A method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor

Abstract

The present invention provides a method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor, comprising the following steps: obtaining the shear strength and stiffness of a grouting layer-surrounding rock interface; obtaining a full stress-strain curve of the anchor under tension, and fitting a tensile curve constitutive model of the anchor; substituting the shear strength and stiffness of the grouting layer-surrounding rock interface into a load-displacement relationship of a pull-out end of a tension section of the anchor, and obtaining the load and displacement of the pull-out end of the anchor when the tension section of the anchor reaches a peak shear stress at the grouting layer-surrounding rock interface; similarly, obtaining the load and displacement of the pull-out end of the anchor when the compression section of the anchor reaches a peak shear stress at the grouting layer-surrounding rock interface; and obtaining the load and displacement of the ends of the tension section and the compression section of the anchor, under the condition that the grouting layer-surrounding rock interfaces of the tension section and the compression section of the anchor simultaneously reach peak shear stresses. The superposition of the loads is the anchoring force of the multi-stage yield anchor, and the displacement difference is the required yield layer thickness.

Description

Technical Field

[0001] The invention belongs to the field of yield anchor structure design, and in particular relates to a method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor. Background Art

[0002] Yield anchors are widely used in tunnels with large deformations in soft rock. Compared to conventional full-length bonded and end-anchor anchors, yield anchors have the ability to adapt to surrounding rock deformation and offer higher anchoring force, thereby improving the overall stability of soft rock tunnels. Multi-stage yield anchors, based on the yield principle, achieve multi-stage yielding by incorporating multiple yielding units within the anchor. These units act to divide the anchor into a tension section and several compression sections. Due to the different load-displacement stiffnesses of the tension and compression sections of the anchor, the displacements required to reach peak pullout loads differ significantly between the two sections. To ensure that the peak pullout loads in both the tension and compression sections are reached simultaneously, yielding units are required to coordinate the deformation of the two sections, thereby better maximizing the anchor's overall strength and deformability. Multi-stage yield anchors further address the issue of multi-stage release of surrounding rock deformation, adapting to evolving deformation and providing sufficient strength reserves to ensure long-term stability.

[0003] However, when applying multi-stage yield anchor rods, although the anchoring force of the anchor rods and the thickness of the yield layer can be determined through pull-out tests, the load evolution process of the multi-stage yield anchor rods is not revealed from a mechanistic perspective, making it difficult to quickly and effectively determine the anchoring force of the anchor rods and the thickness of the yield layer. This is the key to ensuring the support effect of the multi-stage yield anchor rods, and is a technical problem that technical personnel in this field urgently need to solve. Summary of the Invention

[0004] The present invention provides a method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor rod to at least solve the above technical problems.

[0005] To solve the above problems, the first aspect of the present invention provides a method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor, wherein the multi-stage yield anchor comprises a tension section, a plurality of compression sections, and a yield unit. The determination method comprises the following steps:

[0006] Step 1: Conducting an indoor direct shear test on the rock-grout bonding interface obtained on site to obtain shear stress-displacement curves of the grouting layer-surrounding rock interface under different normal stress conditions, thereby obtaining the bonding strength and shear stiffness of the grouting layer-surrounding rock interface;

[0007] Step 2: Perform a tensile test on the anchor rod body to obtain the full stress-strain curve of the anchor rod body under tensile conditions, fit the constitutive model of the anchor rod body material, and determine the stress and strain point data of the plastic platform section and hardening section of the anchor rod body;

[0008] Step 3: Substituting the surrounding rock-grouting layer interface bond strength and shear stiffness into the anchor load-displacement relationship formula of the anchor tension section under pull-out conditions, obtaining the shear stress distribution law of the grouting layer-surrounding rock interface of the anchor tension section, and obtaining the peak pull-out force and pull-out displacement of the anchor tension section;

[0009] Step 4: Substitute the surrounding rock-grouting layer interface bond strength and shear stiffness into the anchor bolt load-displacement relationship formula of the anchor bolt compression section under pullout conditions to obtain the shear stress distribution law of the grouting layer-surrounding rock interface of the anchor bolt compression section, and obtain the peak pullout force and pullout displacement of the anchor bolt compression section;

[0010] Step 5 establishes an equation with the load-displacement relationship of the tension section and the compression section of the anchor obtained in steps 2, 3 and 4, the constitutive model of the anchor body material, the stress-strain point data of the plastic platform section and the hardened section of the anchor, and the total pull-out displacement of the anchor end. Under the condition that the shear load of the grouting layer-surrounding rock interface of the tension section and the compression section of the anchor reaches the peak value at the same time, the load and displacement of the tension section and the compression section of the anchor are obtained at this time. The sum of the loads of the tension section and the compression section of the anchor is the anchoring force of the anchor, and the displacement difference between the tension section and the compression section of the anchor is the yield layer thickness of the anchor.

[0011] In the first aspect, the determination method includes preparing a 100*100*50mm cubic sample from the rock obtained on site, pouring grouting material on the other half of the sample to prepare a 100*100*100mm bonding sample, and obtaining the bonding strength and shear stiffness of the grouting layer-surrounding rock interface through an indoor direct shear test; and obtaining the stress-strain curve of the anchor rod during the tensile process through a tensile test of the anchor rod body.

[0012] In the first aspect, the determination method includes obtaining the tensile constitutive model of the anchor rod body by fitting the following formula:

[0013] (1)

[0014] in, σ p0 and σ pf Indicates the initial yield stress and ultimate stress of the anchor; F and u Indicates the tensile force and tensile deformation of the anchor; m and n is the fitting parameter; u e is the elastic limit deformation, which can be expressed as .

[0015] In the first aspect, the determination method includes calculating the load-displacement relationship of the tension section of the anchor rod under the pull-out condition by the following formula:

[0016] (2)

[0017] in, is the shear modulus of the grouting layer, is the drilling diameter, is the anchor diameter, is the elastic modulus of the anchor rod, k 2 is the shear stiffness of the grouting layer-surrounding rock interface, L 1 is the length of the anchor rod in the tension section, P 1 is the pull-out load at the end of the tension section of the anchor, u a1 is the pull-out displacement at the end of the tension section of the anchor rod.

[0018] In the first aspect, the determination method includes calculating the load-displacement relationship of the compression section of the anchor rod under the pulling condition by the following formula:

[0019] (3)

[0020] in, is the elastic modulus of the grouting layer, n is the anchor number of the compression section, n The value range is 1~5. L 2_n For the n Anchor length of compression section, P 2_n For the n The tensile load at the end of the compression section of the anchor bolt, u a2_n For the n The pull-out displacement at the end of the compression section of the anchor bolt.

[0021] In a first aspect, the determination method includes establishing the anchor tension section and the anchoring force of the anchor tension section by the following formula:

[0022] Tensile section: (4)

[0023] Compression section: (5)

[0024] in, is the bonding strength between the grouting layer and the surrounding rock interface, is the anchorage force of the tension section, is the anchoring force of the nth compression section.

[0025] In a first aspect, the determination method includes establishing equations for the tension section and the compression section of the anchor bolt using the following formula:

[0026] The resultant force at the junction of the tension section and the first compression section anchor:

[0027]

[0028] At the junction of the second compression section anchor bolt and the first compression section anchor bolt:

[0029]

[0030] At the junction of the nth compression section anchor bolt and the n-1th compression section anchor bolt:

[0031] .

[0032] In a first aspect, the determination method includes establishing equations for the tension section and the compression section of the anchor bolt using the following formula:

[0033] The thickness of the yield layer required at the junction of the tension section and the first compression section anchor for:

[0034]

[0035] The thickness of the pressure relief layer required between the anchor rod in the second compression section and the first compression section for:

[0036]

[0037] in, is the tensile deformation of the anchor rod in the first compression section

[0038] The thickness of the yield layer required between the anchor rod in the nth compression section and the n-1th compression section for:

[0039]

[0040] in, For the n -1Tensile deformation of anchor bolts in compression section.

[0041] In the first aspect, the determination method includes obtaining the anchoring force of the anchor rod by the following formula: ,in:

[0042] ;

[0043] in, is the drill hole diameter; is the bonding strength of the grouting layer-surrounding rock interface;L 2_n For the n Anchor length of compression section; L 2_1 For the 1 Anchor rod length of compression section.

[0044] In the first aspect, the length of the anchor rod ranges from 3m to 6m, and the number of yield units ranges from 1 to 5.

[0045] The beneficial effects of the present invention are as follows:

[0046] The method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor proposed in the present invention is faster and more effective than a pull-out test, and is convenient for designers and scientific researchers to better understand and calculate; it reveals the load transfer mechanism of the multi-stage yield anchor during the pull-out process, and provides an important calculation basis for evaluating the anchoring effect of the multi-stage yield anchor and designing under different anchor lengths and surrounding rock conditions; it avoids a large number of anchor pull-out tests caused by different anchor diameters, borehole diameters, anchor lengths, number of yield units and distribution patterns; it first determines the bond strength and shear stiffness of the grouting layer-surrounding rock interface, fully considering the distribution pattern of the shear stress at the grouting layer-surrounding rock interface, and avoids the error caused by using the average shear stress of the interface to evaluate the anchoring force of the anchor, so that the anchoring force determined thereby is more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the embodiments of this specification or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0048] Figure 1 This is a flowchart of a method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor rod according to the present invention;

[0049] Figure 2 This is a schematic diagram of the multi-stage yield anchor structure of the present invention;

[0050] Figure 3 The diagrams for analyzing the tension section of the anchor rod according to the present invention are shown in Figure 1. (a) is the overall force diagram, (b) is the anchor rod force diagram, and (c) is the grouting layer force diagram.

[0051] Figure 4 The stress analysis diagram of the compression section of the anchor rod of the present invention; (a) is the overall stress diagram, and (b) is the stress analysis diagram of the grouting layer;

[0052] Figure 5 This is a schematic diagram of the multi-stage yield anchor rod pulling process of the present invention;

[0053] Figure 6 This is a tensile stress-strain curve diagram of the anchor rod body according to the first embodiment of the present invention;

[0054] Figure 7 This is a shear stress-displacement curve diagram of the grouting layer-surrounding rock interface in Example 1 of the present invention;

[0055] In the figure: 1: Anchor rod tension section, 2: Anchor rod first compression section, 3: Anchor rod second compression section, 4: Anchor rod third compression section, 5: First pressure-yielding unit, 6: Second pressure-yielding unit, 7: Third pressure-yielding unit, 8: Anchor plate, 9: Nut. DETAILED DESCRIPTION

[0056] The following will be combined with the accompanying drawings to clearly and completely describe the technical solutions of the present invention. Obviously, the embodiments described are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field are within the scope of protection of the present invention.

[0057] Example 1:

[0058] like Figure 1-Figure 7 As shown, this embodiment 1 provides a method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor, wherein the multi-stage yield anchor consists of a tension section, a plurality of compression sections, and a yield unit. Specifically, the multi-stage yield anchor includes an anchor tension section 1, a first anchor compression section 2, a second anchor compression section 3, a third anchor compression section 4, a first yield unit 5, a second yield unit 6, a third yield unit 7, an anchor plate 8, and a nut 9.

[0059] The method for determining the anchoring force and yield layer thickness of the multi-stage yield anchor includes:

[0060] Obtaining the shear strength and stiffness of the grouting layer-surrounding rock interface: Through indoor direct shear tests on the rock-grouting interface obtained on site, the shear stress-displacement curves of the grouting layer-surrounding rock interface under different normal stress conditions are obtained, thereby obtaining the bond strength and shear stiffness of the grouting layer-surrounding rock interface;

[0061] Performing a tensile test on the anchor rod body to obtain a full stress-strain curve of the anchor rod body under tensile conditions, fitting a constitutive model of the anchor rod body, and determining stress and strain point data of a plastic platform section and a hardening section of the anchor rod body;

[0062] Substituting the surrounding rock-grouting layer interface bond strength and shear stiffness into the anchor bolt load-displacement relationship formula under pullout conditions in the anchor bolt tension section, the shear stress distribution law at the grouting layer-surrounding rock interface in the anchor bolt tension section is obtained, and the peak pullout force and pullout displacement of the anchor bolt tension section are obtained;

[0063] Similarly, the surrounding rock-grouting layer interface bond strength and shear stiffness are substituted into the anchor bolt load-displacement relationship formula under pullout conditions in the anchor bolt compression section to obtain the shear stress distribution law at the grouting layer-surrounding rock interface in the anchor bolt compression section, and the peak pullout force and pullout displacement of the anchor bolt compression section are obtained.

[0064] An equation is established using the previously obtained load-displacement relationship of the tension and compression sections of the anchor rod, the constitutive model of the anchor rod material, the stress-strain point data of the plastic platform section and the hardened section of the anchor rod, and the total pull-out displacement of the anchor rod end. Under the condition that the grouting layer-surrounding rock interface of the tension and compression sections of the anchor rod reaches its peak value at the same time, the load and displacement of the tension and compression sections of the anchor rod at this time are obtained. The sum of the loads of the tension section and all the compression sections is the anchoring force of the anchor rod, and the difference in displacement between the two adjacent sections is the thickness of the yield layer required at the connection between the two sections.

[0065] Specifically, for the technical solution of the first embodiment described above, the bond strength and shear stiffness of the grouting layer-surrounding rock interface are obtained through an indoor direct shear test of the grouting layer-surrounding rock interface. Then, a tensile test is performed on the anchor rod body to obtain the tensile stress-strain curve of the anchor rod body, and a tensile constitutive model of the anchor rod body is fitted. Furthermore, the obtained bond strength and shear stiffness of the grouting layer-surrounding rock interface are substituted into the load-displacement formulas of the tension and compression anchor rods to obtain the peak pullout force and corresponding peak displacement of the tension and compression anchor rods. Finally, based on the deformation coordination relationship, the anchoring force of the multi-stage yield anchor rod is the sum of the anchoring forces of all tension and compression anchor rods, and the required thickness of the nth yield layer is the sum of the thickness of the n-1th yield layer and the tensile deformation of the n-1th compression anchor rod. In particular, for the first yield layer, the required thickness of the yield layer is the difference between the peak displacement of the tension anchor rod and the peak displacement of the first compression anchor rod. Preferably, the anchor rod is made of HPB500 steel with a diameter of D1 = 25 mm and an elastic modulus of E a =210GPa; borehole diameter D2=42mm, anchor length 4m, let pressure unit set 2 ( n =2), the anchor rod is divided into 3 sections, each section is about 1.33m, that is L 1= L 2_1 = L 2_2 =1.33m; grouting material uses OPC 42.5 cement, water-cement ratio 0.35, age 7d, elastic modulus E g =10 GPa, shear modulus G g =8.3 GPa; the surrounding rock type is mudstone, with a uniaxial compressive strength of 4.5 MPa.

[0066] According to the indoor direct shear test of the grouting layer-surrounding rock interface, the bond strength and shear stiffness of the grouting layer-surrounding rock interface are obtained as follows: τ s =3.5 MPa, k 2=15.3 GPa / m

[0067] In some possible implementations, the calculation method includes fitting the following formula to obtain a constitutive model of the tension of the anchor rod body:

[0068] (1)

[0069] in, σ p0 and σ pf Indicates the initial yield stress and ultimate stress of the anchor; F and u Indicates the tensile force and tensile deformation of the anchor; m and n is the fitting parameter; u e is the elastic limit deformation, which can be expressed as .

[0070] Specifically, the following table shows the test parameters of the tensile constitutive model of the anchor rod body obtained by performing a tensile test on the anchor rod body, obtaining the full stress-strain curve of the anchor rod body under tensile conditions, and fitting:

[0071] Table 1 Fitting parameters of the constitutive model of the core material

[0072] Material <![CDATA[σ p0 ]]> <![CDATA[σ pf ]]> m n HPB500 453.5 MPa 634.7 MPa -367.2 1.82

[0073] In some possible implementations, the calculation method includes calculating the peak pull-out force of the tension section and the compression section of the anchor rod using the following formula:

[0074] Tensile section: (2)

[0075] The first pressure section: (3)

[0076] The second compression section: (4)

[0077] Among them, α and β are the influence coefficients of the tension section and the compression section, respectively, which can be expressed as:

[0078] (5)

[0079] Specifically, according to formulas (2) to (4), the anchoring forces of the tension section, the first compression section, and the second compression section of the anchor rod are determined to be 106 kN, 142 kN, and 142 kN, respectively.

[0080] In some possible implementations, the calculation method includes calculating the peak displacements of the tension section and the compression section of the anchor bolt using the following formula:

[0081] Tensile section: (6)

[0082] The first pressure section: (7)

[0083] The second compression section: (8)

[0084] Specifically, according to formulas (6) to (8), the peak displacements of the anchor tension section, the first compression section, and the second compression section are determined to be 0.2 mm, 5 mm, and 5 mm, respectively.

[0085] In some possible implementations, the calculation method includes calculating the axial force of the compression section of the anchor bolt using the following formula:

[0086] The first pressure section: (9)

[0087] The second compression section: (10)

[0088] Specifically, according to formulas (9) and (10), the axial forces of the first and second compression sections of the anchor bolt are determined to be 249 kN and 391 kN, respectively. Substituting the axial forces of the first and second compression sections into the tensile constitutive relationship of the anchor bolt body in formula (1), the tensile deformations of the first and second compression sections of the anchor bolt are obtained to be 32 mm and 140 mm, respectively.

[0089] In some possible implementations, the calculation method includes calculating the required thicknesses of the first yield layer and the second yield layer using the following formula:

[0090] First yield layer: (11)

[0091] Second yield layer: (12)

[0092] Specifically, according to formula (11) and formula (12), the required thicknesses of the first and second yield layers of the anchor rod are determined to be 5 mm and 37 mm, respectively.

[0093] In some possible implementations, the calculation method includes calculating the anchoring force of the anchor rod by the following formula: F a :

[0094] (13)

[0095] Specifically, according to formula (13), the anchoring force of the anchor rod is determined to be 391 kN.

[0096] Since the second embodiment and the first embodiment are embodiments of the same inventive concept and some of their structures are exactly the same, the structures in the second embodiment that are essentially the same as those in the first embodiment will not be elaborated in detail. For the parts not described in detail, please refer to the first embodiment.

[0097] Finally, it should be noted that the above embodiments are only specific implementations of the present invention, which are used to illustrate the technical solutions of the present invention, rather than to limit them. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that any person skilled in the art can modify or easily conceive of changes to the technical solutions described in the above embodiments within the technical scope disclosed by the present invention, or replace some of the technical features therein with equivalents. However, these modifications, changes, or replacements do not deviate from the essence of the corresponding technical solutions within the scope of the technical solutions of the embodiments of the present invention. They should all be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

[0098] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the description and implementation methods. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor, characterized in that: as follows: Step 1: Conducting an indoor direct shear test on the rock-grout bonding interface obtained on site to obtain shear stress-displacement curves of the grouting layer-surrounding rock interface under different normal stress conditions, thereby obtaining the bonding strength and shear stiffness of the grouting layer-surrounding rock interface; Step 2: Perform a tensile test on the anchor rod body to obtain the full stress-strain curve of the anchor rod body under tensile conditions, fit the constitutive model of the anchor rod body material, and determine the stress and strain point data of the plastic platform section and hardening section of the anchor rod body; Step 3: Substituting the surrounding rock-grouting layer interface bond strength and shear stiffness into the anchor load-displacement relationship formula of the anchor tension section under pull-out conditions, obtaining the shear stress distribution law of the grouting layer-surrounding rock interface of the anchor tension section, and obtaining the peak pull-out force and pull-out displacement of the anchor tension section; Step 4: Substitute the surrounding rock-grouting layer interface bond strength and shear stiffness into the anchor bolt load-displacement relationship formula of the anchor bolt compression section under pullout conditions to obtain the shear stress distribution law of the grouting layer-surrounding rock interface of the anchor bolt compression section, and obtain the peak pullout force and pullout displacement of the anchor bolt compression section; Step 5 establishes an equation with the load-displacement relationship of the tension section and the compression section of the anchor obtained in steps 2, 3 and 4, the constitutive model of the anchor body material, the stress-strain point data of the plastic platform section and the hardened section of the anchor, and the total pull-out displacement of the anchor end. Under the condition that the shear load of the grouting layer-surrounding rock interface of the tension section and the compression section of the anchor reaches the peak value at the same time, the load and displacement of the tension section and the compression section of the anchor are obtained at this time. The sum of the loads of the tension section and the compression section of the anchor is the anchoring force of the anchor, and the displacement difference between the tension section and the compression section of the anchor is the yield layer thickness of the anchor.

2. The method for calculating the bond strength and shear stiffness of the grouting layer-surrounding rock interface according to claim 1, characterized in that: The calculation method further includes: The rocks obtained on site were prepared into 100*100*50mm cubic samples. Grouting material of 100*100*100mm was directly poured into the 100*100mm cross section of the sample. After the curing was completed, the bonding strength and shear stiffness of the grouting layer-surrounding rock interface were obtained through indoor direct shear tests.

3. The method for determining the tensile constitutive model of an anchor rod according to claim 1, wherein: The tensile constitutive model of the anchor rod body is obtained by fitting the following formula: in, is the anchor diameter, is the elastic modulus of the anchor rod, σ p0 and σ pf Indicates the initial yield stress and ultimate stress of the anchor; F and u Indicates the tensile force and tensile deformation of the anchor; m and n is the fitting parameter; u e is the elastic limit deformation, which can be expressed as ; L is the anchor rod length.

4. The method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor according to claim 1, characterized in that: The load-displacement relationship of the tension section of the anchor bolt under pull-out conditions is calculated using the following formula: in, is the shear modulus of the grouting layer, is the drilling diameter, is the anchor diameter, is the elastic modulus of the anchor, k2 is the shear stiffness of the grouting layer-surrounding rock interface, L 1 is the length of the anchor rod in the tension section, P 1 is the pull-out load at the end of the tension section of the anchor, u a1 is the pull-out displacement at the end of the tension section of the anchor rod.

5. The method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor according to claim 4, characterized in that: The load-displacement relationship of the compression section of the anchor bolt under tension conditions is calculated using the following formula: in, is the drilling diameter, is the anchor diameter, is the elastic modulus of the grouting layer, n is the anchor number of the compression section, n The value range is 1~5. L 2_n For the n Anchor length of compression section, P 2_n For the n The tensile load at the end of the compression section of the anchor bolt, u a2_n For the n The pull-out displacement of the end of the compression section of the anchor bolt; k 2 is the shear stiffness of the grouting layer-surrounding rock interface; k2 is the shear stiffness of the grouting layer-surrounding rock interface.

6. The method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor according to claim 4, characterized in that: The anchoring forces of the tension and compression sections of the anchor bolts are established using the following formulas: Tensile section: Compression section: in, is the bonding strength between the grouting layer and the surrounding rock interface, is the anchorage force of the tension section, is the anchoring force of the nth compression section.

7. The method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor according to claim 4, characterized in that: The equations for the tension and compression sections of the anchor bolt are established using the following formula: The resultant force at the junction of the tension section and the first compression section anchor: At the junction of the second compression section anchor bolt and the first compression section anchor bolt: At the junction of the anchor rod of the nth compression section and the anchor rod of the n-1th compression section: 。 8. The method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor according to claim 4, characterized in that: The equations for the tension and compression sections of the anchor bolt are established using the following formula: The thickness of the yield layer required at the junction of the tension section and the first compression section anchor for: The thickness of the pressure relief layer required between the anchor rod in the second compression section and the first compression section for: in, is the tensile deformation of the anchor rod in the first compression section The thickness of the yield layer required between the anchor rod in the nth compression section and the n-1th compression section for: in, For the n -1Tensile deformation of anchor bolts in compression section.

9. The method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor according to claim 4, characterized in that: The anchoring force of the anchor rod is obtained by the following formula: ,in: ； in, is the drill hole diameter; is the bonding strength of the grouting layer-surrounding rock interface; L 2_n For the n Anchor length of compression section; L 2_1 For the 1 Anchor rod length of compression section.

10. The method for determining the anchoring force and yield layer thickness of a multi-stage yield anchor according to claim 1, characterized in that: The length of the anchor rod ranges from 3m to 6m, and the number of yield units ranges from 1 to 5.

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