CN111753360B - Tunnel local water storage frost heaving force calculation method, calculation system, storage medium and season frost region tunnel lining frost heaving design method - Google Patents
Tunnel local water storage frost heaving force calculation method, calculation system, storage medium and season frost region tunnel lining frost heaving design method Download PDFInfo
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Abstract
The invention relates to a method for calculating local water-storage frost-swelling force of a tunnel, a calculating system, a storage medium and a method for designing the tunnel lining frost-swelling of a season-frozen area tunnel. The method for calculating the local water-storage frost-heaving force of the tunnel, the calculating system, the storage medium and the method for designing the frost-heaving force of the tunnel lining in the season frozen area have important significance for tunnel engineering construction and design.
Description
Technical Field
The invention relates to the field of rock and soil, namely the field of road or railway tunnel design (corresponding to class number: E02D 29/045), in particular to a method for calculating local water storage frost heaving force of a tunnel, a calculation system, a storage medium and a method for designing lining frost heaving of a tunnel in a quaternary frozen area.
Background
In the prior art, the method for researching the local water storage frost heaving force mainly comprises the following modes:
document 1: wang Jianyu, hu Yuanfang. Initial detection of frost heaving pressure problem in tunnel lining [ J ]. Programming of railway engineering, 2004 (01): 88-94; in the document, a local water-storing frost heaving model is firstly proposed, the cross section shape of a water-storing space is simplified into a triangle, and a calculation method of the local water-storing frost heaving force is deduced; and the method provides constructive suggestions for tunnel construction and frost-resistant design in severe cold areas, well explains the phenomenon of local water storage frost heaving caused by construction defects, and provides a theoretical basis for subsequent research of the local water storage frost heaving.
Document 2: fan Lei, zeng Yanhua, he Chuan, magnitude and distribution law of frost heaving force of hard rock tunnel in cold region [ J ]. China railway science, 2007,28 (1): 44-49; in the document, after the water is subjected to phase change under the low-temperature condition, the ice body is elastic, the method of the document 1 is used as the basis, a calculation formula of the frost heaving force is improved (the frost heaving force stress mode is shown as a figure 3), and an equivalent elastic coefficient method is provided, so that the calculation process of the frost heaving force value is clearer and simpler.
Document 3: song Tianyu calculation of frost heaving force and study of classification of frost damage [ D ]: university of northeast, 2014; the influence of the low-temperature expansion action of surrounding rock and the influence of the ice body as an elastic body after the accumulated water is frozen is ignored in a local frost heaving formula deduced by the former, and the existing local accumulated water frost heaving model is corrected based on the influence.
The documents 1 to 3 make an innovative contribution to the calculation of the frost heaving force of the tunnel, but it is generally assumed that the plane shape of the water storage space is triangular, uniformly distributed in the longitudinal direction of the tunnel, and the calculation formula of the frost heaving force is derived under two-dimensional conditions, although the difference between the two-dimensional derivation and the three-dimensional reality is considered in the existing water storage frost heaving theory, and a reduction coefficient is proposed for converting the two-dimensional result into the three-dimensional result, the result calculated by the above theory is not accurate enough.
For this purpose, document 4: deng Gang, wang Jianyu, zheng Jinlong constrained frost heave model of cold region tunnel frost heave pressure [ J ]. Chinese highway school report, 2010,23 (1): 80-85; document 4 proposes a constrained frost heaving model similar to gas pressure from a three-dimensional space point of view, and the theory considers that the frost heaving pressure is generated after expansion and deformation only when the deformation is constrained in all directions in the process of converting water in a water storage space from a liquid state to a solid state under a low-temperature condition. Once either direction is unconstrained, the frost heave pressure is released and localized frost heave will not occur. The theoretical derivation process is more rigorous than the theoretical model in two-dimensional space, but in this theory, the water storage space is assumed to be in a regular tetrahedron form (document 4 also illustrates that the simplest water storage space is discussed as the simplest case of a regular tetrahedron), which has a large deviation from the actual situation.
The calculation results of documents 1 to 3 are based on two-dimensional plane deduction, and when the calculation results are applied to engineering (three-dimensional) reality, the calculation results are quite different from the engineering reality (from the mechanical mechanism, unreasonable: the frost heaving pressure can be generated after expansion and deformation only when the deformation is subjected to omnibearing restraint in the process of converting water from a liquid state to a solid state, once no restraint exists in any direction, the frost heaving pressure can be released, local frost heaving can not occur, and when the calculation results are studied on the two-dimensional basis, the restraint along the length direction of a tunnel is not considered deeply.
Although literature 4 has been studied in a deduction from a three-dimensional perspective, the result calculated in literature 4 is still greatly different from the actual engineering monitoring data.
Therefore, it is necessary to research a more accurate method for calculating the local water-storing frost heaving force of the tunnel in the season frozen region so as to serve engineering design.
Disclosure of Invention
The invention aims to provide a method and a system for calculating local water-storage frost-heaving force of a tunnel, a storage medium and a method for designing the frost-heaving of a tunnel lining in a quaternary freezing zone, so as to overcome the defects of the prior art.
Another object of the present invention is to provide a system for calculating the local water-storage frost-heaving force of a tunnel.
It is still another object of the present invention to provide a storage medium.
The invention further aims at providing a method for designing frost heaving of the tunnel lining of the quaternary frozen region.
The technical scheme of the invention is as follows:
a method for calculating the frost heaving force of local water storage of a tunnel comprises the following steps:
in the above-mentioned method, the step of,
t-ice depth (m);
K r -the elastic resistance coefficient of the surrounding rock (MPa/m);
K i -coefficient of elastic resistance of the ice mass (MPa/m);
K l -lining the coefficient of elastic resistance (MPa/m);
alpha-frost heaving ratio of ice.
Further, wherein the frost heave rate α of ice is 9%.
Further, wherein the surrounding rock elastic resistance coefficient is determined by consulting railway tunnel design specifications.
Further, wherein the elastic equivalent coefficient of the lining is determined through 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 determined by a test, or the elastic equivalent coefficient of the ice body adopts an empirical value of 50MPa/m.
A tunnel local water storage frost heaving force calculation system, comprising: the device comprises a data input module, a local frost heaving force calculation module and a display module;
the output end of the data input 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 input module is used for inputting the ice accumulation depth, the surrounding rock elastic resistance coefficient, the ice body elastic resistance coefficient, the lining elastic resistance coefficient and the frost heaving rate of ice;
wherein, the local frost heaving force calculation module is used for calculating the local Shui Dongzhang force of the tunnel,
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 in which a program for executing the method described above is stored.
A design method for frost heaving of tunnel lining in a season frozen area comprises the following steps:
firstly, in the construction process, the ice accumulation depth value of a water living space generated by construction collapse and super-excavation is obtained through site survey (a new Olympic method is adopted in tunnel design construction, namely a mode of design-construction at the same time);
secondly, in the calculation of the lining structure, the position corresponding to the construction collapse and the super-excavated water producing space in the first step is added with a local Shui Dongzhang force, and safety checking calculation is carried out;
the local water-storing frost-heaving force in the second step is calculated by the method for calculating the local water-storing frost-heaving force of the tunnel, and the ice-depositing depth required in the method for calculating the local water-storing frost-heaving force of the tunnel is obtained by adopting the field survey in the first step to obtain the ice-depositing depth value of the water-storing space due to construction collapse and super-excavation.
The beneficial effects of this application lie in:
firstly, the method for calculating the local frost heaving force of the tunnel is based on the three-dimensional space. The first basic idea of the present application is: given the three-dimensional shape of the water storage form, the semi-ellipsoid has radians in two directions, which can take into account the curvature change of the water storage space in the tunnel length direction, compared to documents 1 to 3.
Secondly, the second basic concept and difficulty of the application are that the application is based on conservation of volume change, namely volume expansion after water body freezing and volume deformation of surrounding rock and lining;
for documents 1 to 3, it is assumed that the shape of water is a triangular prism (triangular prism extends infinitely), which essentially regards volumetric deformation as two-dimensional area deformation.
While in document 4, although water is considered as a regular tetrahedron, the derivation process is too simplified, and the manner in which it gives the formula is not known in detail.
That is, the volume change of the surrounding rock is
The volume change of the lining is as follows
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: solving from equation (12) to equation (26) is the third major problem in the development process.
Fourth, the calculation method can be used for providing guidance for frost heaving design of the tunnel lining structure of the quaternary frozen area.
Fifth, as known from the development process of the present application, the method of independent claim 1, independent claim 2 of the present application is applicable to forms in which the lining structure includes vertical walls, for example: rectangular tunnel.
Description of the drawings:
fig. 1: schematic representation of the form of the water storage space of the present application.
Fig. 2: frost heaving force stress diagram of the present application.
Fig. 3: the local water storage frost heaving force calculation mode diagram is provided.
Fig. 4: numerical calculation modeling schematic diagrams of the application.
Fig. 5: this application, literature 3 and numerical simulation calculate the contrast graph of the frost heaving force value.
Fig. 6: schematic diagram of a tunnel local water storage frost heaving force calculation system.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention become more apparent, 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 local water-storage frost-swelling force of a tunnel in a quaternary frozen region, wherein the frost-swelling force P is calculated by adopting the following formula:
in the above-mentioned method, the step of,
t—depth of ice accumulation (m) (known by measurement during construction);
K r -the elastic resistance coefficient of the surrounding rock (MPa/m);
K i -coefficient of elastic resistance of the ice mass (MPa/m);
K l -lining the coefficient of elastic resistance (MPa/m);
alpha-frost heaving ratio of ice.
Wherein, the frost heave rate alpha of the ice is 9 percent.
The elastic resistance coefficient of the surrounding rock is determined by consulting railway tunnel design specifications;
wherein the elastic equivalent coefficients of the lining and the ice body can be determined by a test. If the specific numerical value is absent, the numerical value can be calculated by referring to the empirical value. Referring to the research results in the prior literature, the elastic resistance coefficient of the tunnel lining is about 75MPa/m, and the elastic equivalent coefficient of the ice body is 50MPa/m.
The development process of the calculation method is as follows:
firstly, the model assumes isotropy of surrounding rock, the shape of a water storage space between the surrounding rock and a lining is assumed to be a triaxial semi-ellipsoid which is more in line with actual conditions without considering the dead weights of the surrounding rock and the tunnel lining, a three-dimensional local water storage frost heaving model is built, and the water storage space is shown in figure 1. The water in the water storage space is assumed to be 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 vertical to the lining structure, and the stress diagram is shown in figure 2.
The calculation mode of frost heaving force adopts three springs connected in series to simulate deformation conditions and stress conditions of frozen surrounding rock, ice bodies and tunnel lining. It is assumed that the surrounding rock, the ice body and the tunnel lining satisfy a certain deformation coordination condition, that is, deformation displacement of the surrounding rock and the ice body is equal at a contact point (a) of the surrounding rock and the ice, and deformation displacement of the ice and the lining is equal at a contact point (B) of the ice and the lining. The volume conservation is taken as an integral thought, namely, the volume increment of the water body in the process of converting the liquid into the solid under the low-temperature condition is equal to the volume variation generated by the extrusion effect of frost heaving pressure on lining and surrounding rock.
Second, the development process of the calculation method of frost heaving force is as follows:
according to the theory of local deformation, the elastic resistance of the surrounding rock is proportional to the deformation at that point, i.e
σ i ＝Kδ i (1)
In delta i For any point i of the surrounding rock surfaceCompression set (m); sigma (sigma) i Is the 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), K is used r Representing the elastic resistance coefficient of surrounding rock by K i Representing the elastic resistance coefficient of ice body by K l Representing the coefficient of elastic resistance of the lining. The deformation displacement value of the surrounding rock is under the action of the frost heaving force P
The deformation displacement value of the lining is
The magnitude of frost heaving force P can be expressed as
P＝δ(K r +K i )＝Δ(K i +K l ) (4)
Recording device
Therefore, it is
Is obtained by a triaxial ellipsoidal volume formula, and the volume of the water storage space is
The frost heave rate of the obtained ice is alpha, so that after the water storage space is filled with water and frozen under the low temperature condition, the volume expansion of the ice body is
The volume change of the surrounding rock is as follows
The volume change of the lining is as follows
The volume expansion after the water body is frozen is equal to the volume deformation of surrounding rock and lining, namely
V i ＝V r +V l (11)
Therefore, the formulae (8), (9) and (10) are substituted into formula (11)
Is arranged to obtain
The left and right sides of the equation are divided by t (t.noteq.0)
To simplify the calculation process, this command
And from the formula (5), the formula (14) can be prepared as
Therefore, it is
Is arranged to obtain
To simplify the derivation process, this command
1+λ＝θ (19)
Therefore, it is
Is arranged to obtain
For a shape like x 3 The unitary cubic equation for +px+q=0 (p, q e R), solved by the karl dan formula:
wherein the method comprises the steps of
The discriminant is +.>
When xi is more than 0, the equation has a real root and two complex roots; when ζ=0, there are three real roots, when p=q=0, there is one triple zero root, and when p, q is not equal to 0, two of the three real roots are equal; when xi is less than 0, three unequal roots exist. />
In the equation (21),
therefore->
Obviously, μ and α are constantly greater than 0, so ζ > 0, i.e. the equation has one real root and two complex roots.
For practical problems, we only consider the real root situation, so
Substituting formula (5) into the above formula
Obtained according to the formula (4), the formula (15) and the formula (19)
P＝t(K r +K i )λ＝t(K r +K i )(θ-1) (25)
Therefore, the formula (24) is substituted into the formula (25)
In the method, in the process of the invention,
t-ice depth (m);
K r -the elastic resistance coefficient of the surrounding rock (MPa/m);
K i -coefficient of elastic resistance of the ice mass (MPa/m);
K l -lining the coefficient of elastic resistance (MPa/m);
alpha-frost heaving ratio of ice.
In the calculation process, the frost heave rate alpha of the ice is 9 percent; the elastic resistance coefficient of each level of surrounding rock can be determined by consulting the railway tunnel design specification; the elastic equivalent coefficients of the lining and the ice body can be determined by tests. If the specific numerical value is absent, the numerical value can be calculated by referring to the empirical value. For example: referring to the research results in 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 50MPa/m.
And (3) verifying a numerical simulation test:
taking a certain tunnel engineering as an example, setting the horizontal direction of the tunnel as an X axis, the vertical direction as a Y axis and the longitudinal direction as a Z axis, and establishing a three-dimensional local water storage frost heaving calculation model. And selecting stratum structures in the range of 10m in front of and behind the tunnel water storage position in the longitudinal direction as research objects. The water storage space is a semi-ellipsoid, the deepest position of ice accumulation is positioned at the tunnel vault of the Z=0 section, the ice accumulation depth is 0.2m, the circumferential length is 0.4m, and the longitudinal length is 0.4m, as shown in fig. 4. The lining material is C30 concrete with the thickness of 40cm (the elastic resistance coefficient is 75 MPa/m). By adjusting the surrounding rock material parameters, the local frost heaving force of the water stored in different surrounding rock grades is calculated, and the material properties are shown in table 2. For the simulation of the volume expansion phenomenon after water icing, the method of setting a linear expansion coefficient for an ice body and applying a temperature load is adopted in the section, and the method is equivalent to the expansion pressure, namely frost heaving force, generated on a lining by the volume expansion after water icing at low temperature.
Table 2 material properties
TABLE 3 calculation results of theory and numerical simulation of local Water-storage frost heaving force
As can be seen from the comparison of the above calculation results, the mode (formula 26) of the present application is closer to the numerical solution than that of documents 1 to 4. Also, it should be noted that: the calculation results of documents 1 to 4 are mostly smaller than the numerical solution, and therefore, the safety degree is insufficient (i.e., insufficient) when applied to the safety verification of the lining structure.
Claims (7)
1. A method for calculating the local water-storing frost heaving force of a tunnel is characterized in that the frost heaving force P is calculated by adopting the following formula:
in the above-mentioned method, the step of,
t-ice depth (m);
K r -the elastic resistance coefficient of the surrounding rock (MPa/m);
K i -coefficient of elastic resistance of the ice mass (MPa/m);
K l -lining the coefficient of elastic resistance (MPa/m);
alpha-frost heaving ratio of ice.
2. The method for calculating the local water storage frost heaving force of a tunnel according to claim 1, wherein the frost heaving ratio α of ice is 9%.
3. A method for calculating the local frost heaving force of a tunnel according to claim 1 or 2, wherein the surrounding rock elastic resistance coefficient K r By consulting railway tunnel design specifications.
4. A method for calculating local frost heaving capacity of a tunnel according to claim 1 or 2, wherein the lining has an elastic equivalent coefficient K l By experimental determination, or, in accordance with the coefficient of elastic resistance K of the lining l An empirical value of 75MPa/m is adopted;
wherein the elastic equivalent coefficient K of the ice body i By experiment or, alternatively, the coefficient of elastic equivalent K of the ice body i An empirical value of 50MPa/m was used.
5. A tunnel local water-storing frost-heaving force calculation system, comprising: the device comprises a data input module, a local frost heaving force calculation module and a display module;
the output end of the data input 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 input module is used for inputting the ice accumulation depth, the surrounding rock elastic resistance coefficient, the ice body elastic resistance coefficient, the lining elastic resistance coefficient and the frost heaving rate of ice;
wherein, the local frost heaving force calculation module is used for calculating the local storage Shui Dongzhang force of the tunnel, and adopts the calculation method of claim 1;
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. The design method for frost heaving of the tunnel lining in the season frozen area is characterized by comprising the following steps of:
firstly, in the construction process, obtaining an ice accumulation depth value of a water living space produced by construction collapse and overexcavation through site survey;
secondly, in the calculation of the lining structure, the position corresponding to the construction collapse and the super-excavated water producing space in the first step is added with a local Shui Dongzhang force, and safety checking calculation is carried out;
the local water-storing frost heaving force in the second step is calculated by adopting the method for calculating the local water-storing frost heaving force of the tunnel according to claim 1, and the ice accumulation depth required in the method for calculating the local water-storing frost heaving force of the tunnel is obtained by adopting the field survey in the first step to obtain the ice accumulation depth value of the water-storing space due to construction collapse and overexcavation.
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