CN-121638136-B - Method for calculating thickness of secondary lining of water-conveying tunnel by considering plastic deformation of surrounding rock

CN121638136BCN 121638136 BCN121638136 BCN 121638136BCN-121638136-B

Abstract

The invention belongs to the technical field of water delivery tunnels, and relates to a method for calculating the thickness of a secondary lining of a water delivery tunnel by considering plastic deformation of surrounding rocks, which comprises the steps of adopting a three-layer thick-wall cylinder model to simulate a stress system of the water delivery tunnel, sequentially arranging a secondary lining, a primary support and a surrounding rock loosening ring from inside to outside of the model, assuming that the plastic deformation of the surrounding rocks is compliant with an H-B rule, enabling a rock body in the loosening ring to enter a plastic state, assuming that radial stress and radial displacement between layers of the model are continuous, and arranging a tensile strain limit value allowed by the secondary lining ; obtaining radial displacement of the inner wall of the second lining, the outer wall of the second lining, the inner wall of the primary support, the outer wall of the primary support and the inner wall of the loose coil, obtaining interface pressure, and calculating circumferential strain of the inner wall of the second lining and combining the thickness of the two liners Obtaining implicit relation between the two according to Is subjected to an iterative calculation of the convergence criterion of (c), a minimum thickness of the second liner is obtained. According to the invention, by constructing a three-layer thick-wall cylinder model based on the H-B criterion and coupling the two liners to allow tensile strain constraint, accurate calculation of the minimum thickness of the two liners of the water delivery tunnel is realized.

Inventors

YU CHANGYI
ZHANG YURONG
YU YANG
Fan Mingzun
WANG FENQI
YU WENTAO
WANG WEIYAN
XU BINBIN
CAO YONGHUA
FU MINGYI
YUE CHANGXI
LIU SHIGANG
ZHENG YAN
ZHANG YIMING

Assignees

中交天津港湾工程研究院有限公司
中交第一航务工程局有限公司

Dates

Publication Date: 20260512
Application Date: 20260205

Claims (7)

1. The method for calculating the thickness of the secondary lining of the water delivery tunnel considering the plastic deformation of the surrounding rock is characterized by comprising the following steps when applied to the water delivery tunnel of the jointed rock mass: s1, simulating a stress system of the water delivery tunnel by adopting a three-layer thick-wall cylinder model to establish the stress model of the water delivery tunnel, wherein the three-layer thick-wall cylinder model sequentially comprises a secondary lining, a primary support and a surrounding rock loosening ring from inside to outside, the secondary lining and the primary support are both made of linear elastic materials, the surrounding rock plastic deformation is compliant with Hoek-Brown rule, the rock body in the loosening ring enters a plastic state, the interlayer of the secondary lining, the primary support and the surrounding rock loosening ring are assumed to be in full contact and the radial stress and the radial displacement are continuous, and the limit value of the allowable tensile strain of the secondary lining is set as ; S2, obtaining radial displacement of the inner wall of the second lining based on interlayer radial stress continuity of the second lining, the primary support and the surrounding rock loose ring Radial displacement of the outer wall of the second lining Radial displacement of the inner wall of the primary support Radial displacement of the outer wall of the primary support Radial displacement of inner wall of loose ring of surrounding rock ; S3, obtaining the interface pressure between the secondary lining and the primary support based on the interlayer radial displacement continuity of the secondary lining, the primary support and the surrounding rock loose ring Interfacial pressure between primary support and surrounding rock ; S4, calculating the circumferential tensile strain of the inner wall of the second lining according to the formula (1) And the thickness of the second lining is adjusted Bonding to obtain And (3) with Is represented by formula (2), wherein, Is the radius of the inner wall of the second lining, The elastic modulus of the two liners is the elastic modulus of the two liners, Is the poisson's ratio of the two liners, The internal water pressure born by the inner wall of the second lining is given; (1); (2); s5, according to Performing iterative calculation to obtain thickness of the second liner Wherein, The tensile strain error value is allowed for engineering.
2. The method for calculating the thickness of the secondary lining of the water conveying tunnel considering the plastic deformation of the surrounding rock is characterized by comprising the following steps when being applied to a soft rock water conveying tunnel or a deep buried water conveying tunnel: D1, simulating a stress system of the water delivery tunnel by adopting a three-layer thick-wall cylinder model to establish the stress model of the water delivery tunnel, wherein the three-layer thick-wall cylinder model sequentially comprises a secondary lining, a primary support and a surrounding rock loosening ring from inside to outside, the secondary lining and the primary support are assumed to be made of linear elastic materials, the surrounding rock plastic deformation is compliant with Mohr-Coulomb criterion, the rock body in the loosening ring is in a plastic state, the interlayer of the secondary lining, the primary support and the surrounding rock loosening ring are assumed to be in full contact and the radial stress and the radial displacement are continuous, and the allowable deformation of the inner wall of the secondary lining is set to be ; D2, obtaining radial displacement of the inner wall of the second lining based on interlayer radial stress continuity of the second lining, the primary support and the surrounding rock loose ring Radial displacement of the outer wall of the second lining Radial displacement of the inner wall of the primary support Radial displacement of the outer wall of the primary support Radial displacement of inner wall of loose ring of surrounding rock ; D3, obtaining the interface pressure between the secondary lining and the primary support based on the continuous interlayer radial displacement of the secondary lining, the primary support and the surrounding rock loose ring Interfacial pressure between primary support and surrounding rock ; D4, radially displacing the inner wall of the second lining And two lining thickness Bonding to obtain And (3) with Is represented by formula (3), wherein, Is the radius of the inner wall of the second lining, The elastic modulus of the two liners is the elastic modulus of the two liners, Is the poisson's ratio of the two liners, The internal water pressure born by the inner wall of the second lining is given; (3); D5 according to Performing iterative calculation to obtain thickness of the second liner Wherein, The displacement error value is allowed for engineering.
3. The method for calculating the thickness of the secondary lining of the water conveyance tunnel taking the plastic deformation of the surrounding rock into consideration according to claim 1 or 2, wherein in the step S1 and the step D1, the stress model of the water conveyance tunnel is further based on the assumption that the axial symmetry plane strain condition, specifically, the axial dimension of the water conveyance tunnel is far larger than the radial dimension, the stress and the displacement only change along the radial direction, and the influence of the axial stress is ignored.
4. The method for calculating the thickness of the secondary lining of the water-conveying tunnel taking into account plastic deformation of surrounding rock as claimed in claim 3, wherein in the step S2 and the step D2, the radial displacement of the inner wall of the secondary lining is obtained Radial displacement of the outer wall of the second lining Radial displacement of the inner wall of the primary support Radial displacement of the outer wall of the primary support Radial displacement of inner wall of loose ring of surrounding rock Expressed by the following formulas (4) to (8), respectively, For the stress of the original rock born by the outer wall of the surrounding rock loose ring, 、 The elastic modulus of the primary support and the surrounding rock loose coil are respectively, 、 Poisson ratio of the primary support and surrounding rock loose rings respectively, For the radius of the outer wall of the surrounding rock loosening ring, Is the radius of the primary support inner wall and the secondary lining outer wall, Inner wall of loose ring for surrounding rock the radius of the outer wall of the primary support; (4); (5); (6); (7); (8)。
5. The method for calculating the thickness of the secondary lining of the water conveyance tunnel taking into account plastic deformation of surrounding rock as set forth in claim 4, wherein when the method for calculating the thickness of the secondary lining of the water conveyance tunnel taking into account plastic deformation of surrounding rock is applied to a water conveyance tunnel of an jointed rock body, the plastic deformation of the surrounding rock obeys the Hoek-Brown criterion, and the radius of the outer wall of the loose ring of the surrounding rock is calculated according to the formula (9) Calculating the elastic modulus of the surrounding rock loose coil according to the formula (10) Wherein, the method comprises the steps of, The uniaxial compressive strength of the rock mass; 、、 Calculating according to the formula (11) to the formula (13) for the rock mass quality correction coefficient; For the complete rock mass Hoek-Brown parameters, Is an index of the geological strength of the rock mass, As a parameter of the disturbance, For the modulus of elasticity of the surrounding rock, Is the damage coefficient; (9); (10); (11); (12); (13); when the method for calculating the thickness of the secondary lining of the water delivery tunnel considering the plastic deformation of the surrounding rock is applied to the soft rock water delivery tunnel or the deep buried water delivery tunnel, the plastic deformation of the surrounding rock obeys the Mohr-Coulomb criterion, and the radius of the outer wall of the surrounding rock loose ring is calculated according to the formula (14) Calculating the elastic modulus of the surrounding rock loose coil according to the formula (15) Wherein, the method comprises the steps of, Is the cohesive force of the rock mass, Is the internal friction angle of the rock mass, Is the initial support reaction force; is the surrounding rock elastic modulus; (14); (15)。
6. the method for calculating the thickness of the secondary lining of the water-conveying tunnel taking into account plastic deformation of surrounding rock as defined in claim 5, wherein in step S3 and step D3, the interfacial pressure between the secondary lining and the primary support Interfacial pressure between primary support and surrounding rock Expressed by the formula (16) and the formula (17), respectively, 、、 Respectively calculating a secondary lining displacement contribution coefficient, a primary support displacement contribution coefficient and a surrounding rock displacement contribution coefficient according to a formula (18); (16); (17); (18)。
7. The method for calculating the thickness of the secondary lining of the water-conveying tunnel taking into account plastic deformation of surrounding rock as defined in claim 6, further comprising the step of calculating the stress sharing ratio, specifically, the method for calculating the thickness of the secondary lining obtained by iterative calculation According to Calculation of Then, according to the formula (16) to the formula (17) 、 Further, the stress sharing ratio of the two liners is calculated according to the formula (19) Stress sharing ratio of primary support Stress sharing ratio of surrounding rock ; (19)。

Description

Method for calculating thickness of secondary lining of water-conveying tunnel by considering plastic deformation of surrounding rock Technical Field The invention belongs to the technical field of water delivery tunnels, and particularly relates to a calculation method for thickness of a secondary liner of a water delivery tunnel by considering plastic deformation of surrounding rocks. Background The water delivery tunnel is a core facility of important hydraulic engineering such as cross-river basin water diversion, urban water supply and the like, and is subjected to the synergistic effect of internal water pressure and surrounding rock load for a long time, the secondary lining is used as a permanent bearing structure of the water delivery tunnel, and the thickness design directly relates to engineering safety and economy. In the tunnel excavation process, an original ground stress field is redistributed, surrounding rocks easily form a plastic region (i.e. a loose coil) with a certain range due to unloading effect, the rock strength of the region is deteriorated, deformation characteristics are changed, the load sharing relation of 'secondary lining (i.e. secondary lining) -primary support (i.e. primary support) -surrounding rocks' is obviously reconstructed, and if the mechanical effect of the region is ignored, structural stress analysis and actual working condition deviation are caused. At present, the conventional design method for the thickness of the second lining of the water conveying tunnel has the following defects: 1) The theory is not in conformity with the situation that plastic deformation usually occurs after the surrounding rock is stressed in actual engineering, and the disturbance of a surrounding rock loosening ring to a displacement field and a stress field is not considered, so that the calculation deviation of the pressure of a secondary lining-primary support interface and the pressure of a primary support-surrounding rock interface is caused, and the redundancy of the thickness of the secondary lining is increased, the cost is increased or the thickness is insufficient, and the cracking risk exists; 2) While some researches have established a stress sharing model considering a surrounding rock plastic region, but have not established a direct correlation of nonlinear damage-stress sharing-thickness-deformation, so that accurate quantification of the thickness of the two liners is difficult, the stress sharing ratio of the primary support and the two liners cannot be accurately quantified, and reliable basis cannot be provided for optimization of support parameters and control of construction time of the water conveyance tunnel; 3) The conventional design method for the thickness of the second lining of the water-conveying tunnel has insufficient universality under different geological conditions, and is difficult to be widely applied to complex and changeable tunnel engineering scenes. In view of this, there is a need to develop a complete, engineered application of the thickness of the two liners of the water transport tunnels that takes account of the plastic deformation of the surrounding rock. Disclosure of Invention Aiming at the defects existing in the related art, the invention provides a method for calculating the thickness of a secondary lining of a water conveyance tunnel by considering plastic deformation of surrounding rock, so as to solve the technical problems in the background art. The invention provides a calculation method of a secondary lining thickness of a water delivery tunnel considering surrounding rock plastic deformation, which comprises the following steps when applied to a jointed rock mass water delivery tunnel: S1, simulating a stress system of the water delivery tunnel by adopting a three-layer thick-wall cylinder model to establish the stress model of the water delivery tunnel, sequentially arranging a secondary lining, a primary support and a surrounding rock loosening ring from inside to outside by adopting the three-layer thick-wall cylinder model, assuming that the secondary lining and the primary support are made of linear elastic materials, the surrounding rock plastic deformation is compliant with Hoek-Brown rule, the rock body in the loosening ring enters a plastic state, assuming that the layers of the secondary lining, the primary support and the surrounding rock loosening ring are in full contact and the radial stress and the radial displacement are continuous, and setting the limit value of the allowable tensile strain of the secondary lining as ; S2, obtaining radial displacement of the inner wall of the second lining based on interlayer radial stress continuity of the second lining, the primary support and the surrounding rock loose ringRadial displacement of the outer wall of the second liningRadial displacement of the inner wall of the primary supportRadial displacement of the outer wall of the primary supportRadial displacement of