A design method for horizontal bearing capacity of variable-section anchor groups considering anchor rod utilization coefficient

Abstract

The present invention discloses a design method for the horizontal bearing capacity of a variable cross-section anchor group considering the anchor rod utilization coefficient. The horizontal bearing capacity of the anchor group foundation is the sum of the horizontal resistance of the anchor rod group and the horizontal resistance of the cap column. It is assumed that the horizontal resistance distribution function of the foundation soil within the horizontal influence depth range is f(x) ; According to the horizontal resistance distribution function of foundation soil f(x) Calculate the ultimate horizontal bearing capacity of the cap column; treat the variable-section anchor as a rock-socketed pile and use the m-method to calculate the ultimate horizontal bearing capacity of a single variable-section anchor; calculate the anchor's horizontal bearing capacity utilization factor ζ based on the cap's burial depth. This method considers the effect of the anchor's horizontal resistance and quantifies the horizontal load distribution ratio between the cap column and the anchor, 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.

Description

Technical Field

[0001] The present invention relates to the technical field of power transmission line foundation design, and in particular to a method for designing the horizontal bearing capacity of a variable-section group anchor taking into account an anchor rod utilization coefficient. Background Art

[0002] Rock anchor foundation is a "resource-saving and environmentally friendly" foundation type because it can fully utilize the pull-out bearing capacity of the rock foundation, has a high degree of construction mechanization, small construction equipment, and little damage to the environment. In recent years, it has been highly favored in the selection of overhead transmission line foundations.

[0003] However, transmission lines are characterized by being numerous and widespread, and inevitably pass through areas with steep terrain and thick overburden. Traditional anchor foundations only consider the horizontal resistance of the pedestal columns during the design process. When the overburden is thick, the side soil resistance of the pedestal is insufficient to resist the horizontal external force, resulting in the anchor foundation pedestal needing to be rock-embedded to meet the horizontal bearing capacity requirements. The pedestal depth and excavation volume increase significantly, making its environmental advantages disappear, limiting the application of anchor foundations in areas with thick overburden.

[0004] To solve the above problems, engineering technicians proposed a new type of variable-section anchor solution. The variable-section anchor foundation increases the diameter of the anchor section in the upper covering layer, improves the horizontal resistance of the anchor, and jointly resists the horizontal load with the pedestal, thereby eliminating the rock embedding requirement of the pedestal, reducing the burial depth and excavation volume of the pedestal, and can be used under geological conditions with a covering layer thickness of 3 to 5 meters, greatly expanding the application range of the anchor foundation.

[0005] However, there is little research on the calculation method of the horizontal bearing capacity of variable-section anchor foundations. The existing calculation and evaluation methods mainly simply add the horizontal resistance of the variable-section anchor and the horizontal resistance of the pedestal column. This method overestimates the contribution of the variable-section anchor 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 response to the shortcomings of the existing technology, the present invention proposes a design method for the horizontal bearing capacity of variable-section group anchors that takes into account the anchor rod utilization coefficient. The present invention considers the contribution of the base and the anchor rod to the horizontal bearing capacity, and analyzes the synergistic effect of the base and the anchor rod for the first time, with good calculation accuracy and practicality.

[0007] To achieve the above objectives, the technical solution of the present invention is:

[0008] The design method for the horizontal bearing capacity of a variable-section anchor group considering the anchor rod utilization coefficient described in S1) consists of two parts: the horizontal bearing capacity of the foundation pile column and the horizontal bearing capacity of the variable-section anchor group. The calculation formula is as follows:

[0009] ;

[0010] Where: represents the horizontal ultimate bearing capacity of the anchor group foundation (kN);

[0011] represents the horizontal ultimate bearing capacity of a single anchor with variable cross-section (kN);

[0012] Indicates the ultimate horizontal bearing capacity of the pedestal column (kN);

[0013] ζ represents the horizontal bearing capacity coefficient of the anchor rod, which is related to the buried depth of the cap;

[0014] n Indicates the number of anchor rods.

[0015] S2) When calculating the horizontal ultimate bearing capacity of the variable cross-section single anchor, only the contribution of the variable cross-section section of the anchor to the horizontal bearing capacity is considered, and the variable cross-section anchor is regarded as a rock-socketed pile. The horizontal ultimate bearing capacity is calculated using the m method. The calculation method is as follows:

[0016] ;

[0017] Where:

[0018] represents the horizontal ultimate bearing capacity of a variable cross-section single anchor (kN);

[0019] represents the characteristic value of the horizontal bearing capacity of a single anchor with variable cross-section (kN);

[0020] γ represents the horizontal deformation coefficient of the variable cross-section anchor;

[0021] EI Indicates the bending stiffness of the variable cross-section anchor;

[0022] represents the elastic modulus of concrete;

[0023] It represents the moment of inertia of the anchor section, including the moment of inertia of the anchor bar and the grouting body;

[0024] Indicates the allowable displacement of the anchor bolt top (m). For variable-section anchor bolt foundations, it is 6mm.

[0025] represents the horizontal displacement coefficient of the anchor bolt top, which can be determined by referring to Article 5.7.2 of the Code for Building Pile Foundations (JGJ94-2008), i.e., assuming that the top of the anchor bolt is constrained to be fixed, and the embedment depth h is the length of the anchor bolt variable cross-section section;

[0026] mThe proportional coefficient representing the horizontal resistance coefficient of the soil on the side of the anchor can be determined by referring to Article 5.7.5 of the Technical Specifications for Building Pile Foundations (JGJ94-2008);

[0027] Indicates the calculated width of the anchor (m), which is calculated from the anchor diameter;

[0028] Indicates the diameter of the anchor rod (m).

[0029] S3) The calculation method of the ultimate horizontal bearing capacity of the pedestal column is as follows:

[0030] ;

[0031] Where:

[0032] Indicates the ultimate horizontal bearing capacity of the pedestal column (kN);

[0033] Indicates the buried depth of the foundation (m);

[0034] f(x) It represents the theoretical distribution function of the horizontal resistance of the foundation soil on the side of the cap column;

[0035] w Indicates the width of the platform or column (m);

[0036] dx Represents differential.

[0037] S4) The theoretical distribution function of the horizontal resistance of the foundation soil on the side of the foundation column is as follows:

[0038] ;

[0039] Where:

[0040] f(x) It represents the theoretical distribution function of the horizontal resistance of the foundation soil on the side of the cap column;

[0041] It represents the saturated undrained shear strength of foundation soil (kPa);

[0042] Indicates the thickness of the foundation soil affected by the horizontal force on the side of the cap column (m);

[0043] Indicates the buried depth of the foundation (m);

[0044] x Indicates the distance from the calculation point to the ground (m).

[0045] S5) The values ​​of the anchor horizontal bearing capacity coefficient are shown in Table 1:

[0046] Table 1 Anchor bolt horizontal bearing capacity utilization coefficient

[0047]

[0048] The beneficial effects of the present invention are:

[0049] 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.

[0050] 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.

[0051] 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

[0052] Figure 1 This is a flow chart of the calculation method of the present invention.

[0053] Figure 2 This is a schematic diagram of the variable-section anchor group foundation structure of the present invention.

[0054] Figure 3 This is a cross-sectional view of the variable-section anchor group foundation of the present invention;

[0055] Figure 4 This is the finite element simulation model diagram of the variable-section group anchor foundation.

[0056] Figure 5 The finite element simulation results of the load distribution of the variable-section group anchor foundation under different foundation burial depths are shown.

[0057] Figure 6 This is a schematic diagram of the horizontal stress distribution in the foundation soil on the side of the cap in the variable-section anchor foundation of the present invention.

[0058] Among them: foundation column 1; anchor rod variable section 2; anchor rod constant section 3; ground line 4; rock surface line 5. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solutions and advantages of the invention clearer, the present invention is further described below with reference to the accompanying drawings.

[0060] The present invention takes into account the contribution of the cap and anchor rods to the horizontal bearing capacity, analyzes the synergistic effect of the cap and anchor rods, and has excellent calculation accuracy and practicality. In the present invention, the cap fully exerts the horizontal resistance, and the anchor rods exert the horizontal resistance in a certain proportion according to the burial depth.

[0061] The novel variable cross-section anchor group foundation of the present invention is as follows Figure 2 As shown in the figure, the new variable-section anchor foundation consists of three parts: the cap column 1, the variable-section anchor section 2, and the constant-section anchor section 3. The diameter of the variable-section anchor section is larger than that of the constant-section anchor section. The constant-section anchor section is placed in the rock stratum, while the variable-section anchor section is mostly placed in the overburden, with a small portion embedded in the rock. The cap column is mostly placed in the overburden, with only the top of the cap column protruding above the ground line 4.

[0062] The present invention provides a method for designing the horizontal bearing capacity of a variable-section group anchor taking into account the anchor rod utilization coefficient, comprising the following steps:

[0063] S1) Figure 2 As shown in the figure, the horizontal bearing capacity of the variable cross-section anchor group considering the anchor rod utilization coefficient takes into account two components: the horizontal resistance of the foundation soil on the side of the cap column and the horizontal resistance of the anchor rod group. The calculation formula is as follows:

[0064] ;

[0065] Where: —Horizontal ultimate bearing capacity of anchor group foundation (kN);

[0066] —Horizontal ultimate bearing capacity of a single anchor with variable cross-section (kN);

[0067] —Ultimate horizontal bearing capacity of the pedestal column (kN);

[0068] ζ—Anchor bolt horizontal bearing capacity utilization coefficient, which is related to the buried depth of the cap;

[0069] n —Number of anchor rods.

[0070] S2) When calculating the horizontal ultimate bearing capacity of the variable cross-section single anchor, only the contribution of the variable cross-section section of the anchor to the horizontal bearing capacity is considered, and the variable cross-section anchor is regarded as the end rock-embedded section. The horizontal ultimate bearing capacity is calculated using the m method. The calculation method is as follows:

[0071] ;

[0072] Where:

[0073] represents the horizontal ultimate bearing capacity of a variable cross-section single anchor (kN);

[0074] represents the characteristic value of the horizontal bearing capacity of a single anchor with variable cross-section (kN);

[0075] γ represents the horizontal deformation coefficient of the variable cross-section anchor;

[0076] EI Indicates the bending stiffness of the variable cross-section anchor;

[0077] represents the elastic modulus of concrete;

[0078] It represents the moment of inertia of the anchor section, including the moment of inertia of the anchor bar and the grouting body;

[0079] Indicates the allowable displacement of the anchor bolt top (m). For variable-section anchor bolt foundations, it is 6mm.

[0080] represents the horizontal displacement coefficient of the anchor bolt top, which can be determined by referring to Article 5.7.2 of the Code for Building Pile Foundations (JGJ94-2008), i.e., assuming that the top of the anchor bolt is constrained to be fixed, and the embedment depth h is the length of the anchor bolt variable cross-section section;

[0081] m The proportional coefficient representing the horizontal resistance coefficient of the soil on the side of the anchor can be determined by referring to Article 5.7.5 of the Technical Specifications for Building Pile Foundations (JGJ94-2008);

[0082] Indicates the calculated width of the anchor (m), which is determined by the anchor diameter Calculated;

[0083] Indicates the diameter of the anchor rod (m).

[0084] S3) The calculation method of the ultimate horizontal bearing capacity of the pedestal column is as follows:

[0085] ;

[0086] Where:

[0087] Indicates the ultimate horizontal bearing capacity of the pedestal column (kN);

[0088] Indicates the buried depth of the foundation (m);

[0089] f(x) It represents the theoretical distribution function of the horizontal resistance of the foundation soil on the side of the cap column;

[0090] w Indicates the width of the platform or column (m);

[0091] dx Represents differential.

[0092] S4) To determine the theoretical distribution function of the horizontal resistance of the foundation soil on the side of the cap column, a finite element simulation model of a variable cross-section group anchor foundation with different cap depths is established, such as Figure 4 shown.

[0093] The calculation results are as follows Figure 5 As shown in the figure, as the cap depth increases from 1m to 2m, the horizontal load borne by the cap columns increases significantly. When the cap depth continues to increase to 3m, the horizontal load borne by the cap columns remains almost unchanged. It can be assumed that when the cap columns are subjected to horizontal loads, their resistance is only resisted by a certain thickness of soil layer. This thickness is defined as the impact thickness of the horizontal force of the foundation soil on the side of the cap column. For the clay soil in this example, the impact thickness is 2m.

[0094] The ultimate horizontal bearing capacity of the pedestal column is calculated using the ultimate foundation reaction method, assuming that the horizontal resistance distribution function of the foundation soil is f(x) like Figure 6 As shown: In the horizontal influence thickness of the foundation soil on the side of the pedestal column, that is, within the range of 2m of burial depth, the horizontal resistance of the foundation soil is evenly distributed, and the value is For parts buried deeper than 2m, the horizontal resistance is It decreases linearly and drops to 0 at the bottom of the anchor rod. The theoretical distribution function of the horizontal resistance of the foundation soil on the side of the cap column is shown as follows:

[0095] ;

[0096] Where:

[0097] f(x) It represents the theoretical distribution function of the horizontal resistance of the foundation soil on the side of the cap column;

[0098] Indicates the saturated undrained shear strength of the foundation soil (kPa), determined based on the geotechnical survey report for the specific tower location;

[0099] The thickness of the foundation soil on the side of the cap column that is affected by the horizontal force (m) can be determined through finite element simulation or field test research. For silty clay, 2m can be used.

[0100] Indicates the buried depth of the foundation (m);

[0101] x Indicates the vertical distance (m) from the calculation point to the ground. The calculation point is a point between the bottom surface of the pedestal and the ground.

[0102] S5) When a variable-section anchor group foundation is subjected to horizontal loads, the proportion of the load borne by the anchor rods is related to the buried depth of the cap. In order to determine the anchor rod horizontal bearing capacity coefficient ζ, a finite element simulation model of a variable-section anchor group foundation with different cap buried depths was established, as shown in the following example: Figure 4 shown.

[0103] The calculation results are as follows Figure 5 As shown in Table 1, as the buried depth of the foundation increases from 1m to 3m, the horizontal bearing capacity utilization coefficient of the anchor rod decreases linearly from 96.7% to 23.5%. Therefore, the horizontal bearing capacity utilization coefficient of the anchor rod can be conservatively valued, as shown in Table 1:

[0104] Table 1 Anchor bolt horizontal bearing capacity utilization coefficient

[0105]

[0106] In the present invention, the anchor rod horizontal bearing capacity exertion coefficient ζ is obtained by interpolation according to a table.

[0107] Taking a certain UHV transmission line project as an example, the overburden is silty clay with thicknesses of 3m, 4m, and 5m. The corresponding pedestal burial depths are 1m, 2m, and 3m. The length of the variable-section anchor rods is 2.25m, of which 2m is placed in the overburden and 0.25m is embedded in the rock. The rock layer is moderately weathered sandy conglomerate.

[0108] The anchor bars for the foundation are 36mm diameter HRB400 rebar with an elastic modulus of 200GPa. The grouting material uses a high-performance grouting material with an elastic modulus of 40GPa and a Poisson's ratio of 0.2. The diameter of the anchor rods in the variable-section section is 250mm, and the diameter of the anchor rods in the uniform-section section is 110mm. The anchor rod spacing is 750mm. The platform width is 2.1m.

[0109] The horizontal bearing capacity design method of variable-section anchor groups that considers the anchor rod utilization coefficient proposed in this invention is used to predict the horizontal bearing capacity of a single variable-section anchor rod and an anchor group foundation. The calculated results are compared with the results of the real-type test and finite element analysis to verify the accuracy of the design method. The results are shown in Tables 2 and 3:

[0110] Table 2 Comparison of calculation results of ultimate horizontal bearing capacity of variable cross-section single anchor (unit: kN)

[0111]

[0112] In Table 2 above: P Lu 、P test 、P FEM They represent the ultimate horizontal bearing capacity of a variable-section single anchor obtained by theoretical calculation, real-type test, and finite element results, respectively, in KN.

[0113] Table 3 Comparison of calculation results of horizontal bearing capacity of variable-section anchor group foundation (unit: kN)

[0114]

[0115] In Table 3 above: Fy1 and Fy2 represent the finite element calculation results of the horizontal resistance provided by the anchor rods and the pedestal columns under the action of horizontal loads, respectively, and the unit is kN; Fl1 and Fl2 represent the theoretical calculation results of the horizontal resistance provided by the anchor rods and the pedestal columns under the action of horizontal loads, respectively, and the unit is kN.

[0116] As can be seen from Table 2, under the above geological conditions, the ultimate horizontal bearing capacity of the variable-section single anchor calculated by the design method provided by the present invention has a difference of less than 5% from the test and finite element results, which is in good agreement.

[0117] As shown in Table 3, under the above geological conditions, the ultimate horizontal bearing capacity of the variable-section group anchor calculated by the design method provided by the present invention differs from the finite element results by less than 8%, which is in good agreement.

[0118] In summary, the new variable-section group anchor horizontal bearing capacity design method proposed in the present invention has a clear mechanical concept, quantifies the horizontal load distribution ratio of the pedestal column and the anchor rod for the first time, has a simple formula, and has good calculation accuracy.

[0119] Finally, it should be noted that the contents not described in detail in this specification belong to the prior art known to professional and technical personnel in this field. The above description is only the preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments or to replace some of the technical features therein with equivalents. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included in the scope of protection of the present invention.

Claims

1. A method for designing the horizontal bearing capacity of a variable-section group anchor considering the anchor rod utilization coefficient, characterized in that: The method comprises: Calculate the ultimate horizontal bearing capacity of the pedestal column and horizontal resistance of anchor groups, horizontal ultimate bearing capacity of variable cross-section anchor group foundation The ultimate horizontal bearing capacity of the pedestal column The sum of the horizontal resistance of the anchor group and the horizontal ultimate bearing capacity of the anchor group foundation The calculation formula is: ； Where: represents the horizontal ultimate bearing capacity of the anchor group foundation; It represents the horizontal ultimate bearing capacity of a single anchor with variable cross-section; Indicates the ultimate horizontal bearing capacity of the pedestal column; ζ represents the horizontal bearing capacity coefficient of the anchor rod; n Indicates the number of anchor rods; The determination of the horizontal bearing capacity coefficient of the anchor rod includes: establishing a finite element simulation model of a variable-section group anchor foundation with different pedestal burial depths, and determining the horizontal bearing capacity coefficient of the anchor rod. When the pedestal burial depth is less than or equal to 1m, ζ is taken as 0.95; when the pedestal burial depth is 2m, ζ is taken as 0.55; when the pedestal burial depth is 3m, ζ is taken as 0.25; when the pedestal burial depth is other values, the horizontal bearing capacity coefficient of the anchor rod is obtained by interpolation.

2. The method for designing the horizontal bearing capacity of a variable cross-section anchor group considering the anchor rod utilization coefficient according to claim 1 is characterized in that: The horizontal ultimate bearing capacity of the variable cross-section single anchor The calculation formula is: ； Where: It represents the horizontal ultimate bearing capacity of a single anchor with variable cross-section; represents the characteristic value of horizontal bearing capacity of a single anchor with variable cross-section; γ represents the horizontal deformation coefficient of the variable cross-section anchor; EI means Bending stiffness of variable cross-section anchor bolt; Indicates the allowable displacement of the anchor top; It represents the horizontal displacement coefficient of the anchor top; m represents Proportional coefficient of horizontal resistance coefficient of soil on the side of anchor bolt; Indicates the calculated width of the anchor rod; Indicates the diameter of the anchor rod.

3. The method for designing the horizontal bearing capacity of a variable cross-section anchor group considering the anchor rod utilization coefficient according to claim 1 is characterized in that: The ultimate horizontal bearing capacity of the pedestal column The calculation formula is: ； Where: Indicates the ultimate horizontal bearing capacity of the pedestal column; Indicates the buried depth of the foundation; 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; dx Represents differential.

4. A method for designing the horizontal bearing capacity of a group anchor considering the utilization coefficient of variable cross-section anchor rods according to claim 3, characterized in that: The theoretical distribution function of horizontal resistance of foundation soil on the side of the pedestal column f(x) The number is: ； Where: f(x) represents Theoretical distribution function of horizontal resistance of foundation soil on the side of the cap column; It represents the saturated undrained shear strength of foundation soil; Indicates the thickness affected by the horizontal force of the foundation soil on the side of the cap column; Indicates the buried depth of the foundation; x Indicates the distance from the calculation point to the ground.

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