Dispersing type anchor cable elongation value calculation method based on differential whole-bundle tensioning theory

Abstract

According to the method for calculating the elongation value of the dispersed anchor cable based on the differential whole-bundle tensioning theory, relevant known conditions can be found according to a project design blueprint or a construction scheme and the like, and the elongation value of the dispersed anchor cable can be calculated according to a corresponding formula on the basis of pre-tightening. The tension force is uniformly distributed to each steel strand according to the designed locking force P; and the difference tension force is generated when the single steel strand of each group of anchoring units and the shortest steel strand anchoring unit is tensioned to the designed locking force. The method comprises the following steps: establishing an ideal model of the dispersive anchor cable, solving a functional equation of a linear relationship between a tension value and an elongation value when the dispersive anchor cable adopts differential whole-bundle tensioning, and finally, respectively substituting each stage of tensioning force of integral graded tensioning specified by a design blueprint or a construction scheme into the formula, so as to obtain an ideal model of the dispersive anchor cable. Therefore, the scientific, correct and unique theoretical elongation value of each stage when the anchor cable is subjected to differential whole-bundle tensioning in the whole graded tensioning process can be obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of anchor cable construction, and specifically to a calculation method for the elongation value of a dispersed anchor cable based on the differential integral tensioning theory. Background Technique

[0002] Comparing the actual elongation value measured during the tensioning of the anchor cable with the calculated theoretical elongation value is a necessary path to determine the tensioning quality. Therefore, the calculated theoretical elongation value must be scientific, consistent, and accurate as a standard. Currently, there is no complete, scientific, and unified standard method for calculating the theoretical elongation value when using the differential integral tensioning method for dispersed anchor cables. As a result, for the calculation method of the theoretical elongation value when using the differential integral tensioning method for this type of anchor cable, due to the lack of reasonable basis, a rigorous, correct, and unique conclusion cannot be obtained, and it is difficult to accurately judge whether the tensioning process of this type of anchor cable is normal and what the tensioning effect is. Summary of the Invention

[0003] To solve the current technical problems, the main purpose of the present invention is to provide a calculation method for the elongation value of a dispersed anchor cable based on the differential integral tensioning theory. By analyzing the characteristics of the differential integral tensioning method for dispersed anchor cables, this calculation method constructs an ideal elastic material model that conforms to this type of anchor cable. Based on the formula for calculating the differential tension force of each group on page 64, clause 5.7.5 of the "Code for Construction of Hydropower and Water Conservancy Prestressed Anchorage" DL / T 5083-2019, a complete, scientific, and rigorous calculation formula and method for the theoretical elongation value of a dispersed anchor cable using the differential integral tensioning method are reasonably derived. Using this calculation method, a rigorous, correct, and unique conclusion can be obtained for the theoretical elongation value when using the differential integral tensioning method for this type of anchor cable, and thus an accurate conclusion can be drawn for the determination of the tensioning quality of this type of anchor cable.

[0004] To achieve the above technical features, the object of the present invention is realized as follows: A calculation method for the elongation value of a dispersed anchor cable based on the differential integral tensioning theory, including the following steps: Step 1: For any dispersed anchor cable using differential integral tensioning, obtain the relevant known conditions such as the pre-tightening load coefficient, the cross-sectional area of a single steel strand, the elastic modulus of the steel strand, the difference in the tensioning section length between each anchoring unit and the shortest steel strand anchoring unit, and the number of steel strands in the whole bundle of the anchor cable according to the design blueprint or construction plan. According to the relevant corresponding formulas, obtain the differential elongation amount generated when each anchoring unit and the shortest steel strand anchoring unit are tensioned to the design locking force on the basis of pre-tightening, the tension force evenly distributed to each steel strand according to the design locking force P, and the differential tension force generated by a single steel strand of each anchoring unit and the shortest steel strand anchoring unit when tensioned to the design locking force; Step 2: By establishing an ideal model of the dispersed cable anchor, the functional equation of the linear relationship between the tensile force value and the elongation value of the dispersed cable anchor during differential integral tensioning is obtained. This functional equation is applicable to the overall hierarchical tensioning after differential tensioning is completed. Step 3: According to the tensile forces at each level of the overall hierarchical tensioning specified in the design blueprint or construction plan, substitute them into the functional equation respectively, and the scientific, correct and unique theoretical elongation values at each level of this type of cable anchor during differential integral tensioning in the overall hierarchical tensioning can be obtained.

[0005] The relevant corresponding formulas in the above Step 1 include: On the basis of pre-tightening, the differential elongation ΔL generated by each group of anchoring units and the shortest strand anchoring unit when tensioned to the design locking force: ΔL = (1 - M)FS / (AE) = (1 - M)PS / (nAE); (1) The tensile force evenly distributed to each strand according to the design locking force P: F = P / n; (2) The differential tensile force generated by each group of anchoring units and the single strand of the shortest strand anchoring unit when tensioned to the design locking force: ΔP = (1 - M)ΔLAE / L = (1 - M)PS / (nL); (3) In the formula: ΔL is the differential elongation generated by each group of anchoring units and the shortest strand anchoring unit when tensioned to the design locking force on the basis of pre-tightening, with the unit of mm; M is the pre-tightening load coefficient; F is the tensile force evenly distributed to each strand according to the design locking force P, with the unit of KN; S is the difference in the tensioning section length between each group of anchoring units and the shortest strand anchoring unit, with the unit of mm; A is the cross-sectional area of a single strand, with the unit of mm 2 ; E is the elastic modulus of the strand, with the unit of GPa; n is the number of strands of the integral cable anchor; P is the design locking tensile force, with the unit of KN; ΔP is the differential tensile force generated by each group of anchoring units and the single strand of the shortest strand anchoring unit when tensioned to the design locking force, with the unit of KN; L is the tensioning section length of each group of anchoring units, with the unit of mm.

[0006] The model establishment and derivation of the calculation of the differential integral tension elongation value of the dispersed cable anchor in Step 2 are specifically as follows: Assume that the length of each anchor section in each anchoring unit is α, that is, assume that the cable in the ideal state has m groups of anchoring units and the difference in the tension section length between each adjacent anchoring unit is α. The number of steel strands in each group of anchoring units from short to long is n 1 、n 2 、……n m . After pre-tightening according to the design requirements and completing the differential load compensation tensioning for each anchoring unit with the shortest group of anchoring units, under this premise, a through-hole jack is used for overall step-by-step tensioning to determine the relationship between the tension value P z and the elongation value Q z ; When an elastic substance is stretched within the elastic deformation range, the tension value and the elongation value show a linear relationship. Therefore, as long as two known points of the linear equation are found, its linear equation can be established.

[0007] Process of establishing the linear equation: It is known that the first point (Q 1 , P 1 ) is the starting point of the overall step-by-step tensioning after the pre-tightening and differential load compensation are completed. Its elongation value Q 1 is 0, and its tension P 1 is the sum of the pre-tightening force P y and the differential load compensation force P c , that is: Q 1 = 0; P 1 = P y + P c ; And P y is known, and P c can be obtained according to the above formula (3). The specific calculation steps are as follows: Let the differences between the tension section lengths of each group of anchoring units and the shortest steel strand anchoring unit from small to large be S 1 、S 2 、……S m-1 , then there is: P c = (1 - M)Pn 2 S 1 / (nL) + (1 - M)Pn 3 S 2 / (nL) + …… + (1 - M)Pn m S m-1 / (nL); (4) When S 1 、S 2 、……S m-1 is an arithmetic sequence, there is: S 1 = α; S 2 = 2α; …… S m-1 = (m - 1)α; Then there is: P c = (1 - M)[n 2 α + 2n 3 α + …… + (m - 1)n m α]P / (nL); (5) That is, when S 1 , S 2 , …… S m-1 is an arithmetic progression, P can be obtained through formula (5) c ; When S 1 , S 2 , …… S m-1 is a non - arithmetic progression, P can be obtained through formula (4) c , then there is: P 1 = P y + P c ; When S 1 , S 2 , …… S m-1 is an arithmetic progression, there is: P 1 = P y + (1 - M)[n 2 α + 2n 3 α + …… + (m - 1)n m α]P / (nL); (6) It is known that at the 2nd point (Q 2 , P 2 ), when the overall staged tensioning reaches 100% of the designed locking tension, the tension P 2 is 100%P, and the elongation value Q 2 is the difference between the theoretical elongation value Q d when the shortest group of anchoring units is tensioned to the designed locking tension and the elongation value Q dy caused by its pre - tightening. Among them, Q d and Q dy are known, that is: Q 2 = Q d - Q dy ; P 2 = 100%P; Therefore, based on the known 2 points (Q 1 , P 1 ), (Q2 , P 2 ) Establish the relationship equation between the tensile force P z and the elongation value Q z as follows: (Q z - Q 1 ) / (P z - P 1 ) = (Q 2 - Q 1 ) / (P 2 - P 1 ), that is: Q z = Q 2 (P z - P 1 ) / (P - P 1 ); (7)

[0008] The present invention has the following beneficial effects: By analyzing the characteristics of the differential integral tensioning method for the dispersed anchor cable, the present invention constructs an ideal elastic material model that conforms to this type of anchor cable. Based on the calculation formula of the differential tensile force for each group on page 64, clause 5.7.5 of the "Code for Construction of Hydropower and Water Conservancy Prestressed Anchorage" DL / T 5083-2019, a complete, scientific, and rigorous calculation formula and method for the theoretical elongation value of the dispersed anchor cable using the differential integral tensioning method are reasonably derived. Using this calculation method, a rigorous, correct, and unique conclusion can be obtained for the theoretical elongation value of this type of anchor cable when using the differential integral tensioning method, so that an accurate conclusion can be drawn for the determination of the tensioning quality of this type of anchor cable. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] The present invention will be further described below in conjunction with the drawings and embodiments.

[0010] Figure 1 is a schematic diagram of the ideal elastic material model constructed by the present invention based on the characteristics of the differential integral tensioning method for the dispersed anchor cable.

[0011] Figure 2 is a schematic diagram of the relationship equation curve between the tensile force Pz and the elongation value Qz during the overall grading tensioning stage of the dispersed anchor cable using the differential integral tensioning method established by the present invention from the known first point (Q1, P1) and the known second point (Q2, P2). DETAILED DESCRIPTION OF THE EMBODIMENTS

[0012] The embodiments of the present invention will be further described below in conjunction with the drawings.

[0013] See Figure 1-2, Step 1: For any dispersed anchor cable, differential integral tensioning is adopted. According to the design blueprint or construction plan, obtain the known conditions such as the pre-tightening load coefficient, the cross-sectional area of a single steel strand, the elastic modulus of the steel strand, the difference in the tensioning section length between each anchoring unit and the shortest steel strand anchoring unit, and the number of steel strands in the integral anchor cable. Based on the relevant corresponding formulas, calculate the differential elongation generated when each anchoring unit and the shortest steel strand anchoring unit are tensioned to the design locking force on the basis of pre-tightening, the tension force evenly distributed to each steel strand according to the design locking force P, and the differential tension force generated by a single steel strand of each anchoring unit and the shortest steel strand anchoring unit when tensioned to the design locking force; Step 2: By establishing an ideal model of the dispersed anchor cable, obtain the function equation of the linear relationship between the tension force value and the elongation value when the dispersed anchor cable adopts differential integral tensioning. This function equation is applicable to the overall hierarchical tensioning after differential tensioning; Step 3: According to the tension forces at each level of the overall hierarchical tensioning specified in the design blueprint or construction plan, substitute them into the function equation respectively, and the scientific, correct and unique theoretical elongation values at each level of this type of anchor cable when adopting differential integral tensioning in the overall hierarchical tensioning can be obtained.

[0014] The relevant corresponding formulas in Step 1 include: On the basis of pre-tightening, the differential elongation ΔL generated when each anchoring unit and the shortest steel strand anchoring unit are tensioned to the design locking force: ΔL = (1 - M)FS / (AE) = (1 - M)PS / (nAE); (1) The tension force evenly distributed to each steel strand according to the design locking force P: F = P / n; (2) The differential tension force generated by a single steel strand of each anchoring unit and the shortest steel strand anchoring unit when tensioned to the design locking force: ΔP = (1 - M)ΔLAE / L = (1 - M)PS / (nL); (3) In the formula: ΔL is the differential elongation generated when each anchoring unit and the shortest steel strand anchoring unit are tensioned to the design locking force on the basis of pre-tightening, and the unit is mm; M is the pre-tightening load coefficient; F is the tension force evenly distributed to each steel strand according to the design locking force P, and the unit is KN; S is the difference in the tensioning section length between each anchoring unit and the shortest steel strand anchoring unit, and the unit is mm; A is the cross-sectional area of a single steel strand, and the unit is mm 2 ; E is the elastic modulus of the steel strand, and the unit is GPa; n is the number of steel strands in the integral anchor cable; P is the designed locked tension force, with the unit of kN; ΔP is the differential tension force generated by each anchoring unit and a single steel strand of the shortest steel strand anchoring unit when tensioned to the designed locked force, with the unit of kN; L is the tensioned section length of each anchoring unit, with the unit of mm.

[0015] The establishment and derivation of the calculation model for the elongation value of the differentiated integral bunch tensioning of the dispersed anchor cables in step 2 are specifically as follows: Assume that the length of the inner anchor section of each anchoring unit is α, that is, assume an anchor cable in an ideal state. There are m groups of anchoring units, and the difference in the tensioned section length between adjacent anchoring units is α. The number of steel strands in each group of anchoring units from short to long is n 1 、n 2 、……n m . After pre-tightening according to the design requirements and completing the differential load compensation tensioning of each anchoring unit with the shortest group of anchoring units, on this premise, a through-hole jack is used for overall step-by-step tensioning to determine the relationship between the tension force value P z and the elongation value Q z ; When an elastic substance is under tension within the elastic deformation range, the tension force value and the elongation value are linearly related. Therefore, as long as two known points of this linear equation are found, its linear equation can be established.

[0016] Process of establishing the linear equation: It is known that the first point (Q 1 , P 1 ) is the starting point for overall step-by-step tensioning after pre-tightening and differential load compensation. Its elongation value Q 1 is 0, and its tension force P 1 is the sum of the pre-tightening force P y and the differential load compensation force P c , that is: Q 1 = 0; P 1 = P y + P c ; And P y is known, and P c can be obtained according to the above formula (3). The specific calculation steps are as follows: Let the differences in the tensioned section lengths between each group of anchoring units and the shortest steel strand anchoring unit be S 1 、S 2 、……S m-1 from small to large, then there is: P c = (1 - M)Pn 2 S 1 / (nL) + (1 - M)Pn 3 S 2 / (nL) + …… + (1 - M)Pn m S m-1 / (nL); (4) When S 1 、S 2 、…… S m-1 is an arithmetic progression, there is: S 1 = α; S 2 = 2α; …… S m-1 = (m - 1)α; Then there is: P c = (1 - M)[n 2 α + 2n 3 α + …… + (m - 1)n m α]P / (nL); (5) That is, when S 1 、S 2 、…… S m-1 is an arithmetic progression, P c can be obtained through formula (5); When S 1 、S 2 、…… S m-1 is a non - arithmetic progression, P c can be obtained through formula (4), then there is: P 1 = P y + P c ; When S 1 、S 2 、…… S m-1 is an arithmetic progression, there is: P 1 = P y + (1 - M)[n 2 α + 2n 3 α + …… + (m - 1)n m α]P / (nL); (6) It is known that for the second point (Q 2 、P 2 ), when the overall staged tensioning reaches 100% of the designed locked tension, the tension P 2 is 100%P, and the elongation value Q 2 is the theoretical elongation value Q d when the shortest group of anchoring units is tensioned to the designed locked tension and the elongation value Q dy caused by its pre - tighteningThe difference, where Q d and Q dy is known, i.e.: Q 2 = Q d - Q dy ; P 2 = 100%P; Thus, based on the known two points (Q 1 , P 1 ), (Q 2 , P 2 ), the relationship equation between the tensile force P z and the elongation value Q z for the overall staged tension is established as follows: (Q z - Q 1 ) / (P z - P 1 ) = (Q 2 - Q 1 ) / (P 2 - P 1 ), i.e.: Q z = Q 2 (P z - P 1 ) / (P - P 1 ); (7)

[0017] Example 2: Extension of the calculation formula for the differential tensile force in Clause 5.7.5 on Page 64 of the Explanation of the Provisions of the "Code for Construction of Hydropower and Water Conservancy Prestressed Anchorage" DL / T 5083 - 2019: Step 1: The unit of the elastic modulus of the steel strand in this formula should be gigapascal (GPa), and the unit of the length of the steel strand should be millimeter (mm).

[0018] Step 2: To avoid calculation errors caused by an incomplete understanding of ΔL, it should be supplemented that: ΔL is the differential elongation produced when there is a difference S in the tensioned section length for different anchoring units and equal force F is applied to each single steel strand in each anchoring unit.

[0019] Since it is necessary to achieve the ideal state of equal stress on each single steel strand in each anchoring unit as much as possible when tensioning and locking to 100% of the designed locking tensile force P, it is more reasonable to calculate ΔL according to the force F evenly distributed to each single steel strand by the designed locking force P, where: ΔL = (1 - M)FS / (AE) = (1 - M)PS / (nAE); (1) F = P / n; (2) ΔP = (1 - M)ΔLAE / L = (1 - M)PS / (nL); (3) In the above formula (3): ΔL is the differential elongation (mm) generated by each group of anchoring units and the shortest strand anchoring unit when tensioned to the design locking force on the basis of pre-tightening; M is the pre-tightening loading coefficient; F is the tensile force (KN) evenly distributed to each strand according to the design locking force P; S is the difference in the tensioning section length between each group of anchoring units and the shortest strand anchoring unit (mm); A is the cross-sectional area of a single strand (mm 2 ); E is the elastic modulus of the strand (GPa); n is the number of strands in a whole bunch of anchor cables; P is the design locking tensile force (KN); ΔP is the differential tensile force (KN) generated by each group of anchoring units and the single strand of the shortest strand anchoring unit when tensioned to the design locking force; L is the tensioning section length of each group of anchoring units (mm); Model establishment and derivation for calculating the differential elongation value of the whole bunch of dispersed anchor cables during tensioning: The designed inner anchor section lengths of most of the anchoring units of dispersed anchor cables are equal. Therefore, it can be assumed that the inner anchor section length of each anchoring unit is α. That is, it is assumed that for an anchor cable in an ideal state, there are m groups of anchoring units and the difference in the tensioning section length between adjacent anchoring units is α. The number of strands in each group of anchoring units from short to long is n 1 , n 2 , …… n m . After pre-tightening according to the design requirements and completing the differential load compensation tensioning for each anchoring unit with the shortest group of anchoring units, on this premise, a through-hole jack is used for overall step-by-step tensioning. The relationship between the tensile force P z and the elongation value Q z is discussed.

[0020] When an elastic material is in tension within the elastic deformation range, the tensile force value and the elongation value are linearly related. Therefore, as long as two known points of this linear equation are found, its linear equation can be established.

[0021] Step 3: It is known that the first point (Q 1 , P 1 ) is the starting point for overall step-by-step tensioning after pre-tightening and differential load compensation are completed. Its elongation value Q 1 is 0, and its tensile force P 1 is the sum of the pre-tightening force P y and the differential load compensation force P c . That is Q 1= 0; P 1 = P y + P c ; And P y is known, P c can be obtained according to the above formula ③. The specific calculation steps are as follows: Let the differences between each group of anchoring units and the tensioning section length of the shortest strand anchoring unit be S 1 、S 2 、……S m-1 , then there is: P c = (1 - M)Pn 2 S 1 / (nL)+(1 - M)Pn 3 S 2 / (nL)+ ……+(1 - M)Pn m S m-1 / (nL); (4) When S 1 、S 2 、……S m-1 is an arithmetic progression, there is: S 1 = α; S 2 = 2α; …… S m-1 = (m - 1)α; Then there is: P c = (1 - M)[n 2 α + 2n 3 α + ……+(m - 1)n m α]P / (nL); (5) That is, when S 1 、S 2 、……S m-1 is an arithmetic progression, P c can be obtained through formula (5); when S 1 、S 2 、……S m-1 is a non - arithmetic progression, P c can be obtained through formula (4), then there is: P 1 = P y + P c ; It is emphasized that when S 1 、S 2 、……S m-1 is an arithmetic progression, there is: P1 = P y + (1 - M)[n 2 α + 2n 3 α + …… + (m - 1)n m α]P / (nL); (6) Step 4: Given that at point 2 (Q 2 , P 2 ), when the overall graded tensioning reaches 100% of the designed locking tension, the tension P 2 is 100%P, and the elongation value Q 2 is the difference between the theoretical elongation value Q d when the shortest group of anchoring units is tensioned to the designed locking tension and the elongation value Q dy caused by its pre-tightening. Among them, Q d and Q dy are known, that is Q 2 = Q d - Q dy ; P 2 = 100%P.

[0022] Example 3: Step 1: For any dispersed anchor cable, differential integral tensioning is adopted. According to the design blueprint or construction plan, etc., known conditions such as M, A, E, S, n, etc. can be obtained. According to the above formulas (1), (2), (3), ΔL, F, and ΔP can be obtained.

[0023] Step 2: Establish an ideal model of the dispersed anchor cable. Through scientific derivation, formulas (4), (5), and (6) can be obtained. According to the law that when an elastic substance is in tension within the elastic deformation range, the tension value and the elongation value are linearly related, the known two-point coordinates (Q 1 , P 1 ) and (Q 2 , P 2 ) of the linear equation are obtained, so as to obtain the function equation of the linear relationship between the tension value and the elongation value when the dispersed anchor cable adopts differential integral tensioning, that is, formula (7). This formula is applicable to the overall graded tensioning after differential tensioning is completed.

[0024] Step 3: Substitute the tension values at each level of the overall graded tensioning specified in the design blueprint or construction plan, etc. into formula (7) respectively, and the scientific, correct, and unique theoretical elongation values at each level when the anchor cable of this type adopts differential integral tensioning in the overall graded tensioning can be obtained, providing a scientific and correct theoretical basis for judging whether the anchor cable of this type is normal during the tensioning process and judging the tensioning quality.

Claims

1. A method for calculating the elongation value of a dispersed anchor cable based on the differentiated whole-beam tensioning theory, characterized in that: The following steps are involved: Step 1: For any dispersed anchor cable, differentiated whole-bundle tensioning is adopted. According to the design blueprint or construction plan, the preload coefficient, the cross-sectional area of ​​a single steel strand, the elastic modulus of the steel strand, the difference between the tensioning section length of each group of anchor units and the shortest steel strand anchor unit, and the number of steel strands of the whole bundle of anchor cables are obtained. According to the relevant corresponding formulas, the differential elongation generated by each group of anchor units and the shortest steel strand anchor unit when tensioned to the design locking force is obtained on the basis of pretensioning, the tension force evenly distributed to each steel strand according to the design locking force P, and the differential tension force generated by each group of anchor units and a single steel strand of the shortest steel strand anchor unit when tensioned to the design locking force are obtained; Step 2: By establishing an ideal model of dispersed anchor cables, the function equation of the linear relationship between the tension value and the elongation value when the dispersed anchor cables are tensioned by differential whole bundle is obtained. The function equation is applicable to the overall graded tensioning after the differential tensioning is completed; Step 3: Substitute the tensioning forces of each level of the overall graded tensioning specified in the design blueprint or construction plan into the function equation respectively, and you can get the scientific, correct and unique theoretical elongation values ​​of each level when this type of anchor cable adopts differentiated whole-bundle tensioning for overall graded tensioning.

2. The method for calculating the elongation value of a dispersed anchor cable based on the differentiated whole-bundle tensioning theory according to claim 1 is characterized in that: The corresponding formulas in step 1 include: On the basis of pre-tightening, the difference in elongation ΔL between each group of anchor units and the shortest strand anchor unit when tensioned to the designed locking force is: ΔL=(1-M)FS / (AE)=(1-M)PS / (nAE); (1) The tension force evenly distributed to each strand according to the designed locking force P: F = P / n; (2) The difference in tension force between each group of anchor units and a single strand of the shortest strand anchor unit when tensioned to the designed locking force: ΔP=(1-M)ΔLAE / L=(1-M)PS / (nL); (3) Where: ΔL is the difference in elongation between each group of anchor units and the shortest strand anchor unit when tensioned to the design locking force on the basis of pre-tightening, in mm; M is the preload coefficient; F is the tension force uniformly distributed to each steel strand according to the designed locking force P, in KN; S is the difference between the tensioning length of each group of anchor units and the shortest strand anchor unit, in mm; A is the cross-sectional area of ​​a single steel strand, in mm 2 ; E is the elastic modulus of the steel strand, in GPa; n is the number of steel strands in the entire bundle of anchor cables; P is the design locking tension force, in KN; ΔP is the difference in tension force between each group of anchorage units and a single strand of the shortest strand anchorage unit when tensioned to the design locking force, in KN; L is the tensioning section length of each group of anchor units, in mm.

3. The method for calculating the elongation value of a dispersed anchor cable based on the differentiated whole-bundle tensioning theory according to claim 2 is characterized in that: The model establishment and derivation for calculating the differential whole bundle tension elongation value of the dispersed anchor cable in step 2 are specifically as follows: Assume that the length of the anchor section in each anchor unit is α, that is, assume that in an ideal state, there are m groups of anchor units and the difference in the length of the tension section of each adjacent anchor unit is α. The number of steel strands in each group of anchor units from short to long is n1, n2, ... n respectively. m , pre-tightened according to the design requirements, each anchor unit is tensioned with the shortest anchor unit for differential load compensation, and then the through-hole jack is used to perform overall graded tensioning to determine the tensioning force value P during overall graded tensioning z and elongation value Q z relationship; When an elastic material is stretched within the range of elastic deformation, the tension value and the elongation value are linearly related, so as long as two known points of the linear equation are found, its linear equation can be established.

4. The method for calculating the elongation value of a dispersed anchor cable based on the differentiated whole-bundle tensioning theory according to claim 3 is characterized in that: The process of establishing a linear equation: It is known that the first point (Q1, P1) is the starting point of the overall graded tensioning after the preload and differential load compensation are completed. Its elongation value Q1 is 0, and its tension force P1 is the preload force P y and differential load compensation force P c The sum of , that is: Q1=0； P1=P y +P c ; And P y is known, P c It can be obtained according to the above formula (3), and the specific calculation steps are: Assume that the difference between the tensioning length of each group of anchor units and the shortest steel strand anchor unit is S1, S2, ... S m-1 , then: P c =(1-M)Pn2S1 / (nL)+(1-M)Pn3S2 / (nL)+ ……+(1-M)Pn m S m-1 / (nL);(4) When S1, S2, ... S m-1 When it is an arithmetic progression, we have: S1=α； S2=2α； …… S m-1 = (m-1) a; Then we have: P c =(1-M)[n2α+2n3α+ ……+(m-1)n m α]P / (nL);(5) That is, when S1, S2, ... S m-1 When it is an arithmetic progression, P can be obtained by formula (5) c ; When S1, S2, ... S m-1 When it is a non-arithmetic sequence, P can be obtained by formula (4) c , then: P1=P y +P c ; When S1, S2, ... S m-1 When it is an arithmetic progression, we have: P1=P y +(1-M)[n2α+2n3α+ ……+(m-1)n m α]P / (nL);(6) It is known that the second point (Q2, P2) is when the overall staged tension is stretched to 100% of the design locking tension, its tension P2 is 100% P, and the elongation value Q2 is the theoretical elongation value Q when the shortest group of anchor units is stretched to the design locking tension. d The elongation value Q caused by its preload dy The difference between d With Q dy is known, that is: Q2=Q d -Q dy ; P2=100%P; Based on the known two points (Q1, P1) and (Q2, P2), the tension force P during the overall graded tensioning is established. z and elongation value Q z The relationship equation is as follows: (Q z -Q1) / (P z -P1) = (Q2-Q1) / (P2-P1), that is: Q z =Q2(P z -P1) / (P-P1);(7)。

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