A design method for the bearing capacity of a variable cross-section group anchor foundation

Abstract

This invention discloses a design method for the compressive bearing capacity of a variable cross-section group anchor foundation, including calculating the characteristic value N of the compressive bearing capacity of a single variable cross-section anchor rod. a The variable cross-section anchor is considered as a reinforcement, based on the aforementioned N. a Calculate the characteristic value f of the composite bearing capacity of the anchor bolt and the foundation soil. spk ; Calculate the maximum compressive stress p on the bottom surface of the foundation. max Compare the characteristic values ​​f of the bearing capacity of composite foundations spk The maximum compressive stress p at the bottom surface of the foundation max If p max ≤f spk Then the design of the variable cross-section group anchor foundation is completed; if p max >f spk Then, methods such as adjusting the anchor bolt diameter, increasing the number of anchor bolts, or increasing the anchor bolt size are used to iterate repeatedly until p is reached. max ≤f spk The calculation stops when the time is right. This calculation method has a simple formula, can fully utilize the coupled bearing characteristics of the foundation and the anchor body, and has both calculation accuracy and safety margin, enabling a more accurate and reasonable assessment of the bearing capacity of the anchor foundation. Using this calculation method can optimize foundation dimensions, effectively reduce engineering costs, and has significant engineering implications for environmental protection and adaptation to terrain conditions.

Description

Technical Field

[0001] This invention relates to the field of power transmission line foundation design technology, specifically to a method for designing the bearing capacity of a variable cross-section group anchor foundation. Background Technology

[0002] Large-scale hydropower and wind power ultra-high-voltage transmission projects, along with their supporting transmission lines, are entering a peak construction period. This dense power grid construction is leading to increasingly strained transmission corridors, with a growing proportion of lines passing through steep mountainous areas.

[0003] In recent years, the State Grid Corporation of China and China Southern Power Grid have been vigorously promoting the use of full-process mechanized construction in power grid infrastructure. Currently, plains and hilly areas have relatively high levels of mechanized construction due to easier access for machinery. However, mountainous areas are constrained by factors such as high costs of constructing roads for large machinery and significant environmental damage, resulting in relatively lower levels of mechanized construction. Given the current dual requirements of mechanization and environmental protection in mountainous transmission line construction, anchor foundations have become increasingly popular in the selection of foundations for overhead transmission lines in recent years. This is because they can fully utilize the tensile strength of the foundation soil, offer a high degree of mechanization, require small construction equipment, and cause minimal environmental damage.

[0004] However, traditional anchor foundations, due to the small cross-section of the anchor rods, neglect the contribution of the anchor rods to the bearing capacity of the foundation during the design process, and only consider the effect of the ground reaction force at the bottom of the pile cap. However, the bearing capacity of the overburden layer is relatively low. When the pile cap is placed in the overburden layer, the size of the pile cap is usually large in order to meet the bearing capacity requirements. In order to reduce the amount of excavation, the anchor foundation pile cap needs to be embedded in rock to meet the bearing capacity requirements. However, under the condition of thick overburden, the depth of the pile cap and the amount of excavation increase significantly, which negates its environmental advantages and limits the application of anchor foundations in areas with thick overburden.

[0005] To address the aforementioned issues, engineers proposed a novel variable cross-section anchor solution. By increasing the diameter of the anchor section in the upper overburden layer, the variable cross-section anchor foundation enhances the anchor's stiffness and bearing capacity, achieving the effect of resisting downward loads together with the foundation cap. This eliminates the requirement for the foundation cap to be embedded in rock, reduces the foundation cap's burial depth and excavation volume, and can be used in geological conditions with an overburden layer thickness of 3–5 m, greatly expanding the application range of anchor foundations.

[0006] However, the calculation method for the bearing capacity of variable cross-section anchor foundations is still in the exploratory stage. Existing calculation methods cannot accurately evaluate the bearing capacity of anchor foundations. Therefore, it is necessary to propose an accurate design method for the bearing capacity of variable cross-section group anchor foundations and promote the engineering application of new variable cross-section anchor foundations. Summary of the Invention

[0007] In view of the deficiencies of the prior art, the present application provides a method for calculating the bearing capacity of a variable cross-section group anchor foundation, which takes into account the contribution of the anchor rods to the bearing capacity and has good calculation accuracy and practicality.

[0008] To achieve the above object, the technical scheme of the present application is as follows:

[0009] The method for calculating the bearing capacity of a variable cross-section group anchor foundation comprises the following steps:

[0010] S1: calculating the characteristic value N of the bearing capacity of a single variable cross-section anchor rod under pressure a ;

[0011] S2: regarding the variable cross-section anchor rod as a reinforcing body, calculating the characteristic value f of the bearing capacity of the composite foundation of the anchor rod and the ground spk ;

[0012] S3: calculating the maximum compressive stress p of the bottom surface of the bearing platform max ;

[0013] S4: comparing the characteristic value f of the bearing capacity of the composite foundation spk with the maximum compressive stress p of the bottom surface of the bearing platform max , if p max ≤ f spk , the design of the variable cross-section group anchor foundation is completed;

[0014] if p max > f spk , the diameter of the anchor rod is adjusted, the number of anchor rods is increased, or the size of the anchor rod is increased, and the steps S1-S3 are repeated until p max ≤ f spk .

[0015] The bearing capacity of the single variable cross-section anchor rod under pressure is borne by the side friction of the rock-embedded section of the anchor rod and the end resistance at the variable cross-section, and in the calculation process, it is assumed that the side friction between each rock layer and the anchor rod is uniformly distributed, and the calculation formula is as follows:

[0016]

[0017] In the formula:

[0018] N a is the characteristic value of the bearing capacity of a single variable cross-section anchor rod under pressure (kN);

[0019] d i is the diameter of the anchor rod in the i-th rock layer (m);

[0020] L i is the length of the anchor rod in the i-th rock layer (m);

[0021] τ mi—The side friction between the anchor and the interface in the i-th layer of rock, which is valued according to the field exploration test (kPa);

[0022] S—The annular area at the variable cross-section (m 2 )

[0023] p u —The ultimate compressive strength of the rock mass, which is valued according to the field exploration test (kPa).

[0024] The composite foundation bearing capacity characteristic value f spk The calculation formula is as follows:

[0025]

[0026] In the formula:

[0027] f spk —The composite foundation bearing capacity characteristic value (kPa) considering the variable cross-section anchor reinforcement;

[0028] f sk —The bearing platform bottom soil layer bearing capacity characteristic value (kPa), which is valued according to the field exploration report;

[0029] N a —The single variable cross-section anchor under pressure bearing capacity characteristic value (kN);

[0030] A p —The anchor variable cross-section segment cross-sectional area (m 2 );

[0031] β—The soil body bearing capacity development coefficient between anchors, which can be taken as 1.0-1.1;

[0032] m—The area replacement rate, the ratio of the sum of the anchor cross-sectional areas in the cover layer (nA p ) to the bearing platform bottom area (A c ),

[0033] The bearing platform bottom foundation soil maximum compressive stress p max The calculation method is as follows:

[0034]

[0035] If p min ≤0, p max should be calculated according to the following formula:

[0036]

[0037] When calculating, the following formula is required:

[0038]

[0039] In the formula:

[0040] p max Maximum compressive stress of foundation soil at the bottom surface of the pile cap (kPa);

[0041] p min Minimum compressive stress of foundation soil at the bottom surface of the pile cap (kPa);

[0042] F k Standard value of vertical pressure of the superstructure to the bottom surface of the foundation (kN);

[0043] G k Self weight of the foundation and soil weight on the foundation (kN);

[0044] A c Area of the bottom surface of the pile cap (m 2 );

[0045] M kx , M ky Standard value of the moment of force acting on the bottom surface of the pile cap in x and y directions (kN·m);

[0046] W x , W y Resistance moment of the bottom surface of the foundation around x and y axes (m 3 );

[0047] e x , e y Eccentricity of the axial force acting on the x and y directions of the bottom surface of the foundation (m);

[0048] b—M ky Length of the side of the bottom surface of the pile cap in the direction of action (m);

[0049] l—M kx Length of the side of the bottom surface of the pile cap in the direction of action (m)。

[0050] The beneficial effects of the present application are:

[0051] 1. The method of the present application calculates the bearing capacity of the composite foundation of the anchor rod group and the foundation soil by regarding the anchor rod as a reinforcing body, considers the contribution of the anchor rod to the bearing capacity of the foundation under pressure, solves the problem of excessive conservatism of the traditional design method, reduces the redundant design, optimizes the economic efficiency of the structure, reduces the engineering cost, and has significant engineering significance for environmental protection, soil and water conservation and adaptation to terrain conditions.

[0052] 2. The method of the present application supports the design of the variable cross-section anchor rod foundation, promotes the engineering application of the new type of anchor rod foundation, can expand the application scenarios of the anchor rod foundation under complex terrain and soil conditions, and has significant engineering significance for improving the mechanized construction rate of the power transmission line foundation.

[0053] 3. The novel design method for the compressive bearing capacity of variable cross-section group anchor foundation proposed in this invention can accurately evaluate the magnitude of the compressive bearing capacity of the group anchor foundation. The comparison error between the method and the numerical simulation analysis is no more than 15%, demonstrating good calculation accuracy and safety margin. Attached Figure Description

[0054] Figure 1 This is a flowchart of the calculation method of the present invention.

[0055] Figure 2 This is a schematic diagram of the variable cross-section group anchor foundation structure of the present invention.

[0056] Figure 3 This is a schematic diagram of the compressive resistance of a single anchor with a variable cross-section according to the present invention.

[0057] Among them: 1. Foundation column; 2. Anchor bolt variable cross section; 3. Anchor bolt constant cross section; 4. Ground line; 5. Rock surface line. Detailed Implementation

[0058] To make the purpose, technical solution, and advantages of the invention clearer, the invention will be further described below with reference to the accompanying drawings.

[0059] The novel variable cross-section group anchor foundation described in this invention is as follows: Figure 2 As shown, the new type of variable cross-section anchor foundation includes a foundation column 1, a variable cross-section anchor section 2, and a constant cross-section anchor section 3. The diameter of the variable cross-section anchor section 2 is larger than the diameter of the constant cross-section anchor section 3. The constant cross-section anchor section 3 is placed in the rock stratum and is located below the rock surface line 5. Most of the variable cross-section anchor section is placed in the overburden layer, and a small part is embedded in the rock. Most of the foundation column 1 is placed in the overburden layer, and the top of the foundation column 1 protrudes from the ground line 4. Figure 2 In the middle, A represents the ground reaction force.

[0060] The proposed design method for the bearing capacity of variable cross-section group anchor foundations treats the variable cross-section anchors as reinforcements. The variable cross-section anchors and the weak overburden layer form a composite foundation, which together resists the downward load transmitted by the foundation column.

[0061] The bearing capacity of a variable cross-section single anchor under load consists of three parts: the side friction between the strata and the anchor, the end resistance at the variable cross-section, and the end resistance at the bottom of the anchor. Studies have found that the side friction and end resistance at the bottom of the anchor are relatively small in the overburden layer; therefore, their contributions can be disregarded in the calculation and treated as a safety redundancy. Thus, when calculating the characteristic value of the bearing capacity of a variable cross-section single anchor under load, only the contributions of the side friction between the rock strata and the anchor in the embedded rock section and the end resistance at the variable cross-section are considered. Figure 3 As shown, Figure 3 In this context, B represents the end resistance at the variable cross-section, and C represents the side friction resistance of the embedded rock section. It is assumed that the side friction resistance is uniformly distributed throughout the rock strata. The formula for calculating the characteristic value of the bearing capacity under single anchor pressure at a variable cross-section is as follows:

[0062]

[0063] In the formula:

[0064] N a —The characteristic value of the bearing capacity of a single variable cross-section anchor under compression (kN);

[0065] d i —The diameter of the anchor in the i-th layer of rock (m);

[0066] L i —The length of the anchor in the i-th layer of rock (m);

[0067] τ mi —The side friction between the anchor and the interface in the i-th layer of rock, determined based on field exploration tests (kPa);

[0068] S—The annular area at the variable cross-section (m 2 )

[0069] p u —The ultimate compressive strength of the rock mass, determined based on field exploration tests (kN).

[0070] After calculating the bearing capacity of a single variable cross-section anchor under compression, the variable cross-section anchor is considered as a reinforcement in the cover layer, and the strength and bearing area of the foundation soil and the anchor are used to calculate the characteristic value of the bearing capacity of the composite foundation, and the calculation method is as follows:

[0071]

[0072] In the formula:

[0073] f spk —The characteristic value of the bearing capacity of the composite foundation considering the reinforcement of the variable cross-section anchor (kPa);

[0074] f sk —The characteristic value of the bearing capacity of the soil layer at the bottom of the pile cap (kPa), determined based on the field exploration report;

[0075] N a —The characteristic value of the bearing capacity of a single variable cross-section anchor under compression (kN);

[0076] A p —The cross-sectional area of the variable cross-section segment of the anchor (m 2 );

[0077] β—The bearing capacity development coefficient of the soil between the anchors, which can be taken as 1.0-1.1;

[0078] m—The area replacement rate, the ratio of the sum of the cross-sectional areas of the anchors in the cover layer (nA p ) to the area of the bottom of the pile cap (A c ),

[0079] The pile of the bearing platform is regarded as an extended foundation on the composite foundation and the maximum stress p of the foundation soil on the bottom surface of the bearing platform is calculated max The calculation formula is as follows:

[0080]

[0081] If p min ≤ 0, p max should be calculated according to the following formula:

[0082]

[0083] The following formula should be met during the calculation:

[0084]

[0085] In the formula:

[0086] p max — the maximum compressive stress of the foundation soil on the bottom surface of the bearing platform (kPa);

[0087] p min — the minimum compressive stress of the foundation soil on the bottom surface of the bearing platform (kPa);

[0088] F k — the standard value of the vertical pressure of the upper structure transmitted to the bottom surface of the foundation (kN);

[0089] G k — the weight of the foundation and the soil on the foundation (kN);

[0090] A c — the bottom area of the bearing platform (m 2 );

[0091] M kx , M ky — the standard value of the moment of the force acting on the bottom surface of the bearing platform in x and y directions (kN·m);

[0092] W x , W y — the resisting moment of the foundation bottom surface around x and y axes (m 3 );

[0093] e x , e y — the eccentricity of the axial force acting on the x and y directions of the bottom surface of the foundation (m);

[0094] b— the length of the side of the bottom surface of the bearing platform in the direction of M ky ;

[0095] l— the length of the side of the bottom surface of the bearing platform in the direction of M kx .

[0096] Finally, the bearing capacity f of the composite foundation after the variable cross-section anchor is reinforced is compared spk and the maximum compressive stress p of the foundation soil at the bottom of the pile cap max When f spk ≥ p max , it indicates that the bearing capacity of the anchor foundation meets the requirements; when f spk < p max , the size of the variable cross-section anchor can be modified, the number of anchors can be increased, or the area of the bottom of the pile cap can be increased, and then f spk is recalculated until the bearing capacity of the anchor foundation meets the requirements.

[0097] The maximum downward load that the foundation can withstand can also be calculated by the maximum compressive stress p of the foundation soil at the bottom of the pile cap max , and compared with the actual load to verify whether the bearing capacity of the anchor foundation meets the requirements.

[0098] Taking a certain ultra-high voltage transmission line project as an example, the overburden layer is silty clay, the thickness of the overburden layer is 2m, 2.5m and 3m, the bottom of the pile cap is buried 1m deep, the total length of the anchor is 6m, the length of the variable cross-section section is 1.25m, 1.75m and 2.25m respectively (0.25m embedded in rock), and the constant cross-section section is embedded in the rock layer; the rock layer is medium weathered sandy conglomerate.

[0099] Nine variable cross-section anchors are arranged, the anchor reinforcement of the anchor foundation adopts 36mm diameter HRB400 threaded steel with an elastic modulus of 200GPa; the grouting body adopts high-performance grouting material with an elastic modulus and a Poisson's ratio of 40GPa and 0.2 respectively; the diameter of the variable cross-section section of the anchor is 250mm, the diameter of the constant cross-section section of the anchor is 110mm, and the anchor spacing is 750mm. The width of the pile cap is 2.1m.

[0100] The downward bearing capacity design method of the new type of variable cross-section group anchor foundation proposed in the application can be used to predict the downward bearing capacity of a single variable cross-section anchor and a group anchor foundation. By comparing and analyzing the calculation results with the numerical simulation results, the accuracy of the design method is verified, and the results are shown in Table 1:

[0101] Table 1 Comparison of downward bearing capacity design results of variable cross-section group anchor foundation

[0102]

[0103] In the above table, N1 and N2 respectively represent the downward bearing capacity of the variable cross-section group anchor obtained by theoretical calculation and numerical simulation, and the unit is kN.

[0104] As shown in Table 1, under the above geological conditions, the difference between the calculated variable cross-section group anchor foundation bearing capacity and the finite element result is about 15% by using the design method provided by the application. The error is caused by ignoring the side friction of the overburden layer and the end resistance of the anchor bottom in the variable cross-section single anchor calculation process. Therefore, it is considered that the variable cross-section group anchor bearing capacity design method provided by the application can meet the accuracy requirements of practical engineering applications, and has a certain safety redundancy

[0105] In summary, the new variable cross-section group anchor bearing capacity design method provided by the application has clear mechanical concept, first proposes the variable cross-section single anchor and group anchor foundation bearing capacity design method, and first considers the contribution of the anchor to the foundation bearing capacity, and the formula is simple, and has calculation accuracy and safety margin.

[0106] Finally, it should be pointed out that: the contents not described in detail in the specification belong to the prior art known to those skilled in the art, and the above only the preferred embodiments of the application, and not for limiting the application, although the application has been described in detail with reference to the foregoing embodiments, for those skilled in the art, it still can modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the application shall be included in the protection scope of the application.

Claims

1. A method for calculating the load capacity of a variable cross-section group anchor foundation, characterized by, The method comprises: S1: Calculate the characteristic value N of the compression bearing capacity of a single variable cross-section anchor rod a ; S2: the variable cross-section anchor rod is regarded as a reinforcing body, and the N a value is calculated considering the bearing capacity characteristic value f of the composite foundation reinforced by the variable cross-section anchor rod spk ; S3: Calculate the maximum compressive stress p of the bottom surface of the bearing platform max ; S4: Compare the characteristic values ​​f of the bearing capacity of composite foundations spk The maximum compressive stress p at the bottom surface of the foundation max If p max ≤f spk Then the design of the variable cross-section group anchor foundation is completed; If p max > f spk , then repeat S1-S3 by adjusting the anchor rod diameter, increasing the number of anchor rods, or increasing the size of the anchor rod until p max ≤ f spk , and stop the calculation. The single variable cross-section anchor rod down pressure bearing capacity is borne by the anchor rod rock-socketed section side friction and the variable cross-section end resistance, the calculation process assumes that the side friction between each rock stratum and the anchor rod is uniformly distributed, and the calculation formula is as follows: In the formula: N a - characteristic value of the load bearing capacity of the single variable cross-section anchor rod under compression (kN); d i - Diameter of the anchor rod in the i-th layer of rock (m); L i — Length of the anchor in the i-th layer of rock (m); τ mi - the interfacial side friction force (kPa) between the i-th layer of rock and the anchor. S - cross-sectional area of the ring at the point of change (m 2 ); p u — Limit compressive strength of rock mass (kPa).

2. The method of calculating the load capacity of a variable cross-section group anchor foundation according to claim 1, wherein, The composite foundation bearing capacity characteristic value f considering the variable cross-section anchor rod reinforcement spk The calculation formula is as follows: In the formula: f spk — Consider the composite foundation bearing capacity characteristic value (kPa) after the variable cross-section anchor reinforcement; f sk - bearing capacity characteristic value of soil layer at bottom surface of pile cap (kPa); N a - characteristic value of the load bearing capacity of the single variable cross-section anchor rod under compression (kN); A p - cross-sectional area of the anchor rod variable cross-section segment (m 2 ); β—The soil bearing capacity development coefficient between anchor rods; m - area replacement rate, sum of anchor rod cross-sectional area in the cover layer nA p ratio of the bottom area A c of the pile cap to the area A 3. The method of calculating the load carrying capacity of a driven pile of a variable cross-section group anchor foundation according to claim 1, wherein, The maximum compressive stress p of the foundation soil at the bottom surface of the pile cap max The calculation method is shown in the following formula: if p min ≤ 0, p max is calculated as follows: When calculating, the following formula is met: In the formula: p max — maximum compressive stress of the ground soil at the bottom surface of the pile cap (kPa); p min — minimum compressive stress of foundation soil at bottom surface of pile cap (kPa); F k — Standard value of vertical pressure from the superstructure to the base bottom (kN); G k — Subgrade self-weight and surcharge (kN); A c — Pile bottom area (m 2 ) M kx , M ky — moment standard value of force acting on the bottom surface of the pile cap in x and y directions (kN.m); W x , W y — resistance moment of the foundation bottom surface around x and y axes (m 3 ); e x 、e y — acting on the base floor x and y direction axis force eccentricity (m); b - M ky Action direction bearing platform bottom surface side length (m); l - M kx Action direction bearing platform bottom surface side length (m).

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