontal stress distribution of the foundation soil on the side of the bearing platform in the variable cross-section anchor rod foundation of the present invention.

[0020] Wherein: the bearing platform column 1; the variable cross-section section 2 of the anchor rod; the equal cross-section section 3 of the anchor rod; the ground line 4; the rock surface line 5. Specific implementation manner

[0021] In order to make the purpose, technical solution and advantages of the invention clearer, the present invention will be further described below with reference to the accompanying drawings.

[0022] The present invention considers the contributions of the bearing platform and the anchor rod to the horizontal bearing capacity, analyzes the cooperative effect between the bearing platform and the anchor rod, and has excellent calculation accuracy and practicability. In the present invention, the horizontal resistance of the bearing platform is fully exerted, and the anchor rod exerts the horizontal resistance at a certain ratio according to the embedment depth.

[0023] The novel variable cross-section group anchor foundation of the present invention is as Figure 2 shown. The novel variable cross-section anchor rod foundation includes three parts: the bearing platform column 1, the variable cross-section section 2 of the anchor rod, and the equal cross-section section 3 of the anchor rod. The diameter of the variable cross-section section of the anchor rod is larger than that of the equal cross-section section. The equal cross-section anchor rod is placed in the rock stratum, most of the variable cross-section anchor rods are placed in the overburden layer, and a small part is treated by rock embedding. Most of the bearing platform columns are placed in the overburden layer, and only the top of the bearing platform column protrudes above the ground line 4.

[0024] A design method for the horizontal bearing capacity of a variable cross-section group anchor considering the anchor rod utilization factor according to the present invention includes the following steps: S1) As Figure 2 shown, the horizontal bearing capacity of the variable cross-section group anchor considering the anchor rod utilization factor considers two components: namely, the horizontal resistance of the foundation soil on the side of the bearing platform column and the horizontal resistance of the anchor rod group. The calculation formula is as follows: ; In the formula: — Ultimate horizontal bearing capacity of group anchor foundation (kN); — Ultimate horizontal bearing capacity of variable-section single anchor (kN); — Ultimate horizontal bearing capacity of pile cap column (kN); ζ—Coefficient of horizontal bearing capacity of anchor rod, related to the buried depth of pile cap; n — Number of anchor rods.

[0025] S2) When calculating the ultimate horizontal bearing capacity of the variable-section single anchor, only consider the contribution of the variable-section section of the anchor rod to the horizontal bearing capacity, and regard the variable-section section of the anchor rod as the end rock-embedded section, and use the m method to calculate its ultimate horizontal bearing capacity. The calculation method is as follows: ; Where: Represents the ultimate horizontal bearing capacity of the variable-section single anchor (kN); Represents the characteristic value of the horizontal bearing capacity of the variable-section single anchor (kN); γ Represents the horizontal deformation coefficient of the variable-section section of the anchor rod; EI Represents the flexural rigidity of the variable-section section of the anchor rod; Represents the elastic modulus of concrete; Represents the moment of inertia of the anchor rod section, including the moment of inertia of the anchor bars and the grouting body; Represents the allowable displacement at the top of the anchor rod (m). For the variable-section anchor rod foundation, take 6 mm; Represents the horizontal displacement coefficient at the top of the anchor rod, which can be determined by referring to Article 5.7.2 of the "Code for Building Pile Foundations" (JGJ94-2008), that is, assuming that the restraint at the top of the anchor rod is fixed, and the buried depth h takes the length of the variable-section section of the anchor rod; m Represents the proportional coefficient of the horizontal soil resistance coefficient on the side of the anchor rod, which can be determined by referring to Article 5.7.5 of the "Technical Code for Building Pile Foundations" (JGJ94-2008); Represents the calculated width of the anchor rod (m), calculated from the anchor rod diameter Calculated; Represents the diameter of the anchor rod (m).

[0026] S3) The calculation method of the ultimate horizontal bearing capacity of the pile cap column is as follows: ; Where: Denotes the horizontal ultimate bearing capacity of the pile cap column (kN); Denotes the embedment depth of the pile cap (m); f(x) Denotes the theoretical distribution function of the horizontal soil resistance on the side of the pile cap column; w Denotes the width of the pile cap or column (m); dx Denotes differentiation.

[0027] S4) To determine the theoretical distribution function of the horizontal soil resistance on the side of the pile cap column, a finite element simulation model of a variable-section group anchor foundation with different pile cap embedment depths was established, as Figure 4 shown.

[0028] The calculation results are as Figure 5 shown. As the embedment depth of the pile cap increases from 1 m to 2 m, the horizontal load borne by the pile cap column increases significantly. When the embedment depth of the pile cap continues to increase to 3 m, the horizontal load borne by the pile cap column remains almost unchanged. It can be considered that when the pile cap column is under the action of a horizontal load, its resistance is only resisted by a certain thickness of soil layer. This thickness is defined as the influence thickness of the horizontal soil force on the side of the pile cap column. For the cohesive soil in this example, the influence thickness is taken as 2 m.

[0029] The ultimate horizontal bearing capacity of the pile cap column is calculated by the ultimate subgrade reaction method. The assumed theoretical distribution function of the horizontal soil resistance f(x) is as Figure 6 shown: within the influence thickness of the horizontal soil resistance on the side of the pile cap column, that is, within a depth of 2 m, the horizontal soil resistance is uniformly distributed, and the value is ; for the part with a depth exceeding 2 m, the horizontal resistance linearly decreases from to 0 at the bottom of the anchor rod. The theoretical distribution function of the horizontal soil resistance on the side of the pile cap column is as follows: ; In the formula: f(x) Denotes the theoretical distribution function of the horizontal soil resistance on the side of the pile cap column; Denotes the saturated undrained shear strength of the soil (kPa), which is determined according to the geotechnical survey report of the specific tower location; Denotes the influence thickness of the horizontal soil force on the side of the pile cap column (m), which can be determined by finite element simulation or in-situ test research. For silty clay, it can be taken as 2 m; Denotes the embedment depth of the pile cap (m); xIt represents the vertical distance from the calculation point to the ground (m), and the calculation point is a point between the bottom surface of the bearing platform and the ground.

[0030] S5) When the variable-section group anchor foundation bears horizontal loads, the proportion of the load borne by the anchor rods is related to the embedment depth of the bearing platform. To determine the coefficient ζ of the horizontal bearing capacity of the anchor rods, a finite element simulation model of the variable-section group anchor foundation with different embedment depths of the bearing platform is established, as Figure 4 shown.

[0031] The calculation results are as Figure 5 shown. As the embedment depth of the bearing platform increases from 1 m to 3 m, the coefficient ζ of the horizontal bearing capacity of the anchor rods linearly decreases from 96.7% to 23.5%. Therefore, the coefficient ζ of the horizontal bearing capacity of the anchor rods can be conservatively taken as shown in Table 1: Table 1 Coefficient of the horizontal bearing capacity of the anchor rods

[0032] In the present invention, the coefficient ζ of the horizontal bearing capacity of the anchor rods is obtained by interpolation according to the table.

[0033] Taking a certain UHV transmission line project as an example, the overburden is silty clay, the thickness of the overburden is 3 m, 4 m, and 5 m, the corresponding embedment depths of the bearing platform are 1 m, 2 m, and 3 m, the lengths of the variable-section anchor rods are all 2.25 m, of which 2 m is placed in the overburden and 0.25 m is embedded in the rock; the rock layer is moderately weathered sandy conglomerate.

[0034] The anchor bars of the anchor foundation are made of HRB400 deformed steel bars with a diameter of 36 mm, and the elastic modulus is 200 GPa; the grouting body uses high-performance grouting material, and the elastic modulus and Poisson's ratio are 40 GPa and 0.2 respectively; the diameter of the variable-section part of the anchor rod is 250 mm, the diameter of the equal-section part of the anchor rod is 110 mm, and the spacing of the anchor rods is 750 mm. The width of the bearing platform is 2.1 m.

[0035] Using the design method for the horizontal bearing capacity of the variable-section group anchor considering the coefficient of the anchor rod's performance proposed by the present invention to predict the horizontal bearing capacity of a single variable-section anchor rod and the group anchor foundation, and comparing and analyzing the calculation results with the results of the full-scale test and finite element analysis to verify the accuracy of the design method. The results are shown in Tables 2 and 3: Table 2 Comparison of the calculation results of the ultimate horizontal bearing capacity of the variable-section single anchor (unit: kN)

[0036] In Table 2 above: P Lu , P test , P FEM respectively represent the ultimate horizontal bearing capacity of the variable-section single anchor obtained by using the theoretical method, full-scale test, and finite element results, and the unit is kN.

[0037] Table 3 Comparison of Calculation Results of Horizontal Bearing Capacity of Variable Cross-Section Group Anchor Foundation (Unit: kN)

[0038] In Table 3 above: Fy1 and Fy2 respectively represent the finite element calculation results of the horizontal resistance provided by the anchor rod and the pile cap column under the action of horizontal load, with the unit of kN; Fl1 and Fl2 respectively represent the theoretical calculation results of the horizontal resistance provided by the anchor rod and the pile cap column under the action of horizontal load, with the unit of kN.

[0039] As can be seen from Table 2, under the above geological conditions, by using the design method provided by the present invention, the difference between the calculated ultimate horizontal bearing capacity of the variable cross-section single anchor and the test and finite element results is less than 5%, showing good agreement.

[0040] As can be seen from Table 3, under the above geological conditions, by using the design method provided by the present invention, the difference between the calculated ultimate horizontal bearing capacity of the variable cross-section group anchor and the finite element result is less than 8%, showing good agreement.

[0041] In summary, the novel design method for the horizontal bearing capacity of the variable cross-section group anchor proposed by the present invention has clear mechanical concepts, quantifies for the first time the proportion of the horizontal load distribution between the pile cap column and the anchor rod, has a simple formula, and has good calculation accuracy.

[0042] Finally, it should be noted that the content not described in detail in this specification belongs to the prior art well-known to those skilled in the art. The above are only the preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A design method for the horizontal bearing capacity of variable-section group anchors considering the bolt utilization coefficient, characterized in that The method includes: Calculating the ultimate horizontal bearing capacity of the pile cap column and the horizontal resistance of the anchor rod group, the horizontal ultimate bearing capacity of the variable cross-section group anchor foundation is the ultimate horizontal bearing capacity of the pile cap column plus the horizontal resistance of the anchor rod group. The horizontal ultimate bearing capacity of the group anchor foundation The calculation formula is as follows: ； Wherein: represents the horizontal ultimate bearing capacity of the group anchor foundation; Indicates the horizontal ultimate bearing capacity of a single anchor with variable cross-section; Indicates the ultimate horizontal bearing capacity of the pile cap column; ζ represents the coefficient of the horizontal bearing capacity of the anchor rod; n Indicates the number of anchor bolts.

2. A design method for the horizontal bearing capacity of a variable cross-section group anchor considering the bolt utilization coefficient according to claim 1, characterized in that The horizontal ultimate bearing capacity of the variable cross-section single anchor The calculation formula is as follows: ； In the formula: Denote the horizontal ultimate bearing capacity of a single anchor with variable cross-section; Denote the characteristic value of the horizontal bearing capacity of a single anchor with variable cross-section; γ represents the horizontal deformation coefficient of the variable-section anchor rod; EI represents Flexural stiffness of bolts in variable cross-section section Indicates the allowable displacement at the top of the bolt Indicates the horizontal displacement coefficient of the bolt top; m represents Proportionality coefficient of horizontal soil resistance coefficient on the side of anchor rod; Represents the calculated width of the anchor bolt; Denotes the diameter of the anchor rod.

3. A design method for the horizontal bearing capacity of a variable cross-section group anchor considering the bolt utilization coefficient according to claim 1, characterized in that The ultimate horizontal bearing capacity of the pile cap column The calculation formula is as follows: ； In the formula: Denote the horizontal ultimate bearing capacity of the pile cap column; Indicates the embedment depth of the pile cap; f(x) Denote the theoretical distribution function of the horizontal resistance of the foundation soil on the side of the pile cap column; w Represents the width of the pile cap or column; dx Indicates differentiation.

4. A design method for the horizontal bearing capacity of a group of anchors considering the utilization coefficient of variable-section anchor rods according to claim 3, characterized in that The theoretical distribution function of the horizontal resistance of the foundation soil on the side of the pile cap column is as follows: f(x) function: ； In the formula: f(x) represents Theoretical distribution function of horizontal resistance of foundation soil on the side of the pile cap column represents the saturated undrained shear strength of the foundation soil; Indicates the influence thickness of the horizontal force of the foundation soil on the side of the bearing platform column; Indicates the embedment depth of the pile cap; x Indicates the distance from the calculation point to the ground.

5. A design method for the horizontal bearing capacity of a variable-section group anchor considering the bolt utilization coefficient according to claim 1, characterized in that The determination of the coefficient of the horizontal bearing capacity of the anchor rod includes: establishing a finite element simulation model of a variable-section group anchor foundation with different embedment depths of the bearing platform, determining the coefficient of the horizontal bearing capacity of the anchor rod. When the embedment depth of the bearing platform is less than or equal to 1m, ζ takes 0.95; when the embedment depth of the bearing platform is 2m, ζ takes 0.55; when the embedment depth of the bearing platform is 3m, ζ takes 0.25; when the embedment depth of the bearing platform is other values, the coefficient of the horizontal bearing capacity of the anchor rod is obtained by interpolation.

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