Stability Analysis Method for Water Diversion Tunnel Considering Time-Sequenced Excess Hydrostatic Pressure and Flow Stress

Abstract

The application relates to a diversion tunnel stability analysis method considering time sequence superhydrostatic pressure and over-flow stress, according to a design scheme of the diversion tunnel and hydrogeological exploration data of the diversion tunnel, the change range of the superhydrostatic pressure caused by time sequence precipitation of a target tunnel section is calculated, a mechanical model of the diversion tunnel bearing internal and external dynamic loads is established, a stress equation of a critical yield of an elastic-plastic structure is constructed, a stress field equation of the diversion tunnel structure under the action of non-constant loads is established, and then a mechanical criterion equation of the stability of the diversion tunnel is obtained, the safety range of the dynamic load is calculated, and the service safety of the diversion tunnel is evaluated according to the safety range, the change of the superhydrostatic pressure caused by drought, flood season or short-time precipitation is considered, and the potential risk of the damage of the diversion tunnel is reduced.

Description

Technical Field

[0001] This invention belongs to the field of structural stability evaluation, specifically relating to a method for analyzing the stability of a water diversion tunnel that considers temporal excess hydrostatic pressure and flow stress. Background Technology

[0002] A water diversion tunnel is an underground tunnel in a water conservancy project that serves purposes such as water diversion for power generation, irrigation of farmland, or water supply. On one hand, when the water diversion tunnel is connected to the working gate, its entire cross-section is intermittently filled with water. At this time, the tunnel wall experiences significant intermittent flow stress. This alternating phenomenon of open and closed flow can easily cause vibrations, cavitation, and other unfavorable flow conditions, leading to damage to the water diversion tunnel. On the other hand, affected by seasons and drought / flood periods, the excess static water pressure at the location of the water diversion tunnel increases or decreases with changes in water head. In particular, when short-term rainfall occurs, the rapid accumulation of precipitation around the tunnel causes a sharp change in excess static water pressure. This temporal variation in external forces coupled with internal intermittent stress poses a severe challenge to the service safety of the water diversion tunnel. However, existing design and construction processes rarely take into account the changes in internal pressure and the fluctuations in temporal excess static water pressure within the water diversion tunnel. This either leads to an overly optimistic assessment of the tunnel's pressure-bearing capacity or a conservative design, resulting in wasted materials. Summary of the Invention

[0003] The purpose of this invention is to solve the above-mentioned problems and provide a service analysis method for water diversion tunnels that considers the coupling of sequential excess static water pressure and intermittent overflow stress. This invention couples the intermittent internal pressure during the operation of the hydraulic engineering project with the sequential excess static water pressure outside the tunnel to calculate the safe range of dynamic loads, thereby evaluating the serviceability of the water diversion tunnel and providing a reference for design and construction.

[0004] The technical solution of this invention is a method for analyzing the stability of a water diversion tunnel considering time-series excess hydrostatic pressure and flow stress, comprising the following steps:

[0005] Step 1: Based on the design scheme of the water diversion tunnel and the hydrogeological survey data of the water diversion tunnel, calculate the range of variation of excess hydrostatic pressure caused by the time-series precipitation in the target tunnel section;

[0006] Step 1.1: Take a representative rock block overlying the water diversion tunnel for mechanical parameter testing;

[0007] Step 1.2: Based on the design plan of the water diversion tunnel and the preliminary hydrogeological survey data of the water diversion tunnel project, determine the burial depth of the target tunnel and the temporal changes in water head;

[0008] Step 1.3: Obtain the magnitude of the geostress around the tunnel and calculate the range of variation of the time-series hydrostatic pressure;

[0009] Step 2: Establish a mechanical model of the water diversion tunnel subjected to internal and external dynamic loads;

[0010] Step 2.1: To ensure strength requirements and to minimize construction and save materials, a suitable constitutive model of the water diversion tunnel, i.e., a mechanical model of the water diversion tunnel, should be selected.

[0011] Step 2.2: Set internal and external loads for the constitutive model of the water diversion tunnel. The internal load is the intermittent load during the flow, and the external load is the dynamic load composed of the overburden stress of the water diversion tunnel and the time-sequential excess hydrostatic pressure.

[0012] Step 3: Construct the stress equation for the critical yield of the elastoplastic structure;

[0013] Step 4: Based on the actual working state of the water diversion tunnel, and without considering the loading history, establish the physical equations satisfied by the non-failure external loads that are greater than the elastic limit but less than the ultimate limit on the structure of the water diversion tunnel.

[0014] Step 5: Construct the stress field equations under linear elastic conditions when the structure is subjected to non-constant loads inside and outside;

[0015] Step 6: Based on the stress field of the structure being subjected to non-constant loads both inside and outside, obtain the stress relationship equation of the structure under plastic deformation under the influence of non-constant stress field fluctuations inside and outside the water diversion tunnel.

[0016] Step 7: Determine the mechanical criteria for structural stability. Substitute the physical equations, stress field equations, and stress relationship equations obtained in Steps 4-6 into the stress equations in Step 3 to obtain the mechanical criteria equations for the stability of the water diversion tunnel.

[0017] Step 8: Based on the range of time-series excess hydrostatic pressure, use the mechanical criterion equation obtained in Step 7 to solve for the safe value of pressure change inside the water diversion tunnel.

[0018] Step 9: Based on the calculation results of Step 8, analyze and obtain the mechanical requirements and improvement suggestions that the design and construction of the water diversion tunnel need to meet.

[0019] Furthermore, in step 1, the burial depth of the water diversion tunnel is H, and the height by which the groundwater head exceeds the center of the water diversion tunnel during the water-rich period is h. w The maximum hydrostatic pressure is

[0020] P W,d =P max =p 水 gh

[0021] In the formula P W,d Indicates superhydrophobic pressure, P max For the maximum hydrostatic pressure, r 水This indicates the density of water. g It is the acceleration due to gravity;

[0022] During short water periods, the water head drops below the tunnel body, resulting in excess hydrostatic pressure on the tunnel body.

[0023] P W,d = 0;

[0024] Therefore, excess hydrostatic pressure under water level fluctuations P W,d The dynamic range is 0 - P max .

[0025] Preferably, in step 2, the mechanical model of the water diversion tunnel is an ideal elastoplastic constitutive model, and the water diversion tunnel is subjected to intermittent water flow pressure. P s.d The exterior of the tunnel is subjected to compressive forces exerted by the surrounding rock and soil environment. P e,s and time-sequential excess hydrostatic pressure P W,d The resultant force on the outside of the cave P h,d for P e,s and P W,d sum.

[0026] Preferably, in step 2.1, the tunnel body is considered to be an elastic-plastic material.

[0027] Furthermore, in step 3, the stress equation for the critical yield of the elastoplastic structure is:

[0028]

[0029] In the formula s r , s θ These represent the maximum and minimum principal stresses at a specific point in the structure, respectively. f , c These are the cohesion and internal friction angle of the pressurized water diversion tunnel structure, respectively. r and i These represent the polar distance and polar angle in polar coordinates, respectively.

[0030] Furthermore, in step 4, the physical equation for the water diversion tunnel structure bearing the non-failure external load is:

[0031]

[0032] In the formula s eij This represents the purely elastic stress field generated by a changing external load. e p ij For plastic strain rate, v p i Represents the velocity field. s p ij Represents the plastic stress field, where υ is the volume element variable. c The unit weight of the overlying representative rock mass; V This indicates the volume of the water diversion tunnel. dV Volumetric micro-element.

[0033] Furthermore, in step 5, the stress field equations under the linear elastic state of the water diversion tunnel structure subjected to non-constant loads are as follows:

[0034]

[0035] In the formula Indicates the inner diameter of the water diversion tunnel. Indicates the outer diameter of the water diversion tunnel. This represents radial elastic normal stress.

[0036] Furthermore, in step 6, the stress relationship equation of the water diversion tunnel structure in the plastic state is:

[0037]

[0038] In the formula Represents radial plastic normal stress. This represents circumferential plastic normal stress.

[0039] Preferably, in step 7, the mechanical criterion equation for the stability of the water diversion tunnel is:

[0040] .

[0041] Furthermore, in step 8, the safe range for pressure changes within the water diversion tunnel is 0~ P s,d .

[0042] Compared with the prior art, the beneficial effects of the present invention include:

[0043] 1) This invention couples the intermittent internal pressure during the operation of the water diversion tunnel with the temporal excess static water pressure outside the tunnel body to establish a mechanical model of the water diversion tunnel subjected to internal and external dynamic loads. It constructs the stress equation for the critical yield of the elastoplastic structure and the stress field equation for the linear elastic state under non-constant loads inside and outside the water diversion tunnel structure. Then, it obtains the mechanical criterion equation for the stability of the water diversion tunnel, calculates the safe range of dynamic loads, and evaluates the service safety of the water diversion tunnel. It considers the adverse effects of changes in excess static water pressure caused by drought, flood season or short-term precipitation on the tunnel body, and reduces the potential risk of water diversion tunnel damage.

[0044] 2) This invention takes into account the intermittent load caused by the instability of the flow cross section when the pressurized water diversion tunnel is working, and can avoid damage to the water diversion tunnel caused by unfavorable flow states such as tunnel vibration and cavitation.

[0045] 3) The mechanical judgment criteria equation for the stability of the water diversion tunnel involves multiple factors such as material properties, structural dimensions, and hydrogeological conditions. The constructed model has good conformity with actual water conservancy projects and has important guiding significance for the site selection, design, construction, and subsequent production of water conservancy hubs. Attached Figure Description

[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0047] Figure 1 This is a schematic diagram of the water diversion tunnel during the water-rich period according to an embodiment of the present invention.

[0048] Figure 2 This is a schematic diagram of the water diversion tunnel during the low-water season according to an embodiment of the present invention.

[0049] Figure 3 This is a schematic diagram of the mechanical model of the water diversion tunnel according to an embodiment of the present invention. Detailed Implementation

[0050] A method for analyzing the stability of a water diversion tunnel considering temporal excess hydrostatic pressure and flow stress includes the following steps:

[0051] Step 1: Obtain the bulk density and Poisson's ratio of the representative overlying rock sample by bulk density testing and triaxial compression testing. c and m.

[0052] like Figure 1 As shown, the target water diversion tunnel is buried at a depth of H, and the groundwater head during the water-rich period exceeds the center of the water diversion tunnel by a height of h. w The density of water is r 水 , g Given the acceleration due to gravity, the maximum excess hydrostatic pressure can be calculated as follows:

[0053] PW,d =p 水 gh (1)

[0054] like Figure 2 As shown, during the short water period, the water head drops below the tunnel body, resulting in excessive hydrostatic pressure on the tunnel body. P W,d = 0. Therefore, the excess hydrostatic pressure under water level fluctuations P W,d The dynamic range is 0 ~ r 水 gh .

[0055] Step Two: The water diversion tunnel is a circular concrete structure, therefore it is considered as a thick-walled cylindrical model bearing internal and external dynamic pressure. Treating concrete as a linear elastic material would not fully utilize its strength and would not conform to lightweight design, resulting in a waste of resources. Therefore, an ideal elastic-plastic structure is more suitable for the constitutive model.

[0056] like Figure 3 As shown, the interior of the pressurized water diversion tunnel is subjected to intermittent water flow pressure, denoted as . P s.d The tunnel is subjected to two forces: the compressive force exerted by the surrounding rock and soil environment. P e,s With time-sequential excess hydrostatic pressure P W,d The resultant force on the outside of the cave P h,d The sum of the two, its range of variation is P e,s ~P e,s +P W,d .

[0057] Step 3: Based on the continuous stress condition at the elastic-plastic boundary, the critical yield condition of an ideal elastic-plastic structure in polar coordinates can be expressed as follows: (2)

[0058] s r and s θ This represents the maximum and minimum principal stresses at a specific point in the structure. f and c These are the cohesion and internal friction angle of the pressurized water diversion tunnel structure, respectively, which can be obtained through rock mechanics tests; r and i These represent the polar distance and polar angle in polar coordinates, respectively.

[0059] Step 4: Once the water diversion tunnel structure reaches an elastoplastic boundary under load, the constant gravity load and the load under the basic groundwater level conditions are considered as the basic loads. This will generate a stress within the structure. s r ij ; i , j The index represents the stress field tensor; when the groundwater level fluctuates over time and the flow rate changes, the diversion tunnel is considered to be under varying loads. s e ij Purely elastic stress field generated by varying external loads s e ij This is a hypothetical stress field. On the other hand, it is assumed that there exists a dynamically permissible plastic strain rate. e p ij The cycle and its associated velocity field v p i and plastic stress field s p ij The strong form of the statement is: the necessary condition for structural stability is that, at any moment during the load cycle, the power of the external force is less than the power dissipated by the plastic internal energy on the volume element variable υ. The physical equation expression is:

[0060] (3)

[0061] In the formula V Let υ represent the volume of the water diversion tunnel, and υ be a volume element variable. Represents the velocity field. c The unit weight formula (3) of the representative rock sample overlying the water diversion tunnel is equal under critical conditions.

[0062] Step 5: The water diversion tunnel structure is subjected to non-constant loads both inside and outside. When it is in a linear elastic state, the stress field under the action of the two stress couplings satisfies equation (4).

[0063] (4)

[0064] In the formula Indicates the inner diameter of the water diversion tunnel. This indicates the outer diameter of the water diversion tunnel.

[0065] Step Six: Due to the influence of internal and external non-constant stress field fluctuations, the structure exhibits elastoplastic partitioning. The plastic part should simultaneously satisfy the plastic equilibrium condition and equation (2). Therefore, the stress relationship equation under plastic conditions can be obtained as follows:

[0066] (5)

[0067] Step 7: The physical equation of equation (3) is applied in the mechanical model of the water diversion tunnel as the residual stress field obtained during a loading process, namely elastic loading-plastic loading-elastic unloading, as an indicator of energy dissipation and satisfying the critical yield condition of equation (2). Thus, the mechanical criteria for maintaining the stability of the water diversion tunnel structure are calculated.

[0068] Substituting equations (4) and (5) into equation (2) and solving, we obtain the mechanical judgment criterion as follows:

[0069] (6)

[0070] Step 8: According to the mechanical judgment criterion, i.e., equation (6), the safe range of pressure change inside the water diversion tunnel should be 0~ P s,d The critical flow pressure of the water diversion tunnel is related to the excess hydrostatic pressure, burial depth stress, cohesion of the tunnel concrete, internal friction angle, and geometric dimensions.

[0071] Step 9: Through the discussion of equation (6), it can be seen that the fluctuation of hydrostatic pressure will weaken the maximum internal pressure that the water diversion tunnel can withstand. This can be compensated by adjusting the wall thickness during design or construction. At the same time, increasing the cohesion of the concrete material or reducing the internal friction angle is also beneficial to improving the bearing capacity.

[0072] Taking a hydropower station on the Jinsha River in Sichuan Province as an example, four parallel pressure pipelines are arranged in the water diversion tunnel, using a single-unit, single-pipe water supply system. A bend is arranged in the pressure pipeline plane with a turning radius of 40.00m. Before the bend, the distance between pipe axes is 26.00m, and after the bend, the distance between pipe axes is 31.20m. The pipeline axis deviates from S85.5°E to S40°E towards the power station. The pipeline inner diameter is 9.50m, and the flow velocity inside the pipe is 4.58m / s. The water diversion tunnel is buried at a depth of -305.5m, with a surrounding ground stress of 23.25~26.53MPa and a maximum groundwater level of -102.35m during the flood season. C30 grade impermeable concrete is used. Calculations show that the water diversion tunnel can withstand a maximum pressure of 3.05MPa, while the design pressure is 2.90MPa. Therefore, the difference between the design pressure and the ultimate value is small, meeting the strength requirements. However, considering the complex construction conditions, it is best to increase the margin or thicken the inner lining.

Claims

1. A method for stability analysis of a headrace tunnel considering time-dependent hydrostatic pressure and seepage stress, characterized in that, It comprises the following steps: Step 1: according to the design scheme of the diversion tunnel and the hydrogeological exploration data of the diversion tunnel, the change range of the excess hydrostatic pressure caused by the time sequence rainfall of the target tunnel section is calculated; Step 2: a mechanical model of the diversion tunnel bearing internal and external dynamic loads is established; Step 2.1: in order to ensure the strength requirement and make the construction as light as possible, the constitutive model of the diversion tunnel, i.e. the mechanical model of the diversion tunnel, is reasonably selected; Step 2.2: internal and external loads are set for the constitutive model of the diversion tunnel, the internal load is the discontinuous load during flow, and the external load is the dynamic load composed of the overburden stress and the time sequence excess hydrostatic pressure of the diversion tunnel; Step 3: a stress equation of critical yielding of the elastic-plastic structure is constructed; The stress equation of critical yielding of the elastic-plastic structure is ； wherein Step 4: according to the actual working state of the diversion tunnel, the physical equation of the non-failure external load borne by the structure of the diversion tunnel is established without considering the loading history; r , Step 5: a stress field equation of the linear elastic state of the structure of the diversion tunnel under the action of non-constant internal and external loads is constructed; θ respectively represent the maximum and minimum principal stress at a certain point of the structure, Step 6: according to the stress field of the structure of the diversion tunnel under the action of non-constant internal and external loads, a stress relationship equation of the plastic deformation state of the structure of the diversion tunnel is obtained under the influence of the non-constant internal and external stress field fluctuations of the structure of the diversion tunnel; , c respectively represent the cohesion and internal friction angle of the structure of the pressurized diversion tunnel; r and Step 7: the mechanical criterion of the stability of the structure of the diversion tunnel is determined, the physical equation, the stress field equation and the stress relationship equation obtained in steps 4-6 are substituted into the stress equation of step 3, and the mechanical criterion equation of the stability of the diversion tunnel is obtained; respectively represent the polar axis distance and polar angle under the polar coordinates; The mechanical criterion equation of the stability of the diversion tunnel is Step 8: according to the range of the time sequence excess hydrostatic pressure, the mechanical criterion equation obtained in step 7 is used to solve the safety value of the internal pressure change of the diversion tunnel. It further comprises step 9: according to the calculation result of step 8, the mechanical requirements to be met by the design and construction of the diversion tunnel and the improvement suggestions are analyzed and obtained. Step 1 specifically comprises the following sub-steps: Step 1.1: a representative rock block overlying the diversion tunnel is taken for mechanical parameter test; ； wherein, P s.d to withstand intermittent water flow pressure inside the diversion tunnel, P e,s to withstand extrusion pressure applied by the surrounding rock and soil environment outside the tunnel body, P W,d to withstand time-series superhydrostatic pressure, denotes the inner diameter of the diversion tunnel, denotes the outer diameter of the diversion tunnel; Step 1.2: according to the design scheme of the diversion tunnel and the pre-project hydrogeological exploration data of the diversion tunnel, the target tunnel depth and the time sequence water head change are determined; 2. The method of stability analysis of a headrace tunnel considering time-dependent superhydrostatic pressure and over-flow stress according to claim 1, characterized in that, Step 1.3: the ground stress around the tunnel is obtained, and the change range of the time sequence excess hydrostatic pressure is calculated.

3. The method of stability analysis of a headrace tunnel considering time-dependent superhydrostatic pressure and over-flow stress according to claim 1 or 2, characterized in that, The maximum excess hydrostatic pressure of the water head is The excess hydrostatic pressure of the tunnel body when the water head falls below the tunnel body during the short water period is In step 4, the physical equation of the non-failure external load borne by the structure of the diversion tunnel is In step 5, the stress field equation of the linear elastic state of the structure of the diversion tunnel under the action of non-constant internal and external loads is 4. The method of stability analysis of a headrace tunnel considering time-dependent superhydrostatic pressure and over-flow stress according to claim 3, characterized in that, In step 1, the depth of the buried depth of the water tunnel body is H, and the height of the groundwater head exceeding the center of the water tunnel during the water-rich period is h w , In step 6, the stress relationship equation of the plastic state of the structure of the diversion tunnel is P W,d =P max ​ 水 ​ w ； wherein P W,d Pmaxdenotes the maximum hydrostatic pressure, P max Pmaxdenotes the maximum hydrostatic pressure, ​ 水 Pmaxdenotes the maximum hydrostatic pressure, g g denotes the gravitational acceleration; ​ P W,d = 0； Thus, the dynamic range of the excess hydrostatic pressure under water level fluctuations P W,d is 0 - P max .

5. The method of stability analysis of a headrace tunnel considering time-dependent superhydrostatic pressure and over-flow stress according to claim 4, characterized in that, In step 2, the mechanical model of the water tunnel selects an ideal elastic-plastic constitutive model, and the resultant force on the outside of the tunnel body is P h,d To P e,s With P W,d And.

6. The method of stability analysis of a diversion tunnel considering time-dependent super-hydrostatic pressure and over-flow stress according to claim 5, wherein, ​ ； where ​ e ij denotes the pure elastic stress field due to the varying external load, e p ij is the plastic strain rate, v p i denotes the velocity field, ​ p ij denotes the plastic stress field, i 、 j denotes the order of the stress field tensor; υ is the volume variable, ​ is the bulk density of the overlying representative rock mass; V denotes the volume of the diversion tunnel, ​ volume element.

7. The method according to claim 6, wherein the time-dependent superhydrostatic pressure and the excess flow stress are considered in the stability analysis of the headrace tunnel. ​ ； In the formula denotes the inner diameter of the diversion tunnel, denotes the outer diameter of the diversion tunnel, denotes the radial elastic normal stress.

8. The method according to claim 7, wherein the time-dependent superhydrostatic pressure and the excess flow stress are considered in the stability analysis of the headrace tunnel. ​ ； In the formulae denotes the radial plastic normal stress, denotes the circumferential plastic normal stress.

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