CN117390872B - Calculation method for ultimate bearing capacity of tunnel anchorage - Google Patents
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Abstract
The invention discloses a calculation method of ultimate bearing capacity of tunnel anchorage, which relates to the technical field of geotechnical engineering and comprises the following steps: s1: determining surrounding rock mechanical parameters of tunnel anchors and structural design parameters of the anchors: s2: respectively considering the influence of gravity and clamping force on the ultimate bearing capacity of the tunnel anchor to obtain a tunnel anchor calculation model; s3: calculating a tunnel anchor pulling resistance P 1 provided by the dead weight of the tunnel anchor through the tunnel anchor calculation model; s4: calculating the clamping force P 2 of surrounding rock to the tunnel anchor through the tunnel anchor calculation model; s5: the security of the tunnel anchor under this geological condition was evaluated according to P 1 and P 2. The scheme is suitable for the suspension bridge to respectively consider and calculate the ultimate anti-pulling bearing capacity of the tunnel anchor in the inverted cone frustum failure mode by taking the gravity and the clamping force under different geological conditions, and the anti-sliding stable safety coefficient is obtained to evaluate the bearing capacity of the tunnel anchor.
Description
Technical Field
The invention relates to the technical field of geotechnical engineering, in particular to a calculation method of tunnel type anchorage ultimate bearing capacity.
Background
The mountain areas in the middle and western regions of China are widely distributed, a rapid, convenient and efficient traffic network is built in the mountainous areas, and a large number of bridges and tunnels are connected by continuously crossing mountain bodies, valleys and water systems. When the suspension bridge is connected with the tunnel, the suspension bridge usually adopts tunnel type anchorage, and the clear distance between the tunnel type anchorage and the tunnel is smaller. The application range of the tunnel anchor is gradually wide, and the tunnel anchor is not limited to hard surrounding rocks, such as a Ludingham bridge, a Lijiang railway Jinsha river bridge, a Taihong Yangtze river bridge and other projects under different geological conditions. Tunnel anchorage is an important component in a suspension bridge bearing system and plays a quite critical role, so that the safety evaluation of the tunnel anchorage is very important. In recent years, related researches on tunnel anchors at home and abroad are more and more, and different students analyze the damage mode, ultimate bearing capacity, influence conditions and the like of the tunnel anchors through numerical simulation and test results. However, the design theory of tunnel anchors is still not mature enough, and the theoretical research is not perfect. Before 2015, related researches on tunnel anchors have not been widely developed, the safety of the tunnel anchors is mostly judged by adopting tests, some students put forward a calculation formula through the tests, and the ultimate balance theory is adopted in the south of the river, so that the calculation formula of the ultimate bearing capacity of the tunnel anchors under different failure modes is provided on the basis of field tests. And then, due to the promulgation of the design specifications of the highway suspension bridge, a scholars Fan Huoyin and the like calculate the ultimate pullout resistance formula of the tunnel anchor according to the specifications. Then, along with the proposal of the concept of the clamping effect, more research teams begin to research the stress characteristics of the tunnel anchor, and scholars Zhang Jihua analyze the damage mode of the tunnel anchor through a field simulation test by utilizing numerical simulation, consider that the damage surface presents a outwards-diffused truncated cone surface shape, establish force system balance on the damage surface, and put forward a calculation formula of the pulling resistance of surrounding rock of the tunnel anchor, so as to embody the clamping effect and the complex stress change on the damage surface. And the scholars Wang Dongying reversely push the clamping force of the anchorage-rock mass interface through the limit friction force to obtain the anti-pulling safety coefficient of the tunnel anchor considering the clamping effect. The clamping effect of the tunnel anchor can enable the tunnel anchor to resist a design load which is several times, and under the effect of the clamping effect, the ultimate bearing capacity of the tunnel anchor is obviously improved, so that the clamping effect is considered when the ultimate bearing capacity is calculated, the complex stress of surrounding rock can be further analyzed, the current calculation method of the bearing capacity of the tunnel anchor is not conserved any more, the design of the tunnel anchor is optimized, and the tunnel anchor is more reasonable.
Through the retrieval of Chinese patent networks and related paper websites, only the Chinese patent application file of CN201610013796.3, namely a method for evaluating the tunnel type anchorage bearing capacity of a suspension bridge, and the Chinese patent application file of CN202110464256.8, namely a method and equipment for determining the ultimate drawing bearing capacity of the tunnel type anchorage, are related patents of a tunnel type anchorage bearing capacity calculation method at present, but the change of stress distribution caused by additional stress generated by clamping effect is not considered. The scholars Zhang Jihua and Wang Dongying respectively propose different tunnel anchor limit bearing capacity calculation methods considering the clamping effect, but numerical simulation is respectively needed, and the calculation can be performed only by obtaining data through field test. It can be seen that although the research on the tunnel anchor mechanics starts to increase due to the proposal of the clamping effect, the generated problems are gradually solved, but the theoretical basis is still not perfect, and the analysis on the tunnel anchor mechanics needs to be further carried out. Therefore, it is highly desirable to establish an efficient, rational, and convenient computing method.
Disclosure of Invention
The invention aims to solve the defects of the prior art, and provides a method for calculating the ultimate bearing capacity of a tunnel anchorage, which is suitable for a suspension bridge to respectively consider and calculate the ultimate anti-pulling bearing capacity of the tunnel anchor in an inverted cone frustum failure mode by gravity and clamping force under different geological conditions, so as to obtain an anti-slip stable safety coefficient and evaluate the bearing capacity of the tunnel anchor.
The invention is realized by the following technical scheme:
A calculation method of the ultimate bearing capacity of tunnel anchorage comprises the following steps:
s1: determining surrounding rock mechanical parameters of the tunnel anchor and structural design parameters of the anchorage body;
s2: respectively considering the influence of gravity and clamping force on the ultimate bearing capacity of the tunnel anchor to obtain a tunnel anchor calculation model;
s3: calculating a tunnel anchor pulling resistance P 1 provided by the dead weight of the tunnel anchor through the tunnel anchor calculation model;
S4: calculating the clamping force P 2 of surrounding rock to the tunnel anchor through the tunnel anchor calculation model;
S5: the security of the tunnel anchor under this geological condition was evaluated according to P 1 and P 2.
In a further aspect, the step S2 further includes the following steps:
and simplifying a stress model of the tunnel anchor according to the inverted cone frustum failure mode to preliminarily obtain a calculation model of the tunnel anchor.
In a further aspect, the calculation model of the tunnel anchor pullout resistance P 1 is:
wherein: w is the dead weight of the anchorage body; alpha is the inclination angle of the anchorage body; beta is the expansion angle of the anchorage body; Is the internal friction angle of the anchorage body.
In a further aspect, the step S4 includes the following steps:
s41: in order to obtain the clamping force P 2 of the surrounding rock to the tunnel anchor, the surrounding rock is required to be used as a separator, and the section of the separator comprises an upper long side AB, an upper short side BC, a top side CD and a lower side AD;
The forces to which the separator is subjected include: the clamping force N 1 of the AB edge of the isolator and the cohesive force c of the anchorage body and surrounding rock; shear S at the side of the separator AD and lateral rock mass pressure N 2; the dead weight W 2 of the surrounding rock;
s42: and then carrying out stress analysis on the anchorage body to obtain the clamping force P 2 of the surrounding rock on the tunnel anchor.
In a further aspect, the calculation model of the shearing force S is:
wherein: a is the area of the broken surface of the tunnel anchoring truncated cone.
In a further aspect, the calculation model of the lateral rock pressure N 2 is:
Wherein: z is the distance from the front end of the front anchor chamber to the calculation point, gamma 1 is the weight component of the rock mass perpendicular to the direction of the CD edge,
In a further aspect, the step S42 further includes the following steps:
Before the anchorage body is subjected to stress analysis, force balance analysis is further required to be carried out on the clamping force direction, and N 1 is decomposed into two component forces N x、Ny in the x and y directions; and then carrying out stress analysis on the anchorage body according to the balance analysis result.
In a further aspect, the calculation model of N x、Ny is:
Nx＝N2·sin(α+β-θ)+S·cos(α+β-θ)-c·cos(α+β)；
Ny＝N2·cos(α+β-θ)+c·sin(α+β)-S·cos(α+β-θ)-W2；
in the formula, theta is the diffusion angle of the broken surface of the tunnel anchor.
In a further scheme, when the anchorage body is subjected to stress analysis, the calculation model of the tunnel anchor clamping force P 2 is as follows:
P2＝Nx·cosα-Ny·sinα+c·cosβ。
In a further aspect, the step S5 further includes the following specific steps:
Obtaining the ultimate bearing capacity P u＝P1+P2 of the tunnel anchor according to P 1 and P 2, and calculating the stability safety coefficient K=P u/P of the tunnel anchor against pulling, wherein P is the design load of a single anchorage body; and finally, evaluating the safety of the tunnel anchor under the geological condition according to the anti-pulling stable safety coefficient.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. The method for calculating the ultimate bearing capacity of the tunnel anchorage can further analyze the pulling resistance of the tunnel anchor according to the clamping effect proposed in recent years, provides a mode for calculating the clamping force of surrounding rock of the tunnel anchor, considers the influence of the anchorage body and the clamping force of the surrounding rock on the pulling resistance of the tunnel anchor, has simple and understandable calculation model and definite meaning of the mechanics principle.
2. According to the method for calculating the ultimate bearing capacity of the tunnel anchorage, provided by the invention, the ultimate bearing capacity of the tunnel anchorage is estimated under different geological conditions, so that the theoretical basis of the mechanical characteristics of the tunnel anchorage is perfected, the current situation that the tunnel anchorage is conserved in the current design and calculation methods is improved, and the influence of surrounding rock clamping effect on the calculation mode of the anti-pulling bearing capacity of the tunnel anchorage is primarily researched.
3. The calculation method of the tunnel anchorage ultimate bearing capacity is simple and efficient in calculation, results can be directly obtained without numerical simulation and test, the bearing capacity assessment time is greatly shortened, and the calculation method is visual and accurate through comparison of the assessment results and other related research results, and the traditional calculation method without considering the clamping effect is more conservative.
4. The calculation method of the ultimate bearing capacity of the tunnel anchorage provided by the invention is mainly used for researching the damage mode of the inverted cone frustum of the tunnel anchorage, accords with the research of the current damage mode of the tunnel anchorage, and has great significance for the analysis of the anti-pulling action mechanism of surrounding rock of the tunnel anchorage, the calculation research of the anti-pulling force design and the wide popularization and application of the tunnel anchorage.
Drawings
In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the drawings that are needed in the examples will be briefly described below, it being understood that the following drawings only illustrate some examples of the present invention and therefore should not be considered as limiting the scope, and that other related drawings may be obtained from these drawings without inventive effort for a person skilled in the art. In the drawings:
FIG. 1 is a schematic diagram of a calculation model of a tunnel anchoring truncated cone according to an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating a force analysis of a pullout resistance P 1 provided by a tunnel anchor weight according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a stress analysis of a surrounding rock isolator according to an embodiment of the present invention;
FIG. 4 is a force analysis diagram of a tunnel anchor pullout resistance P 2 provided by a tunnel anchor clamping force according to one embodiment of the present invention;
Fig. 5 is an exploded view of the tunnel anchor clamping force according to one embodiment of the present invention.
Detailed Description
For the purpose of making apparent the objects, technical solutions and advantages of the present invention, the present invention will be further described in detail with reference to the following examples and the accompanying drawings, wherein the exemplary embodiments of the present invention and the descriptions thereof are for illustrating the present invention only and are not to be construed as limiting the present invention.
Example 1: the embodiment 1 provides a method for calculating the ultimate bearing capacity of tunnel anchorage, which is shown in fig. 1-5, and comprises the following specific steps:
Step one, determining mechanical parameters of tunnel anchor surrounding rock:
Analyzing according to geological exploration data of the area where the tunnel anchor engineering is located, determining surrounding rock mechanical parameters, including: severe gamma, cohesive force c, internal friction angle Etc.
Step two, structural design of the anchorage body:
And determining the design parameters such as the inclination angle alpha, the expansion angle beta, the tunnel anchor length L, the tunnel anchor burial depth L0, the broken surface diffusion angle theta, the front end face size and the rear end face size of the tunnel anchor according to the engineering profile.
Step three, obtaining a tunnel anchor calculation model:
and simplifying a stress model of the tunnel anchor according to the inverted cone frustum failure mode to preliminarily obtain a calculation model of the tunnel anchor.
Step four, calculating the pulling resistance P 1 of the tunnel anchor provided by the dead weight of the tunnel anchor:
The influence of gravity and clamping force on the ultimate bearing capacity of the tunnel anchor is respectively considered, the pulling-resistant force P 1 of the tunnel anchor provided by the gravity is calculated firstly, the clamping effect is not considered temporarily, and the anchorage body is subjected to stress analysis, so that
Step five, calculating the clamping force P 2 of surrounding rock to the tunnel anchor:
for the clamping force P 2 of the surrounding rock to the tunnel anchor, the surrounding rock is analyzed as a separator, and as shown in fig. 3, the separator is subjected to the following forces:
AB edge: and the clamping force N 1 to be solved is the cohesive force c of the anchorage body and the surrounding rock.
AD edge: shear forceWherein: a is the area of the broken surface of the tunnel anchoring truncated cone. Lateral rock pressureWherein z is the distance from the front end of the front anchor chamber to the calculation point, gamma 1 is the weight component of the rock mass perpendicular to the CD edge direction,
The dead weight W2 of the surrounding rock.
The force balance analysis is carried out on the clamping force direction, N 1 is decomposed into two component forces N x,Ny in the x and y directions, and the calculation is convenient:
Nx＝N2·sin(α+β-θ)+S·cos(α+β-θ)-c·cos(α+β)；
Ny＝N2·cos(α+β-θ)+c·sin(α+β)-S·cos(α+β-θ)-W2；
And carrying out stress analysis on the anchorage body, wherein P 2＝Nx·cosα-Ny. Sin alpha+c. Cos beta.
Step six: evaluating the security of the tunnel anchor under the geological conditions:
Obtaining the ultimate bearing capacity P u＝P1+P2 of the tunnel anchor, and calculating the anti-pulling stable safety coefficient K=P u/P of the tunnel anchor, wherein P is the design load of a single anchorage body; and finally, evaluating the safety of the tunnel anchor under the geological condition.
Example 2: this example 2 was further optimized on the basis of example 1 to provide a specific embodiment.
A calculation method of the ultimate bearing capacity of tunnel anchorage comprises the following steps:
Step one, determining mechanical parameters of tunnel anchor surrounding rock:
according to a certain bridge geological report and a railway tunnel design specification, determining surrounding rock mechanical parameters comprises the following steps: severe gamma, cohesive force c, internal friction angle Etc.
Step two, structural design of the anchorage body:
And determining the design parameters such as the inclination angle alpha, the expansion angle beta, the tunnel anchor length L, the tunnel anchor burial depth L 0, the broken surface diffusion angle theta, the front end face size and the rear end face size of the tunnel anchor according to the engineering profile.
Step three, obtaining a tunnel anchor calculation model:
as shown in fig. one, according to the inverted cone frustum failure mode, the stress model of the tunnel anchor is simplified, and a calculation model of the tunnel anchor is obtained initially.
Step four, calculating the pulling resistance P 1 of the tunnel anchor provided by the dead weight of the tunnel anchor:
The influence of gravity and clamping force on the ultimate bearing capacity of the tunnel anchor is respectively considered, the pulling-resistant force P 1 of the tunnel anchor provided by the gravity is calculated firstly, the clamping effect is not considered temporarily, and the anchorage body is subjected to stress analysis, so that According to the anchorage design data, the anchorage body weight W= 75023.5kN is obtained, and P 1 is calculated to be 90937.9kN.
Step five, calculating the clamping force P 2 of surrounding rock to the tunnel anchor:
for the clamping force P 2 of the surrounding rock to the tunnel anchor, the surrounding rock is analyzed as a separator, and as shown in fig. 3, the separator is subjected to the following forces:
AB edge: and the clamping force N 1 to be solved is the cohesive force c of the anchorage body and the surrounding rock.
AD edge: shear forceLateral rock pressureWherein, z is the distance from the front end of the front anchor chamber to the calculation point, gamma 1 is the weight component of the rock mass vertical to the CD edge direction, the value is 15.32kN/m 3,N 2 =130307.2kn and s= 847327.04kN were calculated.
The surrounding rock dead weight W 2 = 529161.17kN.
And force balance analysis is carried out on the clamping force direction, N 1 is decomposed into two component forces N x,Ny in the x and y directions, and calculation is convenient.
Nx＝N2·sin(α+β-θ)+S·cos(α+β-θ)-cA·cos(α+β)＝751824.15kN；
Ny＝N2·cos(α+β-θ)+cA·sin(α+β)-S·cos(α+β-θ)-W2＝-1108709.24kN；
Stress analysis was performed on the anchorage, P 2＝Nx·cosα-Ny ·sinα+ca·cosβ= 2307841.09kN.
Step six: evaluating the security of the tunnel anchor under the geological conditions:
the ultimate bearing capacity P u＝P1+P2 = 2398778.99kN of the tunnel anchor is obtained, the stability safety coefficient K=P u/P= 28.85 of the tunnel anchor is calculated, the stability requirement of the tunnel anchor on pulling resistance is met far, and the safety of the tunnel anchor on pulling resistance is high.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the invention, and is not meant to limit the scope of the invention, but to limit the invention to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (6)
1. The calculation method of the ultimate bearing capacity of the tunnel anchorage is characterized by comprising the following steps of:
s1: determining surrounding rock mechanical parameters of the tunnel anchor and structural design parameters of the anchorage body;
s2: respectively considering the influence of gravity and clamping force on the ultimate bearing capacity of the tunnel anchor to obtain a tunnel anchor calculation model;
s3: calculating a tunnel anchor pulling resistance P 1 provided by the dead weight of the tunnel anchor through the tunnel anchor calculation model;
S4: calculating the clamping force P 2 of surrounding rock to the tunnel anchor through the tunnel anchor calculation model;
s5: evaluating the safety of the tunnel anchor under the current geological condition according to P 1 and P 2;
the step S4 includes the steps of:
s41: in order to obtain the clamping force P 2 of the surrounding rock to the tunnel anchor, the surrounding rock is required to be used as a separator, and the section of the separator comprises an upper long side AB, an upper short side BC, a top side CD and a lower side AD;
The forces to which the separator is subjected include: the clamping force N 1 of the AB edge of the isolator and the cohesive force c of the anchorage body and surrounding rock; shear S at the side of the separator AD and lateral rock mass pressure N 2; the dead weight W 2 of the surrounding rock;
s42: then carrying out stress analysis on the anchorage body to obtain the clamping force P 2 of the surrounding rock on the tunnel anchor;
the step S42 further includes the steps of:
Before the anchorage body is subjected to stress analysis, force balance analysis is further required to be carried out on the clamping force direction, and N 1 is decomposed into two component forces N x、Ny in the x and y directions; then carrying out stress analysis on the anchorage body according to the balance analysis result;
The calculation model of N x、Ny is as follows:
Nx＝N2·sin(α+β-θ)+S·cos(α+β-θ)-c·cos(α+β)；
Ny＝N2·cos(α+β-θ)+c·sin(α+β)-S·cos(α+β-θ)-W2；
wherein θ is the diffusion angle of the broken surface of the tunnel anchor;
When the anchorage body is subjected to stress analysis, the calculation model of the tunnel anchor clamping force P 2 is as follows:
P2＝Nx·cosα-Ny·sinα+c·cosβ。
2. The method for calculating the ultimate bearing capacity of a tunnel anchorage according to claim 1, wherein the step S2 further comprises the steps of:
and simplifying a stress model of the tunnel anchor according to the inverted cone frustum failure mode to preliminarily obtain a calculation model of the tunnel anchor.
3. The method for calculating the ultimate bearing capacity of a tunnel anchor according to claim 1, wherein the calculation model of the tunnel anchor pulling resistance P 1 is as follows:
wherein: w is the dead weight of the anchorage body; alpha is the inclination angle of the anchorage body; beta is the expansion angle of the anchorage body; Is the internal friction angle of the anchorage body.
4. The method for calculating the ultimate bearing capacity of a tunnel anchorage according to claim 1, wherein the calculation model of the shearing force S is as follows:
wherein: a is the area of the broken surface of the tunnel anchoring truncated cone.
5. The method for calculating the ultimate bearing capacity of a tunnel anchorage according to claim 1, wherein the calculation model of the lateral rock pressure N 2 is as follows:
Wherein: z is the distance from the front end of the front anchor chamber to the calculation point, gamma 1 is the weight component of the rock mass perpendicular to the direction of the CD edge,
6. The method for calculating the ultimate bearing capacity of a tunnel anchorage according to claim 1, wherein the step S5 further comprises the following specific steps:
Obtaining the ultimate bearing capacity P u＝P1+P2 of the tunnel anchor according to P 1 and P 2, and calculating the stability safety coefficient K=P u/P of the tunnel anchor against pulling, wherein P is the design load of a single anchorage body; and finally, evaluating the safety of the tunnel anchor under the geological condition according to the anti-pulling stable safety coefficient.
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