CN116484568A - Rock mass stability calculation method considering fatigue and time effect - Google Patents
Rock mass stability calculation method considering fatigue and time effect Download PDFInfo
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Abstract
The invention provides a rock mass stability calculation method considering fatigue and time effect, which comprises the following steps: dividing the rock into a plurality of primitives to obtain mechanical parameters of the primitives; the root acquires a Hoek-Brown elastoplastic damage model of the primitive; obtaining aging damage variables of the primitives; obtaining fatigue damage variables of the primitives; obtaining a coupling damage variable: obtaining t m+1 Nominal stress tensor sigma 'at time step' m+1 The method comprises the steps of carrying out a first treatment on the surface of the Acquisition of the t m+1 Coupling damage variable values at time steps; the stability of the rock was analyzed. Aiming at the non-linear and microscopic non-uniformity characteristics of rock mass strength, the invention establishes a Hoek-Brown elastoplastic damage model, obtains the coupling damage variable of the primitive by combining the fatigue damage variable and the load damage variable based on the time effect characteristics of the rock mass, and finally obtains the time-dependent changeAnd (3) the value of the coupling damage variable is changed, so that the stability calculation of the heterogeneous rock mass along with time under the action of the rheological effect and the fatigue effect is realized.
Description
Technical Field
The invention relates to the field of rock mass engineering calculation, in particular to a rock mass stability calculation method considering fatigue and time effect.
Background
In recent years, rock mass engineering construction in various fields of traffic, water conservancy, mining and the like in China is in progress, such as side slopes, hydropower houses, tunnels, foundations and the like. The rock mass is a geological structure body composed of complete rock and a structural surface, and a large number of faults, joints, weak interlayers and the like exist. Because the geological body is in the environment complexity, compared with the common medium, the rock body has the effects of non-uniformity and time, is subjected to the effect of environmental fatigue, and the problem of rock mass engineering stability is increasingly outstanding, so that the research on the rock mass stability calculation method considering the rheological and fatigue effects has important significance, and has important guiding effect on ensuring the construction and operation safety of the rock mass engineering in the complex environment.
At present, an ideal elastoplastic macroscopic calculation model is generally adopted for stability calculation of rock mass engineering, and in a traditional rock mass stability calculation method, a constitutive model with a linear strength criterion is adopted, so that nonlinear characteristics of rock mass strength cannot be reflected; the method is characterized in that each stratum is regarded as a homogeneous material to be provided with calculation parameters, and the heterogeneity of rock mass medium cannot be reflected by adopting macroscopic calculation; the rheological model of the element combination cannot reflect the essence of rock mass degradation under the combined actions of load, aging and fatigue and the corresponding stability change. There are large errors in rock mass stability that take into account both rheological and fatigue effects.
The invention comprises the following steps:
the invention provides a rock mass stability calculation method considering fatigue and time effect, so as to overcome the technical problems.
In order to achieve the above object, the technical scheme of the present invention is as follows:
a rock mass stability calculation method considering fatigue and time effect comprises the following steps:
s1: dividing the rock into a plurality of primitives V to obtain mechanical parameters of the primitives;
the mechanical parameters of the primitive comprise an empirical parameter m reflecting the characteristics of the rock mass b Rock mass breaking and integrity parameters s, rock mass quality parameters a and modulus of elasticity E before injury 0 ；
S2: acquiring a Hoek-Brown elastoplastic damage model of the primitive according to the mechanical parameters of the primitive;
s3: obtaining an aging damage variable D (t) of the primitive;
s4: obtaining fatigue damage variable D of primitive r ；
S5: according to the load damage variable D m The age injury variable D (t) and the fatigue injury variable D r Obtaining a coupling damage variable Dc:
s6: obtaining t according to the Hoek-Brown elastoplastic damage model of the primitive and the coupling damage variable m+1 Nominal stress tensor sigma 'at time step' m+1 ；
S7: according to t m+1 Nominal stress tensor sigma 'at time step' m+1 Obtain the t m+1 Coupling impairment variable values at time steps.
The beneficial effects are that: according to the rock mass stability calculation method considering fatigue and time effects, aiming at the non-linearity and mesoscopic non-uniformity characteristics of rock mass strength, rock is divided into a plurality of primitives, and experience parameters, rock mass breaking and integrity degree parameters, rock mass quality parameters and elastic modulus before damage which can reflect rock mass characteristics are obtained; and a Hoek-Brown elastoplastic damage model is established according to the parameters, then an aging damage variable of the element is obtained based on the time effect characteristics of the rock mass, and a coupling damage variable of the element is obtained by combining a fatigue damage variable and a load damage variable, so that the value of the coupling damage variable which changes along with time is finally obtained, and the stability calculation of the heterogeneous rock mass along with time under the action of the rheological effect and the fatigue effect is realized.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to the drawings without inventive effort to a person skilled in the art.
FIG. 1 is a flow chart of a method for calculating the stability of a rock mass taking fatigue and time effects into consideration;
FIG. 2a is a diagram of x in an embodiment of the present invention 0 Probability density profile for RVE mechanical properties at 10;
figure 2b is a probability density distribution plot of RVE mechanical properties at ζ of 0.5 in an embodiment of the invention;
FIG. 3 is a schematic diagram of a Poytin-thomson model in an embodiment of the invention;
FIG. 4 is a graph showing the variation of rock mass damage variable with fatigue frequency in an embodiment of the invention;
FIG. 5 is a graph of a rock sample calculation model under microscopic distribution in an embodiment of the present invention;
FIG. 6a is a graph of m for zeta 0.5 in an embodiment of the invention b A value distribution cloud map;
FIG. 6b is a graph of m for ζ of 2 in an embodiment of the invention b A value distribution cloud map;
FIG. 6c is a schematic illustration of the present inventionM in the examples where ζ is 4 b A value distribution cloud map;
FIG. 6d is a graph of m for zeta being 6 in an embodiment of the invention b A value distribution cloud map;
FIG. 6e is a graph of m for zeta being 8 in an embodiment of the invention b A value distribution cloud map;
FIG. 6f is a plot of m for zeta being 10 in an embodiment of the invention b A value distribution cloud map;
FIG. 7a is a graph of m for zeta 0.5 in an embodiment of the invention b Value region RVE statistical schematic;
FIG. 7b is a graph of m for ζ of 2 in an embodiment of the invention b Value region RVE statistical schematic;
FIG. 7c is a graph of m for zeta being 4 in an embodiment of the invention b Value region RVE statistical schematic;
FIG. 7d is a graph of m for zeta being 6 in an embodiment of the invention b Value region RVE statistical schematic;
FIG. 7e is a graph of m for zeta being 8 in an embodiment of the invention b Value region RVE statistical schematic;
FIG. 7f is a plot of m for zeta being 10 in an embodiment of the invention b Value region RVE statistical schematic;
FIG. 8a is a graph of m for zeta 0.5 in an embodiment of the invention b And a damage value evolution law map;
FIG. 8b is a graph of m for zeta being 4 in an embodiment of the invention b And a damage value evolution law map;
FIG. 9 is a graph of creep of rock at different stress levels in an embodiment of the invention;
FIG. 10a is a graph showing the time course of a rock sample damage band at ζ of 6 according to the embodiment of the present invention;
FIG. 10b is a graph showing the time course of a rock sample damage band at ζ of 6 according to the embodiment of the present invention;
FIG. 11 is a diagram of a finite element model of a slope calculation in an embodiment of the invention;
FIG. 12a is a graph showing the change rule of the slope elastic modulus and the damaged area when ζ is 2 in the embodiment of the invention;
FIG. 12b is a graph showing the change of the slope elastic modulus and the damaged area when ζ is 6 according to the embodiment of the invention;
FIG. 12c is a graph showing the change of the slope elastic modulus and the damaged area when ζ is 10 according to the embodiment of the invention;
FIG. 13a is a schematic view of a slope damage zone with a time month of 0 (month) according to an embodiment of the present invention;
FIG. 13b is a schematic view of a slope damage zone at a time month of 4 (months) in an embodiment of the invention;
FIG. 13c is a schematic view of a slope damage zone at 8 (months) in an embodiment of the invention;
FIG. 13d is a schematic view of a slope damage zone at a time month of 12 (months) in an embodiment of the invention;
FIG. 13e is a schematic view of a slope damage zone at a time month of 16 (months) in an embodiment of the invention;
FIG. 13f is a schematic view of a slope damage zone at a time month of 20 (months) in an embodiment of the invention;
FIG. 14 is a graph of slope safety factor versus time in an embodiment of the present invention;
FIG. 15 is a graph showing the maximum coupling damage of the side slope with time (t/month) at different freeze thawing times according to the embodiment of the present invention;
FIG. 16a is a schematic view of a slope displacement with a time of 0 (month) after 80 freeze thawing in an embodiment of the present invention;
FIG. 16b is a graph showing the slope displacement at a time of 4 (months) after 80 freeze thawing cycles in an embodiment of the present invention;
FIG. 16c is a graph showing the displacement of a slope with a time of 8 (months) after 80 freeze thawing cycles in an embodiment of the present invention;
FIG. 16d is a graph showing the slope displacement at 12 (months) after 80 freeze thawing cycles in an embodiment of the present invention;
FIG. 16e is a graph showing the displacement of a slope at 16 (months) after 80 freeze thawing cycles in an embodiment of the present invention;
FIG. 16f is a graph showing the displacement of a slope at 20 (months) after 80 freeze thawing cycles in an embodiment of the present invention;
FIG. 17 is a graph showing the time-dependent change of slope monitoring point displacement in an embodiment of the present invention;
FIG. 18a is a schematic view of a damaged area of a slope with 200KN prestress of an anchor line according to an embodiment of the present invention;
FIG. 18b is a schematic view of a damaged area of a slope with 300KN prestress of the anchor line according to an embodiment of the present invention;
FIG. 18c is a schematic view of a damaged area of a slope with 400KN prestress of the anchor line according to an embodiment of the present invention;
fig. 18d is a schematic view of a damaged area of a slope when the prestress of the anchor line is 500KN in an embodiment of the invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of 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, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiment of the invention provides a rock mass stability calculation method considering fatigue and time effect, as shown in figure 1; the method comprises the following steps:
s1: in order to study microscopic discontinuities caused by the influence of cavities and crystals from the viewpoint of continuous medium damage mechanics, homogenization treatment is required for the microscopic mechanical properties of rock mass materials. Firstly dividing a rock into a plurality of primitives V, and secondly describing the physical and mechanical properties of the primitives V by using a statistical method to obtain the mechanical parameters of the primitives;
the mechanical parameters of the primitive include, but are not limited to, empirical parameters m reflecting rock mass characteristics b Rock mass breaking and integrity parameters s, rock mass quality parameters a and modulus of elasticity E before injury 0 Etc.
Specifically, a power function law with a threshold value is used for describing the extremum distribution law of the rock mass material strength. Assuming mechanical parameters P in primitives z May be described by a Weibull statistical distribution function,
the method for acquiring the mechanical parameters of the primitive comprises the following steps:
P z ＝P 0 ·x z (1)
wherein P is 0 Is a macroscopic property of the rock sample; x is x z Is Weibull random number; p (P) z Is the mechanical parameter of the primitive;
weibull random number x z The acquisition method comprises the following steps:
the cumulative distribution function and probability density function according to Weibull distribution are first as follows:
wherein: w (x) is a cumulative distribution function (Cumulative Distribution function, CDF) of the Weibull distribution; w (x) is a probability density function (Probability Density Function, PDF) of the Weibull distribution; x is x 0 >0 is a scale parameter; ζ is a shape parameter; x is a random variable;
in the formula (3), as ζ increases, the rock is
x z ＝x 0 (-ln(u m )) 1/ζ (4)
Wherein: x is x z Is Weibull random number, u m Is a uniformly distributed random number;
s2: acquiring a Hoek-Brown elastoplastic injury model (Hooke-Brown elastoplastic injury model) of the primitive according to the mechanical parameters of the primitive so as to reflect the nonlinear and plastic softening characteristics of the rock mass strength;
specifically, the load damage variable D is generally introduced on the basis of the existing rock mechanical yield function m For characterizing the weakening of the strength by the injury. The present embodiment assumes that the damage versus parameter m during loading b And s produces a weakening effect, a Hoek-Brown elastoplastic damage model is proposed that considers the motifs of plastic damage, the expression of which is as follows:
wherein f is a yield function; j (J) 2 Is the second bias force invariant; θ σ Is the roeder angle; d (D) m Is a load damage variable; sigma (sigma) ci Is the uniaxial compressive strength of the complete rock; p is hydrostatic pressure; m is m bg Is m b Corresponding plastic potential function parameters; s is(s) g The plastic potential function parameter corresponding to s; a, a g A corresponding plastic potential function parameter is a; g is a plastic potential function; when m is bg ＝m b 、s g ＝s、a g When =a, the flow rule is associated, otherwise the flow rule is non-associated.
Wherein the load damage variable D m The acquisition is as follows: the stress redistribution effect generated by engineering excavation can cause plastic damage to the rock mass, and the damage is strained along with equivalent plasticIs aggravated by accumulation of ground, load damage variable D m Can be expressed asIn the form of a power exponent:
wherein, alpha is the initial slope of the softening curve of the rock material after the damage, and the value range is (0, + -infinity); beta is a parameter for determining the maximum damage value of the rock, and the value range is [0, 1);is equivalent plastic strain;
in the method, in the process of the invention,is the principal plastic strain in the x-axis direction of the space coordinate system (i.e., principal stress space); />Is the principal plastic strain in the y-axis direction of the space coordinate system (i.e., principal stress space); />Is the principal plastic strain in the z-axis direction of the spatial coordinate system (i.e., principal stress space);
s3: obtaining an aging damage variable D (t), wherein the method is as follows;
when the axial pressure is smaller than the long-term strength value, the mechanical model of the primitive can be expressed by using a Poytin-thomson model shown in fig. 3, and a creep equation of the primitive is established as follows:
wherein epsilon is strain; sigma (sigma) 0 Is the stress of the axial direction; k (K) 1 、K 2 Are mechanical parameters of the elastic element; η is the viscosity coefficient of the adhesive kettle; t time for rheology; in the present embodiment, the Poytin-thomson model is the prior art, which includes two elastic elements, thus K 1 、K 2 The mechanical parameters of the two elastic elements in the model are respectively.
Can be obtained by simplified method (9)
ε＝σ 0 [P+Qexp(-Rt)] (10)
Wherein P, Q, R is an intermediate parameter, wherein,
as can be derived from the formula (10), the expression that the elastic modulus changes with time t is:
E(t)＝P+Qexp(-Rt) (11)
e (t) is a function of the variation of the modulus of elasticity with time t;
according to the theory of continuous damage mechanics, the damage degree of the modulus of the material can be measured by an elastic modulus method, namely:
wherein D (t) is an aging damage variable, i.e., a damage variable caused by a time effect; e (E) 0 Is the modulus of elasticity before injury;
s4: obtaining fatigue damage variable D r The following are provided:
suppose the nth t The damage value of the section under the action of the secondary fatigue disturbance is D t Can be measured, then:
wherein: d (D) t Is the N t A damage value of the rock section under the action of the secondary fatigue disturbance; d (D) r Variable D for fatigue damage r N, i.e t N times of fatigue damage variation before the secondary fatigue disturbance; n (N) t Numbering the fatigue disturbance times; n is the N t Total number of fatigue disturbances before the secondary fatigue disturbance; w and U are material parameters;
through the N th t Damage value D of rock section under action of secondary fatigue disturbance t Can be obtained by rock porosity and longitudinal wave velocity, and the calculation formula is shown as formula (14):
wherein n is 0 Is the porosity of the rock before fatigue action; n is the porosity after the fatigue action of the rock; v (V) P The wave velocity of longitudinal waves after the fatigue action of the rock; the relationship between the number of fatigue actions and fatigue damage was fitted according to the following equation (13), and the results are shown in fig. 4.
Step 5: according to the load damage variable D m The age injury variable D (t) and the fatigue injury variable D r Obtaining a coupling damage variable Dc:
for northern cold region engineering in the service process, the rock mass generates aging damage and fatigue damage under the long-term action of load, and also can generate freeze thawing fatigue damage. The damage is coupled to analyze the rock stability problem under the influence of various factors. Comprehensively consider the fatigue damage variable D r Variable D of load damage m And an aging damage variable D (t), then the coupling damage variable is obtained at this time as follows:
D c ＝D(t)+D m +D r -D(t)D m -D r D m -D r D t +D(t)D m D r (15)
wherein Dc is a coupling impairment variable; d (D) m Is a load damage variable;
s6: obtaining t according to the Hoek-Brown elastoplastic damage model of the primitive and the coupling damage variable m+1 Nominal stress tensor sigma 'at time step' m+1 ；
S61: the stress-strain constitutive relation considering the time effect-fatigue-load coupling damage is obtained as follows:
wherein σ is stress considering time effect-fatigue-load coupling damage; epsilon e Is elastic strain;to consider a stiffness matrix of coupling impairments; />I s Is a fourth order symmetric tensor->Is Cronecker product; g (D) c ) To damage shear modulus; k (D) c ) For bulk modulusThe method comprises the steps of carrying out a first treatment on the surface of the Wherein (I) s ) ijkl ＝1/2(δ ik δ jl +δ il δ jk ) I, j, k, l are corner labels of fourth-order symmetric tensors; delta ik 、δ jl 、δ il 、δ jk Are components of fourth-order symmetric tensors; wherein G (D) c )、K(D c ) Can use the initial shear modulus G 0 And initial bulk modulus K 0 The representation is:
wherein G is 0 Is the initial shear modulus; k (K) 0 Is the initial bulk modulus; mu is Poisson's ratio, E (D c ) To the damage variable D C Modulus of elasticity at the time; equation (17) represents the weakening of the elastic modulus of the rock mass by time effect-coupling damage.
Damage affects not only the modulus of elasticity, but also the mechanical parameters of the primitive in the Hoek-Brown elastoplastic damage model of the primitive. The law of change of Hoek-Brown elastoplasticity with time is obtained from the following formula:
(m b ) t ＝(1-D(t))m b0 (18a)
(s) t ＝(1-D(t))s 0 (18b)
wherein: (m) b ) t M is time t b A value; m is m b0 For the initial m b A value; (s) t S is the value of s at the time t; s is(s) 0 Is the initial s value;
and (3) selecting a completely implicit stress reflection algorithm for the Hoek-Brown elastoplastic damage model in the formula (5), wherein the whole solving process comprises 3 steps of elastic prediction, plastic correction and damage correction. In general, when the rock starts to deform, the rock is in an elastic stage, and when the deformation reaches a certain degree, the rock enters a plastic deformation stage, so that the rock is considered to be in the elastic deformation stage, and the rock is solved according to the following steps:
s62: acquisition of the t m+1 Predicted stress at time steps to correct for rock ingress to plasticityJudging the segments;
assume thatThe predicted stress expression is obtained from a given strain delta epsilon as:
in the method, in the process of the invention,is t th m+1 Predicted stress at time steps; />To consider a stiffness matrix of coupling impairments; epsilon m Is t th m Strain at time steps; delta epsilon m Is t th m A given strain increment at a time step; />Is t th m+1 Predicting coupling damage variables in the time step; (D) c ) m Is t th m Coupling damage variable under time step; representing double-point multiplication, which is a symbol in tensor operation, and multiplying representative components according to a certain sequence;
s63: will be t m+1 Substituting the predicted stress in the time step into the yield function f in the formula (5) to judge, if the predicted stress is:
then t m+1 Stress sigma at time step m+1 Equal to the t m+1 Predicted stress at time steps, i.e.S62 is performed; otherwise, the step S64 is executed, and the plastic correction phase is entered.
S64: according to the plastic potential function, carrying out plastic correction on the Hoek-Brown elastoplastic damage model to obtain corrected equivalent plastic strain;
to avoid t n+1 The calculated stress at the end of the time step deviates from the yield surface, and the embodiment adopts a completely implicit stress reflection algorithm to correct the elastic predicted stress back to the yield surface. During the plastic correction, the t-th is maintained m Strain increment delta epsilon at time step m+1 And the damage variable is unchanged, and the strain increment comprises elastic strain increment delta epsilon under the plastic state e And plastic strain increment delta epsilon p The incremental expression of plastic strain is:
wherein: delta epsilon p Is the plastic strain increment; delta lambda b The plastic factor of the b-th plastic curved surface is corresponding, because the formulas (5) and (6) are hexagonal pyramids with curved surfaces in the main stress space, and 6 curved surfaces are provided, and in the formula (21), q is the number of the stress exceeding the curved surfaces; g b The plasticity corresponding to the b-th plastic surface is a function, namely a formula (6); when the corresponding return stress is positioned at the yield surface, the ridge line or the sharp point, 1, 2 or 3 plastic factors are needed to be solved respectively;
because the Hoek-Brown elastoplastic damage model has numerical singular points, the singular points cannot be directly derived, and the solution precision is reduced by adopting a smooth processing method, the embodiment is based on the following stepsThe situation of the spatial position of the stress is discussed, and the final updated stress is judged to be positioned at the point, the yield surface or the edge line, so that the difficulty brought by global derivation is avoided. This step is a finite element algorithm technique well known in the art and will not be discussed in detail here.
S65: obtaining t according to the corrected equivalent plastic strain m+1 Nominal stress tensor sigma 'at time step' m+1 The method comprises the steps of carrying out a first treatment on the surface of the Calculating t by using the equivalent plastic strain obtained in the plastic correction step according to the formulas (7) and (15) m+1 Coupling impairment variable at time step (D c ) m+1 And the stress obtained in the previous step is corrected again by using the formula (22).
Thus t m+1 Nominal stress tensor sigma 'at time step' m+1 The acquisition is as follows:
wherein:and->Respectively t m And t m+1 A damage elastic matrix under the time step; />Is t th m+1 Plastic strain increment of time step; (D) c ) m+1 Is the t m+1 Coupling damage variable under time step; (D) c ) m Is t th m Coupling damage variable under time step;
s7: according to t m+1 Nominal stress tensor sigma 'at time step' m+1 Obtain the t m+1 Coupling impairment variable values at time steps.
Specifically, repeatedly executing S6 to perform iterative solution and outputting the t m+1 Coupling impairment variable values at time steps. In order to ensure the secondary convergence rate in the whole iterative solving process, the consistent tangential modulus of the model should be given after the stress solving is completed. The embodiment adopts Fortran language to write the numerical calculation process, and realizes finite element solution of the rock Hoek-Brown elastoplastic damage model. And outputting the damage value result of each primitive solution. This is a prior art and will not be described here.
S8: according to t m+1 And (5) coupling damage variable values in time steps, and analyzing the stability of the rock. Specifically, according to the coupling damage variable value of each time step, the time-dependent change trend of the coupling damage variable can be obtained, and when the coupling damage variable values of two adjacent time steps are smaller than the empirical threshold, the coupling damage is consideredThe trend of the injury variable value with time tends to be stable, and the stability of the rock is good, which is a well-known technology in the field and is not developed in detail here.
Taking a two-dimensional rock uniaxial compression numerical test as an example, the numerical solving process of a rock H-B microscopic elastoplastic injury model taking time effect into consideration, namely a Hoek-Brown elastoplastic injury model is introduced. A two-dimensional planar computational model is first created according to standard test piece dimensions as shown in fig. 5. The model was 0.01m high and 0.005m wide, with fixed boundary conditions imposed on the bottom and displacement boundary conditions imposed on the top. And performing grid division on the model by utilizing quadrilateral Solid units, wherein the model is divided into 1250 units in total.
In m b For example, the parameter assignment process for each primitive is described. At average value m b0 M, under the condition of no change, due to the change of the shape parameter ζ b The distribution pattern in the investigated space is quite different, with a fine disorder. This disorder characterizes the unique discreteness of the rock. The Monte-Carlo method (Monte Carlo method) is adopted for the intensity parameter m with disorder in the physical space b And performing assignment. Firstly, generating c random numbers u which are subject to uniform distribution (c is the total primitive number) in the range of (0, 1) L And mapping the set of random numbers into random numbers obeying Weibull distribution by using an inverse transformation method, wherein the mapping function is as shown in a formula (23):
m b ＝m b0 (-ln(u L )) 1/ζ (23)
carrying out random attribute assignment on each partition unit Material (primitive), firstly generating c random numbers which are compliant with Weibull distribution through a programming program according to the method of the application, then generating c Material arrays (materials) through a circulating statement in PYTHON language, and finally carrying out traversal assignment on the c primitives.
The calculation object is gneiss, and besides the given calculation parameters, the time effect calculation parameters P= 0.7524e-3, Q= -0.5416e-3 and R=0.028 are obtained by using a parameter identification method proposed by Xu Hongfa. Table 1 shows the calculated parameters of the H-B microscopic elastoplastic damage model taking into account the time effect.
TABLE 1 mesoscopic HB-D model calculation parameters
Model mesoscopic parameter impact analysis: let m be b0 Fixed value of 6.36, m at different zeta values b The distribution pattern of (a) is shown in fig. 6 a-6 f. It can be seen that the smaller the zeta value, the m b The greater the dispersion of the maximum value, the greater the magnitude of the deviation from the average value. When ζ=0.5, m in the test piece RVE unit (primitive) b Is 1.97 at a maximum value of 9.85 times the average value; when ζ=10, m in the test piece RVE unit b The maximum value of (2) is 0.22 and 1.1 times the average value. It can also be seen that the greater the zeta value, the m in each RVE unit inside the rock b The value only has a small range of floating near the average value, which indicates that the homogeneity of the rock sample is more obvious, while the smaller the zeta value, the m b The larger value floating around the average value indicates that the rock sample has stronger inhomogeneity.
FIGS. 7 a-7 f statistics of various values of ζ, m b Number of cells between value regions. As can be seen from fig. 7, m in the overall model when ζ=0.5 b The number of RVEs with a value close to the average value of 0.2 is only 133, accounting for about 10% of the total unit number. At the same time, m b The large range of values of the float indicates that the inhomogeneity of the overall model is very pronounced. The greater the zeta value, the m on each RVE unit b The closer the value is to the mean. When ζ=4, m b The RVE cell numbers with values less than 0.01 and greater than 0.3 have been zero. When ζ=10, m on each RVE unit b The values are only distributed between 0.1 and 0.3, and the overall mechanical properties of the rock test piece show obvious homogeneity. Figure 7 illustrates the effect of zeta value on rock homogeneity from the perspective of the number of RVE units between different zones, i.e. the greater the zeta value the more pronounced the homogeneity of the rock, whereas the rock exhibits strong inhomogeneities.
Applying displacement boundary conditions on the top of the model, and recording m under different load steps b The evolution law of the values and the damage values is shown in fig. 8a and 8 b. It can be seen that during the loading process, the damage value gradually accumulates and the mechanical parameter is weakerRV E unit enters into plastic region earlier, its strength parameter m b Weakening occurs continuously under the action of the injury, and finally a fracture injury belt is formed. Due to the difference of the shape parameters ζ, m b Is different in distribution concentration. When ζ is small (ζ=0.5), the simulated sample exhibits strong heterogeneity, and the finally formed damaged zone also differs significantly from that under homogeneous conditions. As zeta value increases, m in each RVE unit in the sample b The value is the average value m b0 The fluctuation range in the vicinity is reduced, and the heterogeneity of the analog sample is gradually weakened. The more the damaged tape morphology of the sample under load approaches that of the completely homogeneous condition. From the calculation results, the rock Hoek-Brown elastoplastic damage model considering the time effect can better describe the heterogeneous characteristics of the rock, and reproduce the cracking process of the loaded rock.
Time and shape parameters in this embodiment affect the analysis of localization: and verifying an aging model built under the condition of the shape parameter ζ=10 (strong test piece homogeneity) by using a triaxial creep test. And in the triaxial creep test process, constant confining pressure is adopted, the confining pressure is kept to be constant at 5MPa, the initial value of the axial pressure is 10MPa, when the creep deformation rate is less than 0.001mm/d, the next stage of loading is carried out, and each stage of loading is 20MPa. The same loading mode is adopted in numerical calculation, and according to a parameter identification method, taking gneiss creep test data as an example, an ageing calculation parameter P= 0.8245e is obtained -3 ，Q＝-0.4731e -3 R=0.025, the parameters of the h-B model were obtained as described above, see in particular table 1.
The result of comparing the calculated value with the test value is shown in fig. 9. As is evident from fig. 9, no significant damage occurs when creep enters the steady state creep phase. At lower stress levels, microscopic damage to the internal structure accumulates, and macroscopic damage to the sample cannot be caused, thus gradually tending to a steady state; at higher stress levels, the macroscopic mechanical properties of the test specimen gradually deteriorate. When microscopic damage accumulates to some extent, the accelerated creep phase begins and the macroscopic mechanical properties of the test specimen are manifested in the form of accelerated creep. The calculation result is closer to the test result, and the correctness of the built model is demonstrated.
Fig. 10a and 10b show the change law of the damage value of the creep acceleration section rock sample with time under the conditions of ζ=6 and 8. It can be seen from the figure that under the load of the last stage, load damage has occurred inside the rock sample. When ζ=6, the maximum damage value in the rock sample was 8.457e -2 The mechanical parameters of the rock sample are weakened along with the change of time, and the damage value is accumulated and increased continuously (the damage value is gradually increased to 1.115e under the condition of unchanged load -1 And 1.504e -1 ) Eventually, damage occurs. When ζ=8, the change rule was similar, but the damaged band shape was changed, and the more homogeneous the sample (the larger the ζ value), the more apparent the damaged band exhibited symmetry.
And (3) evaluating the long-term stability of the slope engineering in the cold region:
the application is used for carrying out the numerical simulation research on the long-term stability development of a certain northern side slope affected by freeze thawing. The selected section K400+184 is located along the line of the Dandong-Altai expressway at the junction of the JiAn and Baishan City. The side slope is close to the forest peak reservoir. The main rock composition of the research section is strong weathering quartz rock, joint cracks are developed, rock bodies are broken, the structural surface is well combined, the block structure is formed, and the basic quality grade of the rock bodies is IV. The geographical location of the side slope is shown in fig. 11.
The slope finite element calculation model is established according to the engineering site condition and is shown in figure 11. The model is 36m long and 22.6m high, and is divided into 4786 nodes and 4610 units. Horizontal constraints are applied to the two sides of the model, and fixed constraints are applied to the bottom. The mean value of the calculated parameters is initially determined from the survey report and the laboratory test is shown in table 2. Assuming the elastic modulus, uniaxial compressive strength sigma of the rock ci ，m b And s values follow Weibull distribution, and the slope safety coefficient and the damage mode are studied by taking shape parameter changes and time changes into consideration. Where ζ=10, the corresponding parameters can be regarded as being equivalent to the mean case.
TABLE 2 Fine-scale HB-D model calculation parameter Table
The analysis of the influence of the shape parameters on the slope stability is that fig. 12 a-12 c show the elastic modulus under different shape parameters zeta (only the distribution rule of the elastic modulus is shown for the sake of brevity) and the distribution cloud diagram of the slope damage zone. As can be seen from the graph, the influence of the shape parameter ζ on the maximum damage value of the slope is small in the selected parameter range (ζ=2 to ζ=10), and the damage variation range is in the order of magnitude of 1×10 -4 Left and right. However, the shape parameter ζ has a larger influence on the damage distribution form, the smaller the zeta value is, the more branches appear in the slope damage zone under the condition of homogeneity, and the slope damage zone is gradually concentrated and smooth and is more similar to the form under the condition of homogeneity along with the increase of the zeta value. The calculation result shows that the Weibull parameter value has small influence on the overall safety of the slope within a certain range, but has great influence on the damage form of the slope.
And (3) analyzing the influence of ageing on the engineering stability of the side slope, namely analyzing the influence of ageing on the engineering stability of the side slope without considering the freeze thawing effect. Fig. 13 a-13 f show the time-dependent change of the maximum damage value of the slope after excavation. As can be seen from the calculation results, the rock mass parameters are weakened continuously and approach to the long-term strength values continuously along with the time, so that the damage values are obviously increased. The maximum damage value in the side slope at the initial stage of excavation is 0.27, and the maximum damage value is continuously increased along with the change of time. When the time t is 20 months, the maximum damage value in the side slope reaches 0.2855, and the maximum damage value is increased by 0.0155 compared with the initial value. The change rate of the damage value is obvious in the early stage and gradually approaches zero in the later stage.
Fig. 14 shows the change law of the slope safety coefficient with time. Similar to the change law of displacement and damage values, the safety coefficient is obviously reduced in the initial stage, the safety coefficient is reduced from 1.59 to 1.27 in the first 12 months, and the safety coefficient is gradually stabilized at 1.26 after 12 months, so that no obvious change occurs.
And (3) analyzing the influence of aging and freeze thawing fatigue on the stability of the slope engineering, wherein according to the on-site investigation, the selected section is subjected to the disturbance of freeze thawing fatigue cycle for a long time. Therefore, it is necessary to analyze its long-term safety reserves under the effects of freeze-thaw fatigue cycles. Because the rock can generate coupling damage under the combined action of freeze thawing and load, the freeze thawing damage value is related to the freeze thawing times, and the relation can be expressed as follows:
wherein D is r As a fatigue damage variable, in this example, a freeze-thaw fatigue damage variable; n is the number of freeze-thaw fatigue times in this example.
Parameters E, m considered in the model during the calculation b And the s value changes with time (month), the time effect related parameters are the same as before. FIG. 15 shows the time-dependent change law of the maximum damage value of the slope after 10 times of freeze thawing, 40 times of freeze thawing and 80 times of freeze thawing, and the whole slope model is assumed to be affected by freeze thawing fatigue damage during calculation. As can be seen from the calculation result, when the freeze thawing number n=10, the maximum coupling damage value in the side slope at the initial excavation stage, i.e. t=0 month, is 0.283. Over time, the rock parameters are weakened continuously, the strength value approaches to the long-term strength value continuously, and therefore the damage value of the rock is obviously increased. When the time t is 20 months, the maximum coupling damage value in the side slope reaches 0.3035, and is increased by 0.0205 compared with the initial value. When the number of freeze thawing times is n=40, the maximum coupling damage value in the side slope is 0.3031 at t=0 month, and the maximum coupling damage value in the side slope is 0.3136 at t=20 months. When the number of freeze thawing times is n=80, the maximum coupling damage value in the side slope is 0.3214 at t=0 month, and the maximum coupling damage value in the side slope is increased to 0.328 at t=20 months. The change rate of the coupling damage value is obvious in the initial stage, and gradually approaches zero in the later stage.
Fig. 16 a-16 f show the change law of slope displacement cloud picture with time after 80 times of freezing and thawing. The calculation result shows that the displacement of the slope can also change with time after the slope is excavated. With the maximum displacement value as a standard, the maximum displacement value of the side slope is 0.016m when t=0 month, and 0.023m when t=20 months, and the maximum displacement value of the side slope is increased by about 41.8%. Fig. 17 shows the time-dependent change of displacement at each monitoring point of the slope. The graph shows that the slope displacement changes obviously in the initial period of excavation, and the slope displacement gradually tends to be stable along with the time and does not change along with the time. Taking the monitoring point No. 2 with the largest displacement value as an example, when t=0, 4, 8, 12, 16 and 20 months, the displacement of the point is 0.015m,0.018m, 0.02m, 0.021m, 0.0214m and 0.216m, the change amplitude is gradually reduced, and finally the change amplitude approaches zero.
The side slope is reinforced by adopting the pre-stress anchor cable on site so as to ensure the long-term stability of the side slope. The length of the anchor cable of the project is 15-18 m, the length of the anchoring section is 8m, each hole of the anchor cable is 6 steel strands, and the inclination angle of the anchor cable is 20 degrees. The cable bolt prestress was designed to be 600kN. In order to reasonably calculate the prestress of the anchor cable, the problem of contact between the soil body and the anchor cable is calculated by using an Embedded region method on the basis of the model. The anchor cable prestress is set through a temperature field method, and the prestress calculation formula is as follows:
wherein DeltaT is a preset reduced temperature value, and the unit is DEG C; f (F) N The prestress value of the anchor cable is expressed as cow; e is the elastic modulus of the material, and the unit is Pa; a is the cross-sectional area in m 2 The method comprises the steps of carrying out a first treatment on the surface of the Alpha' is the coefficient of thermal expansion of the anchor cable in units of 1/°c.
The final damage area distribution of the side slope obtained by calculation is shown in figures 18 a-18 d by setting the prestress of the anchor cable to 200kN,300kN,400kN,500kN and 600kN respectively.
The calculation result shows that after the pre-stress anchor cable is applied, the side slope damage belt moves towards the slope, so that the potential risk of sliding of the slope is reduced. Along with the increase of the prestress, the damage value of the side slope is gradually reduced. Compared with the case of no pre-stress anchor cable, when the anchor cable of 200kN is applied, the damage value of the side slope is obviously reduced, and the maximum damage value is reduced from 0.328 to 0.202. When the prestress is more than 400kN, the damage value of the side slope does not change obviously any more. According to the calculation result and considering the construction cost, the anchor cable prestress in the side slope is recommended to be set to 400 kN.
The rock mass stability calculation method considering rheological and fatigue effects can evaluate the long-term stability of geotechnical engineering under freeze thawing fatigue disturbance, and provide a method basis for engineering construction parameter design in special areas. Under different shape parameters, the method is reasonable in terms of rock sample damage bands obtained in test piece compression numerical tests and damage band distribution conditions in slope engineering stability calculation.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (7)
1. The rock mass stability calculation method considering fatigue and time effect is characterized by comprising the following steps:
s1: dividing the rock into a plurality of primitives V to obtain mechanical parameters of the primitives;
the mechanical parameters of the primitive comprise an empirical parameter m reflecting the characteristics of the rock mass b Rock mass breaking and integrity parameters s, rock mass quality parameters a and modulus of elasticity E before injury 0 ；
S2: acquiring a Hoek-Brown elastoplastic damage model of the primitive according to the mechanical parameters of the primitive;
s3: obtaining an aging damage variable D (t) of the primitive;
s4: obtaining fatigue damage variable D of primitive r ；
S5: according to the load damage variable D m The age injury variable D (t) and the fatigue injury variable D r Obtaining a coupling damage variable Dc:
s6: obtaining t according to the Hoek-Brown elastoplastic damage model of the primitive and the coupling damage variable m+1 Nominal stress tensor sigma 'at time step' m+1 ；
S7: according to t m+1 Nominal stress tensor sigma 'at time step' m+1 Obtain the t m+1 Coupling damage variable values at time steps;
s8: according to t m+1 And (5) coupling damage variable values in time steps, and analyzing the stability of the rock.
2. The method for calculating the stability of a rock mass in consideration of fatigue and time effects according to claim 1, wherein in S1, the method for obtaining the mechanical parameters of the element is as follows:
P z ＝P 0 ·x z (1)
wherein P is 0 Is a macroscopic property of the rock sample; x is x z Is Weibull random number; p (P) z Is the mechanical parameter of the primitive;
wherein Weibull random number x z The acquisition method comprises the following steps:
wherein: w (x) is a cumulative distribution function of Weibull distribution; w (x) is a probability density function of Weibull distribution; x is x 0 >0 is a scale parameter; ζ is a shape parameter; x is a random variable;
x z ＝x 0 (-ln(u m )) 1/ζ (4)
wherein: u (u) m Is a uniformly distributed random number.
3. The method for calculating the stability of a rock mass in consideration of fatigue and time effects according to claim 1, wherein in S2, the Hoek-Brown elastoplastic damage model of the primitive is obtained as follows:
wherein f is a yield function; j (J) 2 Is the second bias force invariant; θ σ Is the roeder angle; d (D) m Is a load damage variable; sigma (sigma) ci Is the uniaxial compressive strength of the complete rock; p is hydrostatic pressure; m is m bg Is m b Corresponding plastic potential function parameters; s is(s) g The plastic potential function parameter corresponding to s; a, a g A corresponding plastic potential function parameter is a; g is a plastic potential function;
wherein, alpha is the initial slope of the softening curve of the rock material after the damage, and the value range is (0, + -infinity); beta is a parameter for determining the maximum damage value of the rock, and the value range is [0, 1);is equivalent plastic strain;
wherein ε p1 Is the principal plastic strain in the x-axis direction of the spatial coordinate system; epsilon p2 Is the main plastic strain in the y-axis direction of the space coordinate system; epsilon p3 Is the principal plastic strain in the z-axis direction of the spatial coordinate system.
4. The method for calculating the stability of the rock mass considering fatigue and time effect according to claim 1, wherein in the step S3, the method for obtaining the aging damage variable D (t) of the element is as follows;
wherein epsilon is strain; sigma (sigma) 0 Is the stress of the axial direction; k (K) 1 、K 2 Are mechanical parameters of the elastic element; η is the viscosity coefficient of the adhesive kettle; t is the time of rheology;
can be obtained by simplified method (9)
ε＝σ 0 [P+Qexp(-Rt)] (10)
Wherein P, Q, R is an intermediate parameter, wherein,
from equation (10) can be derived:
E(t)＝P+Qexp(-Rt) (11)
e (t) is a function of the variation of the modulus of elasticity with time t;
wherein D (t) is an aging damage variable, i.e., a damage variable caused by a time effect; e (E) 0 Is the modulus of elasticity before injury.
5. The method for calculating the stability of a rock mass in consideration of fatigue and time effects according to claim 1, wherein in S4, the fatigue damage variable D of the element r The acquisition is as follows:
wherein: d (D) t Is the N t A damage value of the rock section under the action of the secondary fatigue disturbance; d (D) r Variable D for fatigue damage r N, i.e t N times of fatigue damage variation before the secondary fatigue disturbance; n (N) t Numbering the fatigue disturbance times; n is the N t Total number of fatigue disturbances before the secondary fatigue disturbance; w and U are material parameters;
wherein n is 0 Is the porosity of the rock before fatigue action; n is the porosity after the fatigue action of the rock; v (V) P Is the longitudinal wave velocity after the rock fatigue action.
6. A rock mass stability calculation method taking into account fatigue and time effects according to claim 1, wherein, in S5,
D c ＝D(t)+D m +D r -D(t)D m -D r D m -D r D t +D(t)D m D r (15)
wherein Dc is a coupling impairment variable; d (D) m Is a load damage variable.
7. The method for calculating the stability of a rock mass in consideration of fatigue and time effects according to claim 1, wherein in S6, t is obtained m+1 Nominal stress tensor sigma 'at time step' m+1 The method of (2) is as follows:
s61: the stress-strain constitutive relation considering the time effect-fatigue-load coupling damage is obtained as follows:
wherein σ is stress considering time effect-fatigue-load coupling damage; epsilon e Is elastic strain;to consider a stiffness matrix of coupling impairments; />I s Is a fourth order symmetric tensor->Is Cronecker product; g (D) c ) To damage shear modulus; k (D) c ) Is bulk modulus;
wherein,,
wherein G is 0 Is the initial shear modulus; k (K) 0 Is the initial bulk modulus; mu is Poisson's ratio, E (D c ) To the damage variable D C Modulus of elasticity at the time;
(m b ) t ＝(1-D(t))m b0 (18a)
(s) t ＝(1-D(t))s 0 (18b)
wherein: (m) b ) t M is time t b A value; m is m b0 For the initial m b A value; (s) t S is the value of s at the time t; s is(s) 0 Is the initial s value;
s62: acquisition of the t m+1 Predicting stress in the time step to judge whether the rock enters a plastic correction stage or not;
assume thatThe predicted stress expression is obtained from a given strain delta epsilon as:
in the method, in the process of the invention,is t th m+1 Predicted stress at time steps; />Rigidity moment to account for coupling impairmentsAn array; epsilon m Is t th m Strain at time steps; delta epsilon m Is t th m A given strain increment at a time step; />Is t th m+1 Predicting coupling damage variables in the time step; (D) c ) m Is t th m Coupling damage variable under time step; representing double-point multiplication;
s63: according to the yield function f, if:
then t m+1 Stress sigma at time step m+1 Equal to the t m+1 Predicted stress at time steps, i.e.Fully executing S62; otherwise, executing S64;
s64: according to the plastic potential function, carrying out plastic correction on the Hoek-Brown elastoplastic damage model to obtain corrected equivalent plastic strain;
s65: obtaining t according to the corrected equivalent plastic strain m+1 Nominal stress tensor sigma 'at time step' m+1 The following are provided:
wherein:and->Respectively t m And t m+1 A damage elastic matrix under the time step; />Is t th m+1 Plastic strain increment of time step; (D) c ) m+1 Is the t m+1 Coupling damage variable under time step; (D) c ) m Is t th m Coupling at time step impairs the variable.
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