CN113607770A - A Stability Analysis Method for Geotechnical Engineering Structures in Bedded Rocks in Seasonally Frozen Regions - Google Patents

Abstract

The invention discloses a stability analysis method of rock mass engineering structure in bedding rock in seasonal freezing area. S1: define the bedding-freeze-thaw coupling damage variable of rock mass; S2: establish nonlinear viscoelastic-plastic creep constitutive model; S3: establish a three-dimensional creep equation, and program the nonlinear viscoelastic-plastic creep constitutive model; S4: verify the results of the triaxial creep test of rocks under different bedding angles and different freeze-thaw times Correctness and applicability of the nonlinear visco-elastic-plastic creep constitutive model; S5: Using the nonlinear visco-elastic-plastic creep constitutive model to calculate the freeze-thaw slope stability coefficient under different freeze-thaw times. The nonlinear viscoelastic-plastic creep constitutive model established by the present invention considering the bedding-freeze-thaw coupling damage variable can better reflect the freezing-thawing-bedding damage of the bedding rock mass due to freezing-thawing- Freeze-thaw-bedding coupled damage and creep properties due to bedding effects and time effects.

Description

A Stability Analysis Method for Geotechnical Engineering Structures in Bedded Rocks in Seasonally Frozen Regions

technical field

The invention relates to the field of geotechnical engineering in bedding rocks in seasonally frozen areas, in particular to a stability analysis method for geotechnical engineering structures in bedded rocks in seasonally frozen areas.

Background technique

The freeze-thaw creep characteristics of rock mass is one of the important mechanical characteristics of bedded rock mass engineering, and it is closely related to the long-term stability of bedded rock mass engineering. In slope control, tunnel construction, mining and other projects, the failure of bedded rock mass due to freezing and thawing and long-term load is one of its main failure forms. Especially with the development of rock mass engineering construction in cold regions, the damage and deterioration of bedding rocks under the action of freeze-thaw cycles are serious, and the creep characteristics are more significant, which will adversely affect the long-term stability of cold region engineering.

SUMMARY OF THE INVENTION

The invention provides a stability analysis method for the geotechnical engineering structure in the bedding rock in the seasonal freezing area, so as to overcome the serious damage and deterioration of the bedding rock under the action of freezing and thawing cycle, and the creep characteristic has an adverse effect on the long-term stability of the cold area engineering technical issues.

In order to achieve the above object, the technical scheme of the present invention is:

A method for analyzing the stability of geotechnical engineering structures in bedded rocks in a seasonally frozen area, comprising the following steps:

S1: Define the bedding-freeze-thaw coupled damage variable D _β ,n of the rock, and the bedding-freeze-thaw coupled damage variable D _β,n represents the rock damage caused by different bedding angles and different freeze-thaw cycles;

S2: Establish a nonlinear visco-elastic-plastic creep constitutive model considering the bedding-freeze-thaw coupling damage variable D _{β, n} to characterize the stress-strain relationship under the influence of different bedding angles and different freeze-thaw cycles on rocks ;

S3: Establish a three-dimensional creep equation to analyze the stability of geotechnical engineering in anisotropic rocks;

S4: Verify the correctness and applicability of the nonlinear viscoelastic-plastic creep constitutive model according to the results of the triaxial creep test of rocks under different bedding angles and different freeze-thaw times;

S5: Using the validated nonlinear viscoelastic-plastic creep constitutive model, calculate the freeze-thaw slope stability coefficient under different freeze-thaw times to determine the sliding surface position and short-term failure state of rock and soil in the slope rock. stability.

The present invention provides a stability analysis method for geotechnical engineering structures in bedded rocks in seasonally frozen areas, establishes a nonlinear visco-elastic-plastic creep constitutive model considering bedding-freeze-thaw coupled damage variables, and can better respond Based on the freeze-thaw-bedding damage of the rock, the freeze-thaw-bedding coupling damage and creep characteristics of the bedded rock mass due to the freeze-thaw-bedding effect and the time effect are shown. The technical problem of serious damage and deterioration of bedding rock under the action of freeze-thaw cycles and the adverse effect of creep characteristics on the long-term stability of cold-region engineering is solved.

Description of drawings

In order to illustrate the embodiments of the present invention or the technical solutions in the prior art more clearly, the following will briefly introduce the accompanying drawings used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description These are some embodiments of the present invention, and for those of ordinary skill in the art, other drawings can also be obtained from these drawings without any creative effort.

Fig. 1 is the flow chart of the present invention;

FIG. 2 is a diagram of the layering-freeze-thaw coupling damage software component diagram of the present invention;

FIG. 3 is a diagram of the layering-freeze-thaw coupling damage elastic element of the present invention;

Fig. 4 is the combination diagram of the bedding-freeze-thaw coupling damage Kelvin body element of the present invention;

FIG. 5 is a diagram of the bedding-freeze-thaw coupling damage viscous element of the present invention;

Fig. 6 is the non-linear viscoelastic-plastic creep model element combination diagram of the present invention;

Figure 7 (a) is a comparison diagram of the rock test value and the calculated value of 0 freeze-thaw cycles when the bedding angle of the present invention is 0°;

Figure 7(b) is a comparison diagram of the rock test value and the calculated value of 20 freeze-thaw cycles when the bedding angle is 0°;

Figure 7(c) is a comparison diagram of the rock test value and the calculated value of 40 freeze-thaw cycles of the present invention when the bedding angle is 0°;

Figure 7(d) is a comparison diagram of rock test values and calculated values of 60 freeze-thaw cycles of the present invention when the bedding angle is 0°;

Figure 7(e) is a comparison diagram of rock test values and calculated values for 80 freeze-thaw cycles of the present invention when the bedding angle is 0°;

Fig. 8 (a) is the slope shear strain cloud map of the present invention when the bedding angle is 0° for 80 freeze-thaw cycles;

Figure 8(b) is a cloud diagram of the shear strain of the slope of the present invention when the bedding angle is 30° for 80 freeze-thaw cycles;

Fig. 8 (c) is the slope shear strain cloud map of the present invention when the bedding angle is 45° for 80 freeze-thaw cycles;

Figure 8(d) is a cloud diagram of the shear strain of the slope of the present invention when the bedding angle is 60° for 80 freeze-thaw cycles;

Fig. 8 (e) is the slope shear strain cloud map of the present invention when the bedding angle is 90° for 80 freeze-thaw cycles;

Fig. 9 is a graph showing the relationship between the number of freeze-thaw times of rock mass and the safety factor of rock mass slope when the bedding angle is 0° according to the present invention.

Detailed ways

In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments These are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

The present embodiment provides a method for analyzing the stability of geotechnical engineering structures in bedded rocks in a seasonally frozen area, including the following steps: as shown in FIG. 1 :

S1: Define the bedding-freeze-thaw coupled damage variable D _β ,n of the rock, and the bedding-freeze-thaw coupled damage variable D _β,n represents the damage of the rock caused by different bedding angles and different freeze-thaw cycles;

The method for establishing the bedding-freeze-thaw coupling damage variable D _{β, n} is:

According to the strain equivalence principle proposed by Lemaitre, the strain caused by stress σ acting on damaged material is equivalent to the strain caused by effective stress σ′ acting on non-destructive material, namely:

where E is the elastic modulus of the non-destructive material, and E' is the elastic modulus of the damaged material;

The bedding-freeze-thaw coupled damage variable D _β,n is defined as:

where W _β,n is the elastic modulus of the rock with the bedding angle β and the freeze-thaw number n; W _β,0 is the elastic modulus of the rock with the bedding angle β and the freeze-thaw number of 0.

S2: Establish a nonlinear viscoelastic-plastic creep constitutive model considering the bedding-freeze-thaw coupled damage variable D _β,n to characterize the stress-strain relationship under the influence of different bedding angles and different freeze-thaw cycles on the rock; From the triaxial creep tests of rocks with different bedding angles and different freeze-thaw times, it is known that the rock and soil in the bedded rock undergoes deceleration creep stage, stable creep stage and accelerated creep stage successively after freeze-thaw cycles. The classical creep model can describe the decelerated creep and steady-state creep stages of the bedded rock creep test well, but it cannot reflect the accelerated creep characteristics of the bedded rock. Therefore, based on the classical creep model, this paper replaces the viscous elements in viscoplastic body with freeze-thaw damage viscous elements, and considers the effect of freeze-thaw cycles on model parameters, and establishes the freeze-thaw creep model of bedding slate. Build model.

The nonlinear viscoelastic-plastic creep constitutive model is created based on a combination of classical creep models; the classical creep model combination includes a bedding-freeze-thaw coupled damage Maxwell body, a bedding-freeze-thaw coupled damage Kelvin body and a bedding - Freeze-thaw coupled damage Binham body; the bedding-freeze-thaw coupled damage Maxwell body represents the instantaneous elastic deformation and viscous deformation during the creep process of rock mass materials, including series bedding-freeze-thaw coupled damage elastic elements and layers The bedding-freeze-thaw coupling damages the viscous element; the bedding-freeze-thaw coupling damage Kelvin body represents the viscoelastic deformation of the rock mass material during the creep process, including the parallel bedding-freeze-thaw coupling damage elastic element and the bedding- Freeze-thaw coupled damage software element; the bedding-freeze-thaw coupled damage Binham body represents the viscoplastic deformation during the creep process of rock mass materials, including parallel bedding-freeze-thaw coupled damage plastic elements and bedding-freeze-thaw coupling Damage software components; the present invention replaces the viscous components in the traditional viscoplastic body with bedding-freeze-thaw damaged software components, which can make the rock mass model closer to the state of the real rock, as shown in Figures 2-5.

The steps for establishing the nonlinear viscoelastic-plastic creep constitutive model are as follows:

S21: The soft body element represents the stress-strain characteristic between the ideal elastic body and the ideal fluid or expresses the accelerated creep state of the material. The damaged soft body element under freeze-thaw conditions is essentially a soft body under the action of bedding-freeze-thaw coupling. The constitutive relation of the bedding-freeze-thaw coupled damage software component is:

In the formula: t is the time; σ(t) represents the corresponding stress at time t; ε(t) represents the corresponding strain at time t; η is the viscosity coefficient of the software component; ≤1, when m=0, formula (3) degenerates into the Hooke body stress-strain relationship, when m=1, formula (3) degenerates into the Newton body stress-strain relationship, when 0<m<1, it means between Stress-strain characteristics between an ideal elastomer and an ideal fluid; when m>1, the accelerated creep state of the material is expressed;

S22: Establish the constitutive relation of the layered-freeze-thaw coupled damage elastic element as:

Then the constitutive relation of the Maxwell body considering bedding-freeze-thaw coupling damage is:

where ε _M is the strain component generated by the Maxwell body with bedding-freeze-thaw coupled damage; E _M is the elastic modulus of the Maxwell body with bedding-freeze-thaw coupled damage;

S23: Establish the constitutive relation of the bedding-freeze-thaw coupled damage Kelvin body as:

Where: ε _H is the strain component of the elastic element damaged by bedding-freeze-thaw coupling in the Kelvin body; ε _N is the strain component of the soft element in the Kelvin body with bedding-freeze-thaw coupling damage; E _k is the layer is the elastic modulus of the Kelvin body damaged by the coupling of freezing and thawing; ε _k is the strain component of the Kelvin body damaged by the _coupling of bedding and freezing and thawing; -Fractional order in Kelvin body of freeze-thaw coupling damage, 0≤m1≤1;

From formula (6), we can get:

则公式(7)改写为：When t=0, ε _k (t)=0, assuming

Then formula (7) can be rewritten as:

The main advantage of the Caputo method is that the initial conditions of the fractional differential equations can be in the same form as the integer differential equations; therefore, according to the fractional calculus theory, the Riemann-Liouville fractional derivative is converted into the Caputo fractional derivative as:

Where: C represents the Caputo fractional derivative; k is a positive integer; D _t ^m f(t) is the Riemann-Liouville fractional derivative;

When ε _k (0)=0, D ^m [ε _K (t)] = ^C D ^m [ε _K (t)], then equation (8) is rewritten as:

b=aε _K + ^C D ^m [ε _K (t)] (10)

Laplace transform on both sides of formula (9), we get

In the formula: S=σ+jω is the complex parameter variable;

therefore,

Continuing to perform the Laplace transform, we get

in,

but,

代入可得进过变换后的层理-冻融耦合损伤Kelvin体的本构关系为：Will

Substitute into the transformed bedding-freeze-thaw coupled damage Kelvin body constitutive relation is:

S24: Establish the constitutive relation of the bedding-freeze-thaw coupled damage viscous element:

为Newton体的应变速率，η_M为Newton体黏滞系数；where:

is the strain rate of the Newton body, η _M is the Newton body viscosity coefficient;

S25: Establish the constitutive relation of the bedding-freeze-thaw coupled damage Binham as;

where η _B is the viscosity coefficient of the Binham body with bedding-freeze-thaw coupling damage; m ₂ is the fractional order in the _Binham body with bedding-freeze-thaw coupling damage; the stress threshold of the plastic element;

S26: Figure 6 shows the combination diagram of nonlinear viscoelastic-plastic creep model elements that comprehensively consider bedding-freeze-thaw coupled damage Maxwell body, bedding-freeze-thaw coupled damage Kelvin body and bedding-freeze-thaw coupled damage Binham body , the nonlinear viscoelastic-plastic creep constitutive model is established as follows:

S3: In order to implement the programming of the nonlinear viscoelastic-plastic creep constitutive model using the secondary development platform, a three-dimensional creep equation is established for subsequent analysis of the stability of geotechnical engineering in anisotropic rocks; The establishment method of the creep equation is: deriving the equation through the finite difference method: the present invention adopts the FLAC ^3D secondary development platform to realize the programming of the nonlinear viscoelastic-plastic creep constitutive model.

层理-冻融耦合损伤Kelvin体的应变

和层理-冻融耦合损伤Binham体的应变

即It is assumed that the rock strain εij consists of three parts, namely: the strain of the Maxwell body damaged by bedding-freeze-thaw coupling

Strain of Kelvin bodies damaged by bedding-freeze-thaw coupling

and bedding-freeze-thaw coupling damage to the Binham body strain

which is

The deviatorial strain has the following form:

为偏应变，

为层理-冻融耦合损伤Maxwell体的偏应变、

为层理-冻融耦合损伤Kelvin体的偏应变、

为层理-冻融耦合损伤Binham体的偏应变；in the formula

is the bias strain,

is the deviatorial strain of the Maxwell body damaged by bedding-freeze-thaw coupling,

is the deviatorial strain of the Kelvin body damaged by the bedding-freeze-thaw coupling,

is the deviatorial strain of the Binham body damaged by bedding-freeze-thaw coupling;

Writing the deviatorial strain in incremental form, the relationship between the deviatorial strain increments can be obtained:

为层理-冻融耦合损伤Maxwell体的偏应变增量、

为层理-冻融耦合损伤Kelvin体的偏应变增量和

为层理-冻融耦合损伤Binham体的偏应变增量；where: Δe _ij is the deviatorial strain increment,

is the deviatorial strain increment of the Maxwell body damaged by bedding-freeze-thaw coupling,

are the deviatorial strain increments and

is the deviatorial strain increment of the Binham body damaged by bedding-freeze-thaw coupling;

Continue to deduce the formula, and get: the bedding-freeze-thaw coupling damages the elastic element:

Bedding-freeze-thaw coupling damages Kelvin bodies:

where S _ij is the deviatoric stress, G is the shear modulus; η _K is the viscosity coefficient of the Kelvin body damaged by bedding-freeze-thaw coupling;

The strain rate of the Binham body damaged by bedding-freeze-thaw coupling can be written as

where g is the plastic yield potential function, η _B is the viscosity coefficient of the Binham body damaged by bedding-freeze-thaw coupling, <F> is the switching function, and its expression is as follows:

Write equation (25) in the form of a deviatorial strain rate:

为层理-冻融耦合损伤Binham体的体积应变；where:

is the volumetric strain of the Binham body damaged by bedding-freeze-thaw coupling;

The total strain increment can be obtained from equation (26):

Using the central difference form, the bedding-freeze-thaw coupled damage elastic element can be written as

为中心差分形式的偏应力，

为层理-冻融耦合损伤Maxwell体中心差分形式的的偏应变；Δt为时间增量；in the formula

is the deviatoric stress in the form of central difference,

is the deviatorial strain in the form of the difference in the center of the Maxwell body with bedding-freeze-thaw coupling damage; Δt is the time increment;

Using the central difference form, the bedding-freeze-thaw coupled damage Kelvin body can be written as

为层理-冻融耦合损伤Kelvin体中心差分形式的的偏应变。Δt为时间增量。η_K为层理-冻融耦合损伤Kelvin体的黏滞系数，in the formula

is the deviatorial strain in the differential form of the center of the Kelvin body damaged by the bedding-freeze-thaw coupling. Δt is the time increment. η _K is the viscosity coefficient of the Kelvin body damaged by bedding-freeze-thaw coupling,

in:

代表一个时间增量内的应力偏量的旧值；

代表一个时间增量内的应力偏量的新值，

代表一个时间增量内的应力偏量的旧值；

为一个时间增量内的应变偏量的新值；In the formula,

represents the old value of the stress deflection within a time increment;

represents the new value of the stress deflection within a time increment,

represents the old value of the stress deflection within a time increment;

is the new value of the strain deflection within a time increment;

Deviatorial strain of Kelvin bodies damaged by bedding-freeze-thaw coupling

为层理-冻融耦合损伤Kelvin体偏应变的旧值、

为层理-冻融耦合损伤Kelvin体偏应变的新值。where:

is the old value of the deviatorial strain of the Kelvin body for bedding-freeze-thaw coupling damage,

is the new value of the deviatoric strain of the Kelvin body for bedding-freeze-thaw coupled damage.

in:

Finally, the updated deviatoric stress is obtained

和

分别为层理-冻融耦合损伤Binham体和层理-冻融耦合损伤Maxwell体的偏应变增量；where: Δe _ij is the deviatorial strain increment,

and

are the deviatorial strain increments of the bedding-freeze-thaw coupled damage Binham body and the bedding-freeze-thaw coupled damage Maxwell body, respectively;

in:

According to the knowledge of plastic mechanics, it is considered that the spherical stress does not produce plastic deformation, so the spherical stress of the entire bedding-freeze-thaw damage creep model is written as:

为球应力的新值；

为球应力的旧值，K为体积模量，Δε_vol为体积应变增量；

为层理-冻融耦合损伤Binham体的体积应变增量；in the formula

is the new value of spherical stress;

is the old value of the spherical stress, K is the bulk modulus, and Δε _vol is the volumetric strain increment;

is the volumetric strain increment of the Binham body damaged by bedding-freeze-thaw coupling;

In the Mohr-Coulomb instability criterion:

为层理-冻融耦合损伤Binham体的应变增量，g∞为长期屈服势函数，<F>为开关函数，t_c为进入加速蠕变阶段的起始时间，α为调节时间量纲的系数；where:

is the strain increment of the Binham body damaged by bedding-freeze-thaw coupling, g∞ is the long-term yield potential function, <F> is the switching function, t _c is the start time of entering the accelerated creep stage, and α is the adjustment time dimension coefficient;

The principal stress space is a Cartesian coordinate system composed of three principal stress components σ1, σ2, and σ3 as coordinate axes. In the three-dimensional principal stress space, the principal stress vector at any point can be expressed as the unit vector of the three principal principal axes of stress. The linear superposition of , then in the principal stress space:

可分解为应力偏张量

和球应力张量

stress tensor

can be decomposed into stress deviator

and the spherical stress tensor

For shear yielding, we have:

为剪切屈服时长期屈服势函数，

为中间变量；in the formula

is the long-term yield potential function at shear yielding,

is an intermediate variable;

Available:

in:

为长期摩擦角；where λ _∞ is the plastic hardening factor, c _∞ is the long-term cohesion of the material,

is the long-term friction angle;

For tensile yield:

为拉伸屈服时长期屈服势函数；in the formula

is the long-term yield potential function at tensile yield;

According to formula (20) to formula (45), the three-dimensional creep equation is jointly deduced as follows:

S4: Verify the correctness and applicability of the nonlinear viscoelastic-plastic creep constitutive model according to the results of the triaxial creep test of rocks under different bedding angles and different freeze-thaw times;

The three-dimensional creep equation is converted into a dll file in the FLAC ^3D secondary development platform, and after the calculation is performed by calling the dll file, the nonlinear viscoelastic-plastic creep constitutive model established by the present invention is obtained after calculation. The curves of rocks at different bedding angles and different freeze-thaw cycles are compared with the results obtained from the triaxial creep test, that is, the nonlinear visco-elastic-plastic creep constitutive model established in the present invention can be verified. correctness and applicability.

It can be seen from Figures 7(a) to 7(e) that the two match well, and the model fitting curve can well reflect the slow-down creep and stable creep of bedded rock under different freeze-thaw cycles. The characteristics of deformation and accelerated creep indicate the correctness and applicability of the creep constitutive model for freeze-thaw damage and bedding damage established in this paper.

Figure 8 is the cloud diagram of the shear strain increment of the rock mass slope with different bedding angles, in which, Figure 8(a) is the shear strain cloud diagram of the rock mass slope with the bedding angle of 0°, and the maximum shear strain of the slope is Appears in the area near the upper slope surface of the slope toe, and no potential slip surface has yet formed, indicating that the rock mass slope has good stability; Figure 8(b) shows the rock mass slope shearing with a bedding angle of 30° Strain cloud diagram, compared with Fig. 8(a), Fig. 8(b) shows that the maximum shear strain area of the slope increases continuously, and a potential slope slip surface is formed at the same time, and the stability of the slope decreases; Fig. 8(c) is the shear strain cloud map of the rock mass slope with a bedding angle of 45°. Compared with Figures 8(a) and 8(b), the maximum shear strain area continues to increase, and the potential slip surface of the slope continues to increase. Continue to develop; Figure 8(d) is the cloud map of the shear strain of the rock mass slope with a bedding angle of 60°. The potential slip surface of the slope develops into a circular arc and then expands to the upper left (slope top); Figure 8(e) ) is the shear strain cloud map of the rock mass slope with a bedding angle of 90°. Compared with Fig. 8(d), the potential slip surface of the slope almost reaches the top of the slope, indicating that the possible sliding trend of the slope is banded. Arc sliding. From Figures 8(a)-8(e), it can be seen that with the increase of the rock mass bedding angle, the potential slip plane of the rock mass slope continues to expand to the top of the slope, and the maximum shear strain area gradually increases.

S5: Using the verified nonlinear viscoelastic-plastic creep constitutive model to calculate the freeze-thaw slope stability coefficient under different freeze-thaw times; The method is a strength reduction method based on rock bedding-freeze-thaw coupled damage and creep characteristics:

The slope stability coefficient is the strength reduction coefficient. First, select the initial reduction coefficient, reduce the soil strength parameters, and use the reduced parameters as input to reduce the strength. If the program converges, the soil is still in a stable state. , and then increase the reduction coefficient until it does not converge. The reduction coefficient at this time is the stability safety factor of the slope, and the slip surface at this time is the actual slip surface. This method is called slope stability. coefficient.

The strength reduction method is to gradually reduce the strength parameters of the slope rock (internal friction angle, cohesion and tensile strength) in the numerical calculation until the structure reaches the limit state. The ratio is the required safety factor, and the position of the potential failure sliding surface can be obtained according to the elastic-plastic calculation results.

The basic principle of the strength reduction method is to reduce the shear strength parameter of the rock in the elastoplastic numerical calculation of the rock and soil in the rock, so that the slope reaches the critical failure state, and the slope stability coefficient is obtained. When calculating the strength reduction of the frozen-thawed rock mass slope, the Mohr-Coulomb strength yield criterion is used for the rock mass; at present, the traditional strength reduction method is often used in the calculation of the slope stability. In the strength reduction method, the mechanical properties of the rock mass are represented by an elastic-plastic constitutive model, and the overall slope of the slope is destabilized by reducing the strength parameters of the rock mass. Compared with the traditional strength reduction method, the present invention uses the rock bedding-freeze-thaw coupling damage in the creep viscoelastic-plastic constitutive model to reflect the bedding of the bedding rock mass due to the bedding-freeze-thaw effect and the time effect. - Freeze-thaw coupling damage and creep characteristics, and whether the key point displacement of the slope is stable after a certain period of time and whether the displacement changes abruptly when the strength is reduced to a certain extent are used as the judgment of whether the bedded rock mass slope is unstable or not according to. Since the bedding rock slope adopts the strength reduction method considering the bedding-freeze-thaw coupled damage and creep characteristics, it can better reflect the effect of the freeze-thaw creep characteristics of the bedding rock on the slope deformation and stability.

The Mohr-Coulomb strength yield criterion is used for the rock mass:

为岩体的内摩擦角。where τ _n is the shear strength of the rock mass under different freeze-thaw times, σ” is the initial compressive strength of the rock, C _n is the cohesion of the rock under different freeze-thaw times, and c is the initial cohesion of the unfreeze-thawed rock force,

is the internal friction angle of the rock mass.

同时除以相同的折减系数Fs，降低岩石的强度后再次进行试算，通过逐渐增加折减系数Fs的方法来降低岩石的强度，直到岩石达到临界破坏的状态，临界破坏状态即为边坡塑性区从坡脚到坡顶贯通以及采用力或位移不收敛作为边坡失稳的标志。此时对应的强度折减系数Fs即为冻融边坡稳定性系数。强度折减系数可表示为：When the strength reduction method is used to reduce the strength of the rock, the strength parameters Cn,

At the same time, divide it by the same reduction factor Fs to reduce the strength of the rock and perform the trial calculation again. By gradually increasing the reduction factor Fs, the strength of the rock is reduced until the rock reaches the state of critical failure. The critical failure state is the slope. The penetration of the plastic zone from the toe to the top of the slope and the non-convergence of force or displacement are used as signs of slope instability. At this time, the corresponding strength reduction coefficient Fs is the stability coefficient of the freeze-thaw slope. The strength reduction factor can be expressed as:

where F _s is the strength reduction coefficient, τ _n is the shear strength of the rock mass under different freeze-thaw times, σ” is the initial compressive strength of the rock mass, and τ _s is the shear strength of the rock after reducing F _s ;

in:

为岩体折减F_s后的内摩擦角；where c _s is the cohesion of the frozen-thawed rock mass after F _s is reduced,

is the internal friction angle of the rock mass after reducing F _s ;

Therefore, the strength reduction factor can also be expressed as:

The strength reduction method based on the Mohr-Coulomb strength yield criterion performs the strength reduction according to the method shown in Equation (47). Figure 9 shows a graph showing the relationship between the number of freeze-thaw times of the rock mass and the safety factor of the rock mass when the bedding angle is 0° according to the present invention. The slope stability factor is getting smaller and smaller.

Specifically, before the creep calculation of the slope engineering, the traditional strength reduction method is used to analyze the slope stability, and the sliding surface position and short-term stability coefficient of the slope rock in the critical failure state are determined. At this time, the calculation model is the Mohr-Coulomb model. The traditional strength reduction method is adopted, and the reduction factor is continuously revised to obtain the reduction factor when the slope reaches the critical failure state.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: The technical solutions described in the foregoing embodiments can still be modified, or some or all of the technical features thereof can be equivalently replaced; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the technical solutions of the embodiments of the present invention. scope.

Claims (6)

1. the stability analysis method of geotechnical engineering structure in the bedding rock of a seasonal frozen area, is characterized in that, comprises the steps: S1: Define the bedding-freeze-thaw coupled damage variable D _β ,n of the rock, and the bedding-freeze-thaw coupled damage variable D _β,n represents the rock damage caused by different bedding angles and different freeze-thaw cycles; S2: Establish a nonlinear viscoelastic-plastic creep constitutive model considering the bedding-freeze-thaw coupled damage variable D _β,n to characterize the stress-strain relationship under the influence of different bedding angles and different freeze-thaw cycles on rocks ; S3: Establish a three-dimensional creep equation to analyze the stability of geotechnical engineering in anisotropic rocks; S4: Verify the correctness and applicability of the nonlinear viscoelastic-plastic creep constitutive model according to the results of the triaxial creep test of rocks under different bedding angles and different freeze-thaw times; S5: Using the validated nonlinear viscoelastic-plastic creep constitutive model, calculate the freeze-thaw slope stability coefficient under different freeze-thaw times to determine the sliding surface position and short-term failure state of rock and soil in the slope rock. stability. 2. The method for analyzing the stability of geotechnical engineering structures in a bedded rock in a seasonally frozen area according to claim 1, wherein the method for establishing the bedding-freeze-thaw coupling damage variable D _{β, n} in the S1 is as follows: : According to the principle of strain equivalence, the strain caused by the stress σ acting on the damaged material is equivalent to the strain caused by the effective stress σ′ acting on the non-destructive material, namely:

where E is the elastic modulus of the non-destructive material, and E' is the elastic modulus of the damaged material; The bedding-freeze-thaw coupled damage variable D _β,n is defined as:

where E _β,n is the elastic modulus of the rock with the bedding angle β and the freeze-thaw times n; E _β,0 is the elastic modulus of the rock with the bedding angle β and the freeze-thaw times 0. 3. the stability analysis method of the geotechnical engineering structure in the bedding rock of a kind of seasonal frozen area according to claim 1, is characterized in that, the nonlinear viscoelastic-plastic creep constitutive model in described S2 is based on classical creep Model combination creation; the classical creep model combination includes bedding-freeze-thaw coupled damage Maxwell body, bedding-freeze-thaw coupled damage Kelvin body and bedding-freeze-thaw coupled damage Binham body; the bedding-freeze-thaw coupled damage The damage Maxwell body represents the instantaneous elastic deformation and viscous deformation during the creep process of rock mass materials, including the bedding-freeze-thaw coupled damage elastic element and the bedding-freeze-thaw coupled damage viscous element; The coupled-thaw damage Kelvin body represents the viscoelastic deformation of the rock mass material during the creep process, including the parallel bedding-freeze-thaw coupled damage elastic element and the bedding-freeze-thaw coupled damage software element; the bedding-freeze-thaw coupled damage Binham body represents the viscoplastic deformation of rock mass material during creep, including parallel bedding-freeze-thaw coupled damage plastic element and bedding-freeze-thaw coupled damage soft element. 4. a kind of stability analysis method of geotechnical engineering structure in a bedding rock in a seasonally frozen area according to claim 3, is characterized in that, the step that nonlinear viscoelastic-plastic creep constitutive model is established in described S2 is as follows : S21: Establish the constitutive relationship of the bedding-freeze-thaw coupled damage software component as follows:

In the formula: t is time; σ(t) represents the corresponding stress at time t; ε(t) represents the corresponding strain at time t; η is the viscosity coefficient of the software component; S22: Establish the constitutive relation of the layered-freeze-thaw coupled damage elastic element as:

Then the constitutive relation of the Maxwell body considering bedding-freeze-thaw coupling damage is:

where ε _M is the strain component generated by the Maxwell body with bedding-freeze-thaw coupling damage; E _M is the elastic modulus of the Maxwell body with bedding-freeze-thaw coupling damage; S23: Establish the constitutive relation of the bedding-freeze-thaw coupled damage Kelvin body as:

Where: ε _H is the strain component of the elastic element damaged by bedding-freeze-thaw coupling in the Kelvin body; ε _N is the strain component of the soft element in the Kelvin body with bedding-freeze-thaw coupling damage; E _k is the layer is the elastic modulus of the Kelvin body damaged by the coupling of freezing and thawing; ε _k is the strain component of the Kelvin body damaged by the _coupling of bedding and freezing and thawing; -Fractional order in Kelvin body of freeze-thaw coupling damage; From formula (6), we can get:

When t=0, ε _k (t)=0, assuming

Then formula (7) can be rewritten as:

According to the fractional calculus theory, converting the Riemann-Liouville fractional derivative into the Caputo fractional derivative is:

Where: C represents the Caputo fractional derivative; k is a positive integer; D _t ^m f(t) is the Riemann-Liouville fractional derivative; When ε _k (0)=0, D ^m [ε _K (t)] = ^C D ^m [ε _K (t)], then equation (8) is rewritten as: b=aε _K + ^C D ^m [ε _K (t)] (10) Laplace transform on both sides of formula (9), we get

In the formula: S=σ+jω is a complex parameter; therefore,

Continuing to perform the Laplace transform, we get

in,

but,

Will

Substitute into the transformed bedding-freeze-thaw coupled damage Kelvin body constitutive relation is:

S24: Establish the constitutive relation of the bedding-freeze-thaw coupled damage viscous element:

where:

is the strain rate of the Newton body, η _M is the Newton body viscosity coefficient; S25: Establish the constitutive relation of the bedding-freeze-thaw coupled damage Binham as;

where η _B is the viscosity coefficient of the Binham body with bedding-freeze-thaw coupling damage; m ₂ is the fractional order in the _Binham body with bedding-freeze-thaw coupling damage; the stress threshold of the plastic element; S26: A nonlinear viscoelastic-plastic creep constitutive model is established by comprehensively considering the bedding-freeze-thaw coupled damage Maxwell body, the bedding-freeze-thaw coupled damage Kelvin body and the bedding-freeze-thaw coupled damage Binham body:

5. a kind of stability analysis method of geotechnical engineering structure in a bedding rock in a seasonally frozen area according to claim 4, is characterized in that, the method for establishing three-dimensional creep equation in described S3 is; The equation is derived by the finite difference method: it is assumed that the rock strain ε _ij consists of three parts, namely: the strain of the Maxwell body damaged by bedding-freeze-thaw coupling

Strain of Kelvin body damaged by bedding-freeze-thaw coupling

and bedding-freeze-thaw coupling damage to the Binham body strain

which is

The deviatorial strain has the following form:

in the formula

is the bias strain,

is the deviatorial strain of the Maxwell body damaged by bedding-freeze-thaw coupling,

is the deviatorial strain of the Kelvin body damaged by the bedding-freeze-thaw coupling,

is the deviatorial strain of the Binham body damaged by the bedding-freeze-thaw coupling; Writing the deviatorial strain in incremental form, the relationship between the deviatorial strain increments can be obtained:

where △e _ij is the deviatorial strain increment,

is the deviatorial strain increment of the Maxwell body damaged by bedding-freeze-thaw coupling,

are the deviatorial strain increments and

is the deviatorial strain increment of the Binham body damaged by bedding-freeze-thaw coupling; Continue to deduce the formula, and get: the bedding-freeze-thaw coupling damages the elastic element:

Bedding-freeze-thaw coupling damages Kelvin bodies:

where S _ij is the deviatoric stress, G is the shear modulus; η _K is the viscosity coefficient of the Kelvin body damaged by bedding-freeze-thaw coupling The strain rate of the Binham body damaged by bedding-freeze-thaw coupling can be written as

where g is the plastic yield potential function, η _B is the viscosity coefficient of the Binham body damaged by bedding-freeze-thaw coupling, <F> is the switching function, and its expression is as follows:

Write equation (25) in the form of a deviatorial strain rate:

where:

is the volumetric strain of the Binham body damaged by bedding-freeze-thaw coupling; The total strain increment can be obtained from equation (26):

Using the central difference form, the bedding-freeze-thaw coupled damage elastic element can be written as

in the formula

is the deviatoric stress in the form of central difference,

is the deviatorial strain in the form of the difference between the center of the Maxwell body with bedding-freeze-thaw coupling damage; Δt is the time increment; Using the central difference form, the bedding-freeze-thaw coupled damage Kelvin body can be written as

in the formula

Δt is the time increment; η _K is the viscosity coefficient of the Kelvin body damaged by bedding-freeze-thaw coupling, in:

In the formula,

represents the old value of the stress deflection within a time increment;

represents the new value of the stress deflection within a time increment,

represents the old value of the stress deflection within a time increment;

is the new value of the strain deflection within a time increment; Deviatorial strain of Kelvin bodies damaged by bedding-freeze-thaw coupling

where:

is the old value of the deviatorial strain of the Kelvin body for bedding-freeze-thaw coupling damage,

is the new value of the deviatoric strain of the Kelvin body for bedding-freeze-thaw coupling damage; in:

Finally, the updated deviatoric stress is obtained

where: △e _ij is the deviatorial strain increment,

and

are the deviatorial strain increments of the bedding-freeze-thaw coupled damage Binham body and the bedding-freeze-thaw coupled damage Maxwell body, respectively; in:

According to the knowledge of plastic mechanics, the spherical stress of the whole bedding-freeze-thaw damage creep model is written as:

in the formula

is the new value of spherical stress;

is the old value of the spherical stress, K is the bulk modulus, and Δε _vol is the volumetric strain increment;

is the volumetric strain increment of the Binham body damaged by bedding-freeze-thaw coupling; In the Mohr-Coulomb instability criterion:

in the formula

is the strain increment of the Binham body damaged by bedding-freeze-thaw coupling, g∞ is the long-term yield potential function, <F> is the switching function, tc is the start time of entering the accelerated creep stage, and α is the coefficient for adjusting the time dimension ; Under the principal stress space:

stress tensor

can be decomposed into stress deviator

and the spherical stress tensor

For shear yielding, we have:

in the formula

is the long-term yield potential function at shear yielding,

is an intermediate variable; Available:

in:

where λ _∞ is the plastic hardening factor, c _∞ is the long-term cohesion of the material,

is the long-term friction angle; For tensile yield:

where:

is the long-term yield potential function at tensile yield; According to formula (20) to formula (45), the three-dimensional creep equation is jointly deduced as follows:

6. the stability analysis method of geotechnical engineering structure in a bedding rock in a seasonally frozen area according to claim 5, is characterized in that, in described S5, calculate the freeze-thaw slope stability coefficient under different freeze-thaw times The method used is the strength reduction method: The Mohr-Coulomb strength yield criterion is used for the rock mass:

c _n =c(1-D) where τ _n is the shear strength of the rock mass under different freeze-thaw times, σ” is the initial compressive strength of the rock, C _n is the cohesion of the rock under different freeze-thaw times, c is the initial cohesion of the unfreeze-thawed rock,

is the internal friction angle of the rock mass; Cn, tan

At the same time, divided by the same reduction factor Fs, the strength reduction factor can be expressed as:

where F _s is the strength reduction coefficient, τ _n is the shear strength of the rock mass under different freeze-thaw times, σ” is the initial compressive strength of the rock mass, and τ _s is the shear strength of the rock after reducing F _s ; in:

where c _s is the cohesion of the frozen-thawed rock mass after F _s is reduced,

is the internal friction angle of the rock mass after reducing F _s ; Therefore, the strength reduction factor can also be expressed as:

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