CN111753360A - Tunnel local water storage frost heaving force calculation method, calculation system, storage medium and seasonal freezing region tunnel lining frost heaving design method - Google Patents

Tunnel local water storage frost heaving force calculation method, calculation system, storage medium and seasonal freezing region tunnel lining frost heaving design method Download PDF

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CN111753360A
CN111753360A CN202010576623.9A CN202010576623A CN111753360A CN 111753360 A CN111753360 A CN 111753360A CN 202010576623 A CN202010576623 A CN 202010576623A CN 111753360 A CN111753360 A CN 111753360A
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frost heaving
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CN111753360B (en
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王道远
崔光耀
栾永军
朱永全
崔海龙
孙梁
孙永杰
王悦
袁金秀
孙明磊
皮阳阳
陈春星
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Shijiazhuang Tiedao University
Hebei Construction Group Corp Ltd
Hebei Jiaotong Vocational and Technical College
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Hebei Construction Group Corp Ltd
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Abstract

The invention relates to a method for calculating the partial water storage frost heaving force of a tunnel, a calculation system, a storage medium and a method for designing the lining frost heaving of a tunnel in a seasonal freezing region. The method for calculating the partial water storage frost heaving force of the tunnel, the calculation system, the storage medium and the method for designing the lining frost heaving of the tunnel in the seasonal frozen region have important significance for tunnel engineering construction and design.

Description

Tunnel local water storage frost heaving force calculation method, calculation system, storage medium and seasonal freezing region tunnel lining frost heaving design method
Technical Field
The invention relates to the field of rock and soil, namely the field of highway or railway tunnel design (corresponding classification number: E02D29/045), in particular to a method for calculating the local water storage frost heaving force of a tunnel, a calculation system, a storage medium and a method for designing the lining frost heaving of a tunnel in a seasonal frost region.
Background
In the prior art, the following methods are mainly used for researching the calculation method of the partial water storage frost heaving force:
document 1: 88-94 parts of Wangjiayu, Huyufang, initial exploration of frost heaving pressure problem of tunnel lining [ J ]. Productions of railway engineering, 2004 (01); the method is characterized in that a local water storage frost heaving model is firstly proposed in the literature, the cross section shape of a water storage space is simplified into a triangle, and a calculation method of local water storage frost heaving force is deduced; and a constructive suggestion is provided for tunnel construction and anti-freezing design in severe cold areas, the calculation method well explains the phenomenon of local water storage frost heaving caused by construction defects, and a theoretical basis is provided for the subsequent research on local water storage frost heaving.
Document 2: van Lei, great brilliance, He Chuan, etc. the magnitude and distribution rule of the frost heaving force of hard rock tunnels in cold regions [ J ] China railway science, 2007,28(1): 44-49; in the literature, after the phase change of water under the low-temperature condition is considered, the ice body is also taken as the elasticity, the method of the literature 1 is taken as the basis, the calculation formula of the frost heaving force is improved (the stress mode of the frost heaving force is shown as an attached figure 3), and an equivalent elastic coefficient method is proposed, so that the calculation process of the frost heaving force value is clearer and simpler.
Document 3: songtianyu, calculation of frozen expansive force of rock tunnel and classification of frozen injury grade research [ D ]. Shenyang: northeast university, 2014; the influence of low-temperature expansion of surrounding rock and the influence of ice serving as an elastic body after accumulated water is frozen are ignored in a local frost heaving formula deduced by the predecessor, and an existing local accumulated water frost heaving model is corrected on the basis of the influence.
Documents 1 to 3 make a pioneering contribution to the calculation of the tunnel frost heaving force, however, it is generally assumed that the plane shape of the water storage space is triangular, the water storage space is uniformly distributed along the longitudinal direction of the tunnel, and the calculation formula of the frost heaving force is derived under a two-dimensional condition.
For this reason, document 4: denggang, Wangjiangyu, Zhengjinlong, restriction frost heaving model of frost heaving pressure of cold region tunnel [ J ]. Chinese Highway academic newspaper, 2010,23(1): 80-85; document 4 proposes a constrained frost heaving model similar to gas pressure from the perspective of three-dimensional space, and the theory considers that, in the process of transforming water in a water storage space from a liquid state to a solid state under a low-temperature condition, only when deformation is constrained in all directions, the effect of frost heaving pressure is generated after expansion deformation. Once there is no restriction in either direction, the frost heave pressure will be released and local frost heave will not occur. This theoretical derivation process is more rigorous than a theoretical model in two-dimensional space, but the theoretical model assumes that the water storage space is in the form of a regular tetrahedron (document 4 also indicates that the simplest case of discussing the simplest water storage space as a regular tetrahedron), which is a large deviation from the actual situation.
The calculation results of the documents 1 to 3, which are based on the two-dimensional plane derivation, are greatly different from the actual results of engineering (three-dimensional) when applied to engineering (three-dimensional) practice (from the mechanical mechanism, it is also unreasonable that the frost-heave pressure is generated only when the deformation is constrained in all directions in the process of converting water from liquid to solid, the frost-heave pressure is released once any direction is unconstrained, and local frost-heave will not occur, and when the two-dimensional basis is studied, the constraint along the length direction of the tunnel is not considered in depth in nature.
Although the derivation study is performed in three dimensions, the results calculated in the document 4 still have a large difference compared with the actual engineering monitoring data.
Therefore, a more accurate calculation method of the partial water storage frost heaving force of the tunnel in the seasonal freezing region needs to be researched so as to serve engineering design.
Disclosure of Invention
The invention aims to provide a method for calculating the partial water storage frost heaving force of a tunnel, a calculation system, a storage medium and a method for designing the lining frost heaving of a tunnel in a seasonal freezing region, so as to overcome the defects of the prior art.
The invention further aims to provide a tunnel local water storage frost heaving force calculation system.
It is a further object of the present invention to provide a storage medium.
The invention further aims to provide a design method for frost heaving of the tunnel lining in the seasonal frozen region.
The technical scheme of the invention is as follows:
a method for calculating the partial water-storing frost heaving force of a tunnel is disclosed, wherein the frost heaving force P is calculated by adopting the following formula:
Figure BDA0002551284980000021
in the above formula, the first and second carbon atoms are,
t-ice accretion depth (m);
Kr-the elastic resistance coefficient (MPa/m) of the surrounding rock;
Ki-ice bulk elastic resistance coefficient (MPa/m);
Kl-lining elastic resistance coefficient (MPa/m);
alpha-frost heaviness of ice.
Further, the frost heaviness α of ice was 9%.
Further, wherein the elastic resistance coefficient of the surrounding rock is determined by consulting the design specification of the railway tunnel.
Further, wherein the elastic equivalent coefficient of the lining is determined by a test, or an empirical value of 75MPa/m is adopted according to the elastic resistance coefficient of the lining;
wherein, the elastic equivalent coefficient of the ice body is measured by experiments, or the elastic equivalent coefficient of the ice body adopts an empirical value of 50 MPa/m.
A tunnel local water frozen expansion force calculation system comprises: the system comprises a data entry module, a local frost heaving force calculation module and a display module;
the output end of the data entry module is connected with the input end of the local frost heaving force calculation module;
the output end of the local frost heaving force calculation module is connected with the input end of the display module;
the data entry module is used for inputting the ice accumulation depth, the elastic resistance coefficient of surrounding rocks, the elastic resistance coefficient of ice bodies, the elastic resistance coefficient of lining and the frost heaving rate of ice;
wherein, the local frost heaving force calculation module is used for calculating the local water storage frost heaving force of the tunnel,
and the display module is used for displaying the calculated calculation result of the local water storage frost heaving force of the tunnel.
A storage medium, characterized in that a program for executing the method as described above is stored in the storage medium.
A lining frost heaving design method for a tunnel in a seasonal frozen region comprises the following steps:
firstly, in the construction process, the depth value of the ice accumulation in the water storage space caused by construction collapse and overexcavation is obtained through site survey (the tunnel design and construction adopt a new Olympic method, namely a mode of simultaneous design and simultaneous construction);
secondly, in the calculation of the lining structure, local water storage frost heaving force is increased corresponding to the construction collapse of the first step and the position of a water storage space generated by overbreak, and safety checking calculation is carried out;
and the local water storage frost heaving force in the second step is obtained by calculating the tunnel local water storage frost heaving force, and the ice deposition depth required in the tunnel local water storage frost heaving force calculation method is obtained by adopting the field survey in the first step to obtain the ice deposition depth value of the water storage space generated by construction collapse and overexcavation.
The beneficial effect of this application lies in:
firstly, the method for calculating the local frost heaving force of the tunnel is provided based on the three-dimensional space. The first basic idea of the application is that: given the three-dimensional shape of the water holding form, the semi-ellipsoid has curvature in two directions, which can account for the change in curvature of the water holding space in the tunnel length direction, as compared to documents 1-3.
Secondly, the second basic concept and difficulty of the application is that the application is based on volume change conservation, namely volume expansion and surrounding rock and lining volume deformation after the water body is frozen;
for documents 1 to 3, it is assumed that the shape of water is a triangular prism (triangular prism extends indefinitely), which essentially sees the volume deformation as a two-dimensional area deformation.
While in document 4, water is considered to be a regular tetrahedron, the derivation process is too simplified, and it is not known in which way the formula is given.
That is, the volume change amount of the surrounding rock is
Figure BDA0002551284980000041
The volume change of the lining is
Figure BDA0002551284980000042
Is the second inventive concept of the present application and is the second important issue in the development process.
Third, the third inventive concept of the present application is: the solution from equation (12) to equation (26) is the third important problem in the development process.
Fourthly, the calculation method can be used for providing guidance for frost heaving design of the tunnel lining structure in the seasonal frozen region.
Fifth, as is apparent from the development process of the present application, the methods of independent claims 1 and 2 of the present application are applicable to the form of lining structure including vertical walls, for example: and (4) a rectangular tunnel.
Description of the drawings:
FIG. 1: schematic view of the water holding space form of the present application.
FIG. 2: the frost heaving force stress sketch of the application.
FIG. 3: the application discloses a local water storage frost heaving force calculation mode diagram.
FIG. 4: the numerical calculation modeling schematic diagram of the application.
FIG. 5: the present application, document 3, and a comparison graph of the numerical simulation calculation frozen expansion force values.
FIG. 6: the application discloses a schematic diagram of a tunnel local water storage frost heaving force calculation system.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention.
The invention provides a method for calculating the partial water storage frost heaving force of a tunnel in a seasonal freezing region, wherein the frost heaving force P is calculated by adopting the following formula:
Figure BDA0002551284980000051
in the above formula, the first and second carbon atoms are,
t-depth of ice accretion (m) (known by measurement during construction);
Kr-the elastic resistance coefficient (MPa/m) of the surrounding rock;
Ki-ice bulk elastic resistance coefficient (MPa/m);
Kl-lining elastic resistance coefficient (MPa/m);
alpha-frost heaviness of ice.
Wherein the frost heaviness alpha of the ice is 9 percent.
Wherein the elastic resistance coefficient of the surrounding rock is determined by looking up the design specification of the railway tunnel;
among them, the elastic equivalent coefficient of the lining and the ice body can be determined by experiments. If the specific numerical value is lacked, the calculation can be carried out by referring to the value of the empirical value. Referring to the research results in the prior documents, the elastic resistance coefficient of the tunnel lining is about 75MPa/m, and the elastic equivalent coefficient of the ice body is 50 MPa/m.
The research and development process of the calculation method is as follows:
firstly, the model assumes that surrounding rocks are isotropic, the self weight of the surrounding rocks and tunnel linings is not considered, the shape of a water storage space between the surrounding rocks and the linings is assumed to be a triaxial semi-ellipsoid body which is more consistent with the actual situation, a three-dimensional local water storage frost heaving model is established, and the form of the water storage space is shown in figure 1. And (3) assuming that water in the water storage space is in plane contact with the lining after being frozen, wherein the circumferential length of the ice body is l, the longitudinal length of the ice body is B, and the depth of the ice body is t. The direction of frost heaving force is perpendicular to the lining structure, and the stress diagram is shown in figure 2.
The calculation mode of the frost heaving force adopts three springs connected in series to simulate the deformation and stress conditions of the frozen surrounding rock, the ice body and the tunnel lining. And (3) assuming that the surrounding rock, the ice body and the tunnel lining meet a certain deformation coordination condition, namely at a contact point (A) of the surrounding rock and the ice, the deformation displacement of the surrounding rock and the ice body is equal, and at a contact point (B) of the ice and the lining, the deformation displacement of the ice and the lining is equal. The volume conservation is taken as the whole idea, namely the volume increment of the water body in the process of converting liquid into solid under the low-temperature condition is always equal to the volume variable quantity generated by the extrusion of frost heaving pressure on the lining and the surrounding rock.
Secondly, the development process of the calculation method of the frost heaving force is as follows:
according to the local deformation theory, the elastic resistance of the surrounding rock is proportional to the deformation of the point, i.e.
σi＝Ki(1)
In the formula (I), the compound is shown in the specification,icompression deformation (m) of any point i on the surface of the surrounding rock; sigmaiThe elastic resistance (MPa) generated by the surrounding rock at the point i; k is the elastic resistance coefficient (MPa/m) of the surrounding rock.
Based on formula (1) with KrExpressing the elastic resistance coefficient of the surrounding rock by KiExpressing the coefficient of resistance to elasticity of the ice mass, by KlRepresenting the lining elastic resistance coefficient. The deformation displacement value of the surrounding rock under the action of the frost heaving force P is
Figure BDA0002551284980000061
The lining has a deformation displacement value of
Figure BDA0002551284980000062
So the magnitude of the frost heaving force P can be expressed as
P＝(Kr+Ki)＝Δ(Ki+Kl) (4)
Note the book
Figure BDA0002551284980000063
Therefore, it is
Figure BDA0002551284980000064
Obtained by a three-axis ellipsoid volume formula, the volume of the water storage space is
Figure BDA0002551284980000065
Since the frozen expansion rate of ice is alpha, when the water storage space is filled with water and frozen at low temperature, the volume expansion amount of the ice is alpha
Figure BDA0002551284980000066
Volume change of the surrounding rock is
Figure BDA0002551284980000067
The volume change of the lining is
Figure BDA0002551284980000071
The volume expansion amount of the frozen water body is equal to the volume deformation amount of the surrounding rock and the lining, namely
Vi＝Vr+Vl(11)
So that the formulae (8), (9) and (10) are substituted for the formula (11)
Figure BDA0002551284980000072
Is finished to obtain
Figure BDA0002551284980000073
The left and right sides of the equation are divided by t (t ≠ 0) to obtain
Figure BDA0002551284980000074
To simplify the calculation process, the instructions herein
Figure BDA0002551284980000075
And from formula (5), formula (14) can be arranged as
Figure BDA0002551284980000076
Therefore, it is
Figure BDA0002551284980000077
Is finished to obtain
Figure BDA0002551284980000078
To simplify the derivation process, the instructions are
1+λ＝θ (19)
Therefore, it is
Figure BDA0002551284980000079
Is finished to obtain
Figure BDA0002551284980000081
For the form x3A one-dimensional cubic equation of + px + q ═ 0(p, q ∈ R), solved by the kardan equation:
Figure BDA0002551284980000082
wherein
Figure BDA0002551284980000083
Has a discriminant of
Figure BDA0002551284980000084
When ξ is greater than 0, the equation has one real root and two complex roots, when ξ is 0, there are three real roots, when p is q 0, there is a triple zero root, when p, q is not equal to 0, two of the three real roots are equal, when ξ < 0, there are three unequal real roots.
In the equation (21), the process is as follows,
Figure BDA0002551284980000085
therefore, it is not only easy to use
Figure BDA0002551284980000086
It is clear that μ and α are constantly greater than 0, so ξ > 0, i.e., the equation has one real root and two complex roots.
For practical problems, we only consider the real root situation, so
Figure BDA0002551284980000087
Replacing formula (5) with the above formula to obtain
Figure BDA0002551284980000088
According to formula (4), formula (15) and formula (19) to obtain
P＝t(Kr+Ki)λ＝t(Kr+Ki)(θ-1) (25)
So that formula (24) is substituted for formula (25)
Figure BDA0002551284980000091
In the formula (I), the compound is shown in the specification,
t-ice accretion depth (m);
Kr-the elastic resistance coefficient (MPa/m) of the surrounding rock;
Ki-ice bulk elastic resistance coefficient (MPa/m);
Kl-lining elastic resistance coefficient (MPa/m);
alpha-frost heaviness of ice.
In the calculation process, the frost heaving rate alpha of the ice is 9 percent; elastic resistance coefficients of surrounding rocks at all levels can be determined by consulting railway tunnel design specifications; the elastic equivalent coefficients of the lining and the ice mass can be determined by tests. If the specific numerical value is lacked, the calculation can be carried out by referring to the value of the empirical value. For example: referring to the research results of the prior art, the elastic resistance coefficient of the tunnel lining is about 75MPa/m, and the elastic equivalent coefficient of the ice body is 50 MPa/m.
And (3) verifying by a numerical simulation test:
taking a certain tunnel project as an example, a horizontal direction of the tunnel is taken as an X axis, a vertical direction is taken as a Y axis, and a longitudinal direction is taken as a Z axis, and a three-dimensional local water storage frost heaving calculation model is established. And selecting stratum structures in the range of 10m longitudinally before and after the tunnel water storage position as research objects. The water storage space is a semi-ellipsoid, the deepest position of the accumulated ice is located at the tunnel arch top with the section Z equal to 0, the depth of the accumulated ice is 0.2m, the annular length is 0.4m, and the longitudinal length is 0.4m, as shown in fig. 4. The lining material is C30 concrete with a thickness of 40cm (the elastic resistance coefficient is 75 MPa/m). The size of the local water storage frost heaving force at different surrounding rock levels is calculated by adjusting the surrounding rock material parameters, and the material properties are shown in Table 2. For the simulation of the volume expansion phenomenon after water is frozen, the section adopts a method of setting a linear expansion coefficient on an ice body and applying a temperature load, and is equivalent to that the volume expansion of the frozen water generates expansion pressure, namely frost heaving force, on the lining.
TABLE 2 Material Properties
Figure BDA0002551284980000092
Figure BDA0002551284980000101
TABLE 3 calculation results of theoretical and numerical simulation of local water-storage frost heaving force
Figure BDA0002551284980000102
As can be seen from the comparison of the above calculation results, the method (expression 26) of the present application is closer to the numerical solution than the methods of documents 1 to 4. Further, it should be noted that: the calculation results of documents 1 to 4 are mostly smaller than the numerical solution, and therefore, when the calculation results are applied to the safety check calculation of the lining structure, the safety degree is insufficient (i.e., insufficient).

Claims (7)

1. A method for calculating the partial water-storing frost heaving force of a tunnel is characterized in that the frost heaving force P is calculated by adopting the following formula:
Figure FDA0002551284970000011
in the above formula, the first and second carbon atoms are,
t-ice accretion depth (m);
Kr-the elastic resistance coefficient (MPa/m) of the surrounding rock;
Ki-ice bulk elastic resistance coefficient (MPa/m);
Kl-lining elastic resistance coefficient (MPa/m);
alpha-frost heaviness of ice.
2. The method for calculating the partial water freezing expansion force of the tunnel according to claim 1, wherein the frost heaving ratio α of ice is 9%.
3. The method for calculating the local water-storing frost heaving force of the tunnel according to claim 1 or 2, wherein the elastic resistance coefficient K of the surrounding rockrDetermined by consulting the specifications of the design of the railway tunnel.
4. The method for calculating the partial water freezing expansion force of the tunnel according to claim 1 or 2, wherein the elastic equivalent coefficient K of the lining islDetermined by tests, or, according to the elastic resistance coefficient K of the lininglAn empirical value of 75MPa/m is adopted;
wherein the elastic equivalent coefficient K of the ice bodyiBy experimental determination, or, of the elastic equivalent coefficient K of the ice massiAn empirical value of 50MPa/m was used.
5. A tunnel local water storage frost heaving force calculation system is characterized by comprising: the system comprises a data entry module, a local frost heaving force calculation module and a display module;
the output end of the data entry module is connected with the input end of the local frost heaving force calculation module;
the output end of the local frost heaving force calculation module is connected with the input end of the display module;
the data entry module is used for inputting the ice accumulation depth, the elastic resistance coefficient of surrounding rocks, the elastic resistance coefficient of ice bodies, the elastic resistance coefficient of lining and the frost heaving rate of ice;
the local frost heaving force calculation module is used for calculating the tunnel local water frost heaving force and adopts the calculation method of claim 1;
and the display module is used for displaying the calculated calculation result of the local water storage frost heaving force of the tunnel.
6. A storage medium in which a program for executing the calculation method according to claim 1 is stored.
7. A lining frost heaving design method for a tunnel in a seasonal frozen region is characterized by comprising the following steps of:
firstly, in the construction process, obtaining the depth value of ice accumulation in a water storage space caused by construction collapse and overexcavation through site survey;
secondly, in the calculation of the lining structure, local water storage frost heaving force is increased corresponding to the construction collapse of the first step and the position of a water storage space generated by overbreak, and safety checking calculation is carried out;
the local water storage frost heaviness force in the second step is calculated by the tunnel local water storage frost heaviness force calculation method according to claim 1, and the ice accumulation depth required in the tunnel local water storage frost heaviness force calculation method is obtained by the aid of site survey in the first step, so that the ice accumulation depth value of the water storage space generated due to construction collapse and overexcavation is obtained.
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