A calculation method for axial force distribution of core soil full-length bonded tension anchor

Abstract

The present invention provides a method for calculating the axial force distribution of a core soil full-length bonded tension anchor rod, the method comprising: performing a force analysis on the anchor rod stress micro-unit to obtain the corresponding anchor body control differential equation and the axial force analytical formula; according to the anchor body control differential equation and the axial force analytical formula of the stress micro-unit, a full-length bonded tension anchor rod mechanical model is established according to the deformation continuity at the stress micro-unit segment and the linear elastic relationship between the shear stress and the shear displacement; according to the mechanical model, the formation and anchor rod parameters are substituted to calculate the axial force of the full-length bonded tension anchor rod. The present invention proposes a core soil full-length bonded tension anchor rod mechanical model, which conforms to the actual working state of the tension anchor rod and can consider the influence of the excavation sequence of the double-side wall method side pilot hole, and is used to predict the axial force of the tension anchor rod at a certain position, providing a reference for the design and construction of the tension anchor rod, and can further obtain the distribution curve of the axial force of the full-length bonded tension anchor rod along the entire length of the rod body, and the axial force distribution curve can be obtained by only inputting simple geological survey parameters.

Description

Technical Field

[0001] The invention relates to the technical field of geotechnical engineering measurement and calculation, and in particular to a method for calculating the axial force distribution of a core soil full-length bonded tension anchor. Background Art

[0002] The double sidewall method is an excavation method used for large-span tunnels in soft rock formations. It refers to dividing the large-span tunnel into three small-span sections, excavating the left and right pilot tunnels in turn, and finally excavating the reserved core soil. In specific construction, the excavation of the left and right pilot tunnels will cause severe disturbance to the core soil, causing the core soil to be in an unfavorable unidirectional or bidirectional stress state. If the core soil is damaged on a large scale, the risk of instability of the large-span tunnel will increase dramatically. Therefore, the core of the double sidewall method is to ensure the stability and firmness of the reserved core soil. In order to ensure the safe construction of large-span tunnels using the double sidewall method, full-length bonded tension anchors (referred to as tension anchors) are usually used to effectively support the core soil.

[0003] The full-length bonded tension anchor directly penetrates the core soil, with prestress applied at both ends. Its layout range is generally from the inner arch foot to the inner arch waist of the guide holes on both sides, with a layout interval of 0.5m-1.5m. The anchor length is the width of the core soil at the location. Depending on the surrounding rock conditions, the applied prestress range is 50-150kN.

[0004] However, the mechanical properties of full-length bonded tension anchors, especially the distribution law of the longitudinal axial force along the rod body, are still unclear. It is necessary to distinguish full-length bonded tension anchors from non-bonded anchors and traditional grouting anchors, and design an analysis method for the axial force of full-length bonded tension anchors considering the excavation sequence of side guide tunnels. Summary of the invention

[0005] The purpose of the present invention is to provide a method for calculating the axial force distribution of a core soil full-length bonded tension anchor rod to solve the problems raised in the above-mentioned background technology.

[0006] To achieve the above object, the present invention adopts the following technical solution:

[0007] A method for calculating the axial force distribution of a core soil full-length bonded tension anchor includes the following steps:

[0008] S1. Perform force analysis on the anchor micro-unit to obtain the corresponding anchor body control differential equation and axial force analytical formula;

[0009] S2. According to the anchor body control differential equation and axial force analytical formula of the stressed micro-unit, the deformation of the stressed micro-unit segment is continuous and the shear stress and shear displacement are in a linear elastic relationship, and a full-length bonded tension anchor mechanical model is established;

[0010] S3. According to the mechanical model, the formation and anchor parameters are substituted to calculate the axial force of the full-length bonded tension anchor.

[0011] Furthermore, the stress analysis of the anchor micro-unit is carried out to obtain the corresponding anchor body control differential equation and axial force analytical formula, including:

[0012] S11, separating the tension anchor from the slurry and dividing it into a concrete section and a surrounding rock section;

[0013] S12. Perform stress analysis on the concrete segment separately and obtain the corresponding anchor body control differential equation and axial force analytical formula:

[0014] According to the actual force of the tension anchor rod being in a balanced state, it can be obtained:

[0015]

[0016] Simplified, we get:

[0017] Where: d s is the diameter of the full-length bonded tension anchor, dr is the length of the micro-unit to be removed, σ s (r) is the axial stress of the tension anchor, τ(r) is the shear stress at the anchor or slurry interface;

[0018] According to the Hooke elasticity assumption, we have:

[0019] Where: E a is the elastic modulus of the full-length bonded tension anchor, S e is the deformation of the anchor rod;

[0020] Combining equation (2) and equation (3), we get:

[0021] Assuming that the relationship between the shear stress and shear displacement of the bolt or slurry interface is in a linear elastic state, we get:

[0022]

[0023] Where: S s is the shear displacement of the anchor or slurry interface;

[0024] Assuming that the deformation of the anchor and the grout is coordinated, we get: S s =S e (6)

[0025] By combining equations (4)-(6), we can get the differential governing equation of the full-length bonded tension anchor system:

[0026]

[0027] Where: G c is the shear modulus of the concrete segment;

[0028] For the full-length bonded tension anchor, the boundary equation of the concrete segment is:

[0029]

[0030] Where: P is the preload at both ends of the full-length bonded tension anchor, A is the cross-sectional area of ​​the rod, and A = πds 2 / 4;

[0031] Substituting the length of the concrete segment r = a, the boundary equation of the concrete segment is:

[0032]

[0033] Where: P a is the axial force at the segmentation between the concrete segment and the surrounding rock segment;

[0034] Substituting formula (8) into formula (7), we get:

[0035]

[0036]

[0037] Among them: Undetermined coefficient

[0038] Taking the length of the concrete section r = a, for the concrete section, the shear displacement of the anchor or slurry interface at the connection between the concrete section and the surrounding rock section is expressed as:

[0039]

[0040] S13. Perform stress analysis on the surrounding rock section separately and obtain the corresponding anchor body control differential equation and axial force analytical formula:

[0041] According to step S12, the governing differential equation of the surrounding rock segment is obtained:

[0042]

[0043] Where: G s is the shear modulus of the surrounding rock segment;

[0044] For an anchor with a length of l, the boundary equation of the surrounding rock section is:

[0045]

[0046]

[0047] Substituting formula (14) into formula (13), we get:

[0048]

[0049]

[0050] Among them: Undetermined coefficient

[0051]

[0052] Taking the length of the concrete section r = a, for the surrounding rock section, the shear displacement of the anchor or slurry interface at the connection between the concrete section and the surrounding rock section is expressed as:

[0053]

[0054] The concrete section and the surrounding rock section are combined into a whole for stress analysis, and the axial force values ​​at the segment are obtained according to the continuous deformation of the concrete section and the surrounding rock section:

[0055]

[0056] Furthermore, according to the anchor body control differential equation and axial force analytical formula of the stressed micro-unit, the deformation of the stressed micro-unit segment is continuous and the shear stress and shear displacement are in a linear elastic relationship. A mechanical model of the full-length bonded tension anchor is established, including:

[0057] S21. Substitute formula (18) into steps S12 and S13 to obtain the analytical formula for the axial stress of the full-length bonded tension anchor:

[0058]

[0059] S22. Multiply the anchor axial stress by the cross-sectional area of ​​the rod to obtain the analytical formula of the mechanical model of the axial force of the full-length bonded tension anchor: P r =Aσ s (20).

[0060] Furthermore, based on the mechanical model of the axial force of the full-length bonded tension anchor, the corresponding axial force distribution curve can be established in combination with the length of the tension anchor and the corresponding anchor axial force.

[0061] It can be seen from the above technical scheme that the present invention proposes a mechanical model of the core soil full-length bonded tension anchor rod, which conforms to the actual working state of the tension anchor rod and is used to predict the axial force of the tension anchor rod at a certain position, providing a reference for the design and construction of the tension anchor rod, and can consider the influence of the excavation sequence of the double-side wall method side guide tunnel, and can further derive the distribution curve of the axial force of the full-length bonded tension anchor rod along the entire length of the rod body. Only by inputting simple geological survey parameters, the axial force distribution curve can be obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1Schematic diagram of the double-side wall method core soil full-length bonded tension anchor

[0063] Figure 2 It is a schematic diagram of the steps of the present invention;

[0064] Figure 3 It is a schematic diagram of the mechanical model of the full-length bonded tension anchor;

[0065] Figure 4 This is the on-site measured layout diagram of the full-length bonded tension anchor rod;

[0066] Figure 5 A corresponding axial force distribution curve is established for a mountain tunnel according to the calculation method of the present invention.

[0067] In the figure: 1. Left pilot tunnel; 2. Right pilot tunnel; 3. Reserved core soil; 4. Tension anchor rods; 5. Anchor pads; 6. Initial support concrete; A is the concrete section; B is the surrounding rock section. DETAILED DESCRIPTION

[0068] A preferred embodiment of the present invention is described in detail below with reference to the accompanying drawings.

[0069] like Figure 1 The schematic diagram of the double-side wall method core soil full-length bonded tension anchor is shown. The large-span tunnel is excavated using the double-side wall method. The left pilot tunnel 1 is excavated first, the right pilot tunnel 2 is excavated later, and the reserved core soil 3 is excavated last; the full-length bonded tension anchor 4 is used to support the core soil 5. The tension anchor runs through the core soil, including a rod body and anchor pads arranged on the inner sides of the left and right pilot tunnels, and prestress P is applied at both ends; the rod body material of the tension anchor is HRB335 steel bar, and its yield elongation can reach 18%; after the first pilot tunnel is excavated, the initial support concrete 6 is applied, so that the full-length bonded tension anchor has two anchoring layer media, which can be divided into a concrete section and a surrounding rock section.

[0070] like Figure 2 The calculation method of the axial force distribution of the core soil through-length bonded tension anchor shown in the figure includes the following steps:

[0071] S1. Perform force analysis on the anchor micro-unit to obtain the corresponding anchor body control differential equation and axial force analytical formula;

[0072] Specifically, Figure 3 As shown in the figure, the tension anchor is first separated from the grout and divided into a concrete section and a surrounding rock section, and the following reasonable assumptions are made:

[0073] (1) It is generally believed that the bolt or slurry is the most dangerous interface, so the present invention only studies the mechanical response of this interface;

[0074] (2) In addition, according to existing actual measurements, after the tension anchor rods were installed and the full-length grouting was performed, the stress state of the core soil was significantly improved, and the internal relative deformation was less than 8 mm. Therefore, the present invention assumes that the relative deformation of the anchor rod, grout and rock and soil is small, and that the deformation of the anchor rod and grout is coordinated with each other;

[0075] (3) Engineering practice shows that the tension anchor rod usually does not enter the plastic yield stage due to the good ductility of the steel bar body and the high material strength. Therefore, the present invention considers that it is in an elastic working state, and the axial force analytical formula derived from it is relatively simple and convenient for application and promotion;

[0076] (4) For large-span tunnels constructed by the double-sidewall method, the left and right pilot tunnels are usually excavated in sequence, usually with a lag distance of more than twice the tunnel diameter. The present invention assumes that the left pilot tunnel is excavated first. The full-length bonded tension anchor rods are installed immediately after the excavation of the rear right pilot tunnel. At this time, the initial support of the left pilot tunnel has been closed into a ring, and the strength and stiffness are relatively large; while the rear right pilot tunnel is still in a rough hole state, or the initial support has been installed not long ago, and the support structure is far from reaching the design strength value, and it is regarded as ordinary surrounding rock.

[0077] (5) Based on the above assumptions and the advantages and disadvantages of mechanical properties, the anchoring medium of the full-length bonded tension anchor is divided into two sections: the concrete section and the surrounding rock section. The concrete section is a stronger concrete anchoring medium near the leading left guide tunnel, and the surrounding rock section is a weaker surrounding rock anchoring medium near the trailing right guide tunnel. The length of the tension anchor is l, and the length of the concrete section is the concrete section. The concrete section and the surrounding rock section can be called the concrete section and the surrounding rock section respectively. The main difference between the two sections is that the friction resistance that the two sections of the anchor / paste interface can provide is different, which leads to different shear moduli. The shear modulus of the concrete section is Gc, and the shear modulus of the surrounding rock section is Gs. The shear modulus is closely related to the friction resistance of the anchor / paste interface and the normal stress, and the value is generally determined by on-site pull-out tests.

[0078] Then, the stress analysis of the concrete segment is performed separately to obtain the corresponding anchor body control differential equation and axial force analytical formula:

[0079] According to the actual force of the tension anchor rod being in a balanced state, it can be obtained:

[0080]

[0081] Simplified, we get:

[0082] Where: d s is the diameter of the full-length bonded tension anchor, dr is the length of the micro-unit to be removed, σ s (r) is the axial stress of the tension anchor, τ(r) is the shear stress at the anchor or slurry interface;

[0083] According to the Hooke elasticity assumption, we have:

[0084] Where: E a is the elastic modulus of the full-length bonded tension anchor, S e is the deformation of the anchor rod;

[0085] Combining equation (2) and equation (3), we get:

[0086] Assuming that the relationship between the shear stress and shear displacement of the bolt or slurry interface is in a linear elastic state, we get:

[0087]

[0088] Where: S s is the shear displacement of the anchor or slurry interface;

[0089] Assuming that the deformation of the anchor and the grout is coordinated, we get: S s =S e (6)

[0090] By combining equations (4)-(6), we can get the differential governing equation of the full-length bonded tension anchor system:

[0091]

[0092] Where: G c is the shear modulus of the concrete segment;

[0093] For the full-length bonded tension anchor, the boundary equation of the concrete segment is:

[0094]

[0095] Where: P is the preload at both ends of the full-length bonded tension anchor, A is the cross-sectional area of ​​the rod, and A = πds 2 / 4;

[0096] Substituting the length of the concrete segment r = a, the boundary equation of the concrete segment is:

[0097]

[0098] Where: P a is the axial force at the segmentation between the concrete segment and the surrounding rock segment;

[0099] Substituting formula (8) into formula (7), we get:

[0100]

[0101]

[0102] Among them: Undetermined coefficient

[0103] Taking the length of the concrete section r = a, for the concrete section, the shear displacement of the anchor or slurry interface at the connection between the concrete section and the surrounding rock section is expressed as:

[0104]

[0105] Then the stress analysis of the surrounding rock section is carried out separately, and the corresponding anchor body control differential equation and axial force analytical formula are obtained:

[0106] According to the above steps, the governing differential equation of the surrounding rock section is obtained:

[0107]

[0108] Where: G s is the shear modulus of the surrounding rock segment;

[0109] For an anchor with a length of l, the boundary equation of the surrounding rock section is:

[0110]

[0111]

[0112] Substituting formula (14) into formula (13), we get:

[0113]

[0114]

[0115] Among them: Undetermined coefficient

[0116]

[0117] Taking the length of the concrete section r = a, for the surrounding rock section, the shear displacement of the anchor or slurry interface at the connection between the concrete section and the surrounding rock section is expressed as:

[0118]

[0119] The concrete section and the surrounding rock section are combined into a whole for stress analysis, and the axial force values ​​at the segment are obtained according to the continuous deformation of the concrete section and the surrounding rock section:

[0120]

[0121] S2. According to the anchor body control differential equation and axial force analytical formula of the stressed micro-unit, the deformation of the stressed micro-unit segment is continuous and the shear stress and shear displacement are in a linear elastic relationship, and a full-length bonded tension anchor mechanical model is established;

[0122] Specifically, by substituting formula (18) into step S1, the analytical formula for the axial stress of the full-length bonded tension anchor is obtained:

[0123]

[0124] Then multiply the anchor axial stress by the cross-sectional area of ​​the rod body to obtain the analytical formula of the mechanical model of the axial force of the full-length bonded tension anchor: P r =Aσ s (20).

[0125] S3. According to the mechanical model, the formation and anchor parameters are substituted to calculate the axial force of the full-length bonded tension anchor.

[0126] In the specific measurement, based on the mechanical model of the axial force of the full-length bonded tension anchor, the corresponding axial force distribution curve can also be established in combination with the length of the tension anchor and the corresponding anchor axial force.

[0127] For example, a mountain tunnel uses a full-length bonded tension anchor, and its mechanical parameters are shown in Table 1;

[0128] Table 1 Design parameters of tension anchors

[0129]

[0130] By adopting the calculation method of the present invention and substituting the formation and tension anchor parameters, an analytical solution for the axial force of the full-length bonded tension anchor can be obtained.

[0131] like Figure 4 As shown, anchor dynamometers are used for on-site measurement, and five steel dynamometers, A1, A2, A3, A4, and A5, are arranged on the tension anchors; Figure 5 As shown, the calculated axial force value of the full-length bonded tension anchor rod and the field measured value are compared and analyzed. It can be seen from the theoretical curve of the present invention and the field measured scatter points that the axial force distribution of the full-length bonded tension anchor rod obtained by the calculation method of the present invention is basically consistent with the measured results, showing reliable prediction performance and can provide guidance for design and construction.

[0132] As mentioned above, the present invention has established a mechanical model of the double-side wall method of core soil full-length grouting tension anchor rod, which is different from the bonded or partially bonded anchor rod. It is believed that the anchor rod achieves the anchoring effect through the friction between the anchor rod and the slurry, which can be specifically reflected by the interface shear modulus. The mechanical model is concise and clear, and is convenient for engineering application.

[0133] At the same time, the present invention also proposes a bidirectional tensile stress mode for the full-length bonded tension anchor rod, which is different from the traditional grouting anchor rod and conforms to the actual working state of the tension anchor rod. It assumes that the shear stress and shear displacement are in a linear elastic relationship. The calculation formula is relatively simple and easier to be understood and accepted by designers and construction personnel.

[0134] The present invention also proposes a method for calculating the axial force of a full-length bonded tension anchor rod, taking into account the different anchoring media of the tension anchor rod caused by the different construction sequences of the left and right guide tunnels of the double-side wall method of a large-span tunnel. The calculation results of this method are relatively consistent with the actual situation, thereby improving the scientificity and economy of the design of the full-length bonded tension anchor rod.

[0135] The above-described embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for calculating the axial force distribution of a core soil full-length bonded tension anchor, characterized in that: The following steps are involved: S1. Perform force analysis on the anchor micro-unit to obtain the corresponding anchor body control differential equation and axial force analytical formula; S2. According to the anchor body control differential equation and axial force analytical formula of the stressed micro-unit, the deformation of the stressed micro-unit segment is continuous and the shear stress and shear displacement are in a linear elastic relationship, and a full-length bonded tension anchor mechanical model is established. The specific steps include: S21. Calculate the analytical formula of the axial stress of the full-length bonded tension anchor: （19） S22. Multiply the anchor axial stress by the cross-sectional area of ​​the rod to obtain the analytical formula of the mechanical model of the axial force of the full-length bonded tension anchor: (20); S3. According to the mechanical model, the formation and anchor parameters are substituted to calculate the axial force of the full-length bonded tension anchor.

2. The method for calculating the axial force distribution of the core soil full-length bonded tension anchor according to claim 1 is characterized in that: The stress analysis of the anchor micro-unit is carried out to obtain the corresponding anchor body control differential equation and axial force analytical formula, including: S11, separating the tension anchor from the slurry and dividing it into a concrete section and a surrounding rock section; S12. Perform stress analysis on the concrete segment separately and obtain the corresponding anchor body control differential equation and axial force analytical formula: According to the actual force of the tension anchor rod being in a balanced state, it can be obtained: （1） Simplified, we get: (2) in: is the diameter of the full-length bonded tension anchor rod, To get the length of the microunit, is the axial stress of the tension anchor, is the shear stress at the bolt or slurry interface; According to the Hooke elasticity assumption, we have: (3) in: is the elastic modulus of the full-length bonded tension anchor. is the deformation of the anchor rod; Combining equation (2) and equation (3), we get: (4) Assuming that the relationship between the shear stress and shear displacement of the bolt or slurry interface is in a linear elastic state, we get: (5) in: is the shear displacement of the anchor or slurry interface; Assuming that the deformation of the anchor and the grout is coordinated, we get: (6) Combining equations (4)-(6), we get the differential governing equation of the full-length bonded tension anchor system: ； （7） in: is the shear modulus of the concrete segment; For the full-length bonded tension anchor, the boundary equation of the concrete segment is: （8） in: is the preload at both ends of the full-length bonded tension anchor rod. is the cross-sectional area of ​​the rod, and ; Length of concrete section , then the boundary equation of the concrete segment is: （9） in: is the axial force at the segmentation between the concrete segment and the surrounding rock segment; Substituting formula (8) into formula (7), we get: （10） （11） Among them: Undetermined coefficient ; ; Length of concrete section , for the concrete segment, the shear displacement of the anchor or grout interface at the connection between the concrete segment and the surrounding rock segment is expressed as: （12） S13. Perform stress analysis on the surrounding rock section separately and obtain the corresponding anchor body control differential equation and axial force analytical formula: According to step S12, the governing differential equation of the surrounding rock segment is obtained: ； （13） in: is the shear modulus of the surrounding rock segment; For length The boundary equation of the surrounding rock section is: （14） （15） Substituting equation (14) into equation (13), we get: （15） （16） Among them: Undetermined coefficient Length of concrete section , for the surrounding rock section, the shear displacement of the anchor or grout interface at the connection between the concrete section and the surrounding rock section is expressed as: （17） The concrete section and the surrounding rock section are combined into a whole for stress analysis, and the axial force values ​​at the segment are obtained according to the continuous deformation of the concrete section and the surrounding rock section: （18）。 3. The method for calculating the axial force distribution of the core soil full-length bonded tension anchor according to claim 1 is characterized in that: Based on the mechanical model of the axial force of the full-length bonded tension anchor, the corresponding axial force distribution curve can be established by combining the length of the tension anchor and the corresponding anchor axial force.

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