CN112711868A - Pseudo-static method for calculating power safety coefficient of homogeneous slope under earthquake action - Google Patents

Pseudo-static method for calculating power safety coefficient of homogeneous slope under earthquake action Download PDF

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CN112711868A
CN112711868A CN202110151671.8A CN202110151671A CN112711868A CN 112711868 A CN112711868 A CN 112711868A CN 202110151671 A CN202110151671 A CN 202110151671A CN 112711868 A CN112711868 A CN 112711868A
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方宏伟
张雨慧
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Jilin Jianzhu University
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Abstract

The invention provides a quasi-static method for calculating the power safety coefficient of a homogeneous slope under the action of an earthquake, which is characterized in that intensity parameters (cohesive force and internal friction angle) are reduced to obtain reduced intensity parameters; according to the earthquake action stress balance equation set and the Morkolem criterion stress expression, a characteristic line method is applied to derive two groups of characteristic line differential equation sets of a glide line field, and the differential equation sets are solved by adopting a finite difference method according to the dynamic boundary conditions of active, transition and passive regions under the earthquake action to obtain a glide line field under the earthquake action and a slope curve (power limit slope curve for short) of a side slope under a power limit state; different power limit slope curves can be calculated according to different reduction strength parameters, the dynamic stability of the side slope under the earthquake action is judged according to the positive and negative of the abscissa of the intersection point of the power limit slope curve and the slope bottom, when the abscissa of the intersection point is zero, the side slope is judged to be in a power limit state, and the reduction coefficient is the power safety coefficient.

Description

Pseudo-static method for calculating power safety coefficient of homogeneous slope under earthquake action
Technical Field
The invention belongs to the field of slope stability evaluation, and particularly relates to a quasi-static method for calculating the power safety coefficient of a homogeneous slope under the action of an earthquake.
Background
China is a country with frequent earthquakes, particularly in mountainous areas and hilly lands, landslides caused by the action of earthquakes often have the characteristics of wide distribution, large quantity, large harm and the like, so that the problem of slope stability under the action of earthquake loads is always a research difficulty and a hotspot in the geotechnical and earthquake engineering circles. The pseudo-static method is simple in calculation and high in practicability, and is brought into corresponding specifications to be applied to slope dynamic stability analysis. The essence of the quasi-static method is that the earthquake inertia force is regarded as the static load and is applied to the slope body, and then the dynamic safety coefficient of the slope under the earthquake action is calculated by adopting a limit balance bar method or a strength reduction finite element method.
When the extreme balance bar quasi-static method is adopted, two problems mainly exist: one is that when the pseudo-static force strip division method divides the soil strips of the slope rock-soil mass, the pseudo-static force method generates errors even unreasonable results are obtained due to different strip division directions; the other is that a critical sliding surface form needs to be assumed or searched, and the power safety coefficient calculation formula considering the earthquake inertia force has a large difference to the results obtained by different critical sliding surface forms, so that the engineering practice application is not facilitated. When the numerical calculation is carried out by adopting the intensity reduction finite element method, although the assumption or search of a critical sliding surface is not needed, how to determine that the slope is in a power limit state is a difficult problem, namely the determination of the instability criterion is a difficult problem, and the slope instability criterion mainly comprises the calculation unconvergence criterion, the displacement mutation criterion and the plastic region through criterion at present. The complexity of a seismic inertia force slope numerical calculation model, the existence of nonlinear problems and other factors can cause calculation non-convergence, the selection of the displacement mutation characteristic point position has no unified standard, sometimes the inflection point of a characteristic point displacement curve is not obvious, subjective factors can exist when the mutation point is judged manually, and the penetration of a plastic zone is a necessary and insufficient condition for slope damage.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide the homogeneous slope dynamic safety coefficient quasi-static method under the earthquake action, which is scientific and reasonable, high in engineering practical value and good in effect.
In order to achieve the purpose, the invention adopts the technical scheme that:
1. a quasi-static method for calculating the power safety coefficient of a homogeneous slope under the action of an earthquake is characterized by comprising the following steps:
1) and (3) reducing the strength parameter:
Figure BSA0000232852750000011
in the formula c0In order to be the initial cohesive force,
Figure BSA0000232852750000012
is an initial angle of friction, clIn order to reduce the cohesive force after the folding,
Figure BSA0000232852750000013
for the post-reduction friction angle, F is the reduction coefficient, Δ F is the increase in the reduction coefficient, and l is a natural number 1, 2, 3.
2) Formula for calculating slip line field by pseudo-static method
Under the action of earthquake, the stress balance equation set is as follows:
Figure BSA0000232852750000021
Figure BSA0000232852750000022
in the formula sigmaxAnd σyDenotes positive stress in x and y directions, respectively, τxyAnd τyxDenotes shear stress in x and y directions, respectively, fx＝γ·kH，fy＝γ·(1-kV) γ represents volume weight, kHAnd kVRepresenting horizontal and vertical seismic coefficients, k, respectivelyV＝ξ·kHAnd xi is a scaling factor.
To give an expression for the normal stress as well as the shear stress in the molar coulomb criterion, the formula for the characteristic stress σ is introduced:
Figure BSA0000232852750000023
the normal and shear stress expressions at this time are:
Figure BSA0000232852750000024
Figure BSA0000232852750000025
in which theta is the maximum principal stress sigma1Intersecting the x-axis at an angle.
And (3) simultaneously substituting the expressions (5) and (6) into the expressions (2) and (3), and obtaining characteristic line differential equations of two families (alpha and beta families) of the glide slope field theory under the action of the earthquake according to a characteristic line method:
Figure BSA0000232852750000026
Figure BSA0000232852750000027
in the formula
Figure BSA0000232852750000028
The mean value of the intersection angles of the two families of slip lines is obtained.
The differential method is adopted to approximately solve the characteristic line equations (7) and (8),
Figure BSA0000232852750000029
Figure BSA00002328527500000210
in the formula Mα(xα，yα，θα，σα) Is a point on the alpha group, Mβ(xβ，yβ，θβ，σβ) Is a point in the beta family, (x, y) are coordinate values,
Figure BSA0000232852750000031
and
Figure BSA0000232852750000032
calculating a point M (x, y, theta, sigma) to be found on the slip line simultaneously by the following equations (9) and (10):
Figure BSA0000232852750000033
Figure BSA0000232852750000034
Figure BSA0000232852750000035
Figure BSA0000232852750000036
the slope curve under the slope dynamic limit state (called dynamic limit slope curve for short) differential equation obtained by the theoretical calculation of the slip line field under the action of earthquake is as follows:
Figure BSA0000232852750000037
the coordinate point M of the curve of the power limit slope can be solved by adopting a finite difference method in conjunction with the equation (8) of the slip line of the beta groupij(xij，yij，θij，σij)：
Figure BSA0000232852750000038
Figure BSA0000232852750000039
Figure BSA00002328527500000310
Figure BSA00002328527500000311
In the formula Mb(xb，yb，θb，σb) And M'β(xβ′，y′β，θ′β，σ′β) The known points of the power limit slope curve and the beta slip line are shown.
3) Pseudo-static method slip line field boundary condition
(1) Active region O1AB boundary conditions
Known calculation point M of alpha and beta families of active regionαAnd Mβ(x, y) is the crest O1A coordinate value, where x is Δ x · i, Δ x is a calculation step, i is a natural number, and i is 0 to N1，N1Step length is the number of steps, the vertical coordinate is the slope height, and the intersection angle of the maximum principal stress of the boundary of the active region and the x axis is as follows:
Figure BSA00002328527500000312
in the formula
Figure BSA0000232852750000041
For the stress deflection angle caused by earthquake dynamic force, according to the formula, the stress deflection angle and the friction angle must satisfy the relational expression
Figure BSA0000232852750000042
Characteristic stress of active zone boundary:
Figure BSA0000232852750000043
formula middle slope top power load
Figure BSA0000232852750000044
Dynamic positive stress sigma0＝P0·(1-kV) Dynamic shear stress tau0＝P0·kH，P0For static load of top of slope，
Figure BSA0000232852750000045
The intersection calculation formulas of the slip lines are (11) - (14);
(2) transition zone O1BC boundary condition
Known boundary point O of transition zone1And (x, y) is a slope shoulder coordinate value, and the characteristic stress is as follows:
Figure BSA0000232852750000046
in the formula
Figure BSA0000232852750000047
k is a natural number, k is 0 to N2，Δθ＝θIII-θI，N2The intersection calculation formula of the transition region sliding lines is (11) - (14) for the subdivision number of the transition region points;
(3) passive region O1CD boundary condition
MbThe first known point is the shoulder O1The (x, y) coordinate value of (c), but the characteristic stress value is
Figure BSA0000232852750000048
By substituting the formula (21)
Figure BSA0000232852750000049
To satisfy Δ θ ≧ 0, θ is necessaryIII≥θIThus minimum value of dynamic load on the top of the hill
Figure BSA00002328527500000410
In this case, Δ θ is 0, the passive region slip line intersection calculation formulas are (11) to (14), and the dynamic limit slope curve OD is calculated using formulas (15) to (18).
4) Dynamic safety coefficient calculated by instability criterion of pseudo-static method
The intersection point of the curve of the power limit slope and the slope bottom is (x)10), based on the abscissa value x1Analysis of slope stability by pseudo-static method under positive and negative judgment seismic actionQualitative criterion of instability: when x is1When the slope is more than 0, the slope is judged to be in a stable state, the reduction coefficient F is increased, namely the increase value delta F is a positive value, and can be 0.01; when x is1When the speed is equal to 0, judging that the slope is in a power limit state, and at the moment, setting a power safety coefficient FS to be F; when x is1If the value is less than 0, the slope is judged to be in a destruction state, the reduction coefficient F is reduced, namely the increase value delta F is a negative value, and can be-0.01.
Compared with the prior art, the quasi-static method for calculating the power safety coefficient of the homogeneous slope under the action of the earthquake has the beneficial effects that:
(1) calculating to obtain a slope surface shape curve (called as a dynamic limit slope surface curve for short) in a dynamic limit state by deducing a slip line field theory under the action of an earthquake, judging the dynamic stability of the slope by the positive and negative of the abscissa of the intersection point of the dynamic limit slope surface curve and the slope bottom, and at the moment, dividing the slope rock-soil body into strips, so that the strip dividing direction of the rock-soil body is not required to be considered;
(2) the dynamic instability criterion of the stability of the homogeneous slope is given, and when the instability criterion is adopted to calculate the dynamic safety coefficient, the slope critical slip fracture surface does not need to be assumed and searched compared with the existing extreme balance bar quasi-static method;
(3) compared with the existing dynamic instability criterion of the slope intensity reduction method, the instability criterion does not need to consider the influence of calculating unconvergence, does not need to select slope characteristic points and judge the displacement reduction curve mutation points of the characteristic points, realizes the objective standard quantification of the dynamic instability criterion, and avoids the influence of artificial subjective factors;
(4) the method is scientific and reasonable, the engineering practical value is high, and the effect is good.
Drawings
FIG. 1 is a schematic diagram of: calculating a curve diagram of a dynamic limit slope surface by a glide slope field theory under the action of an earthquake;
FIG. 2 is a diagram of: the invention discloses a schematic diagram of dynamic instability criterion of a pseudo-static method;
FIG. 3 is a diagram of: the invention relates to a technical flow chart for calculating a power safety coefficient by using a pseudo-static method power instability criterion;
FIG. 4 is a diagram of: when k isH0.1, 0.5 (i.e. k)V0.05) and a reduction factor F11.3, homogeneous slope seismic glide slope line field theory (Δ x 0.5, N)1＝50、N25) calculating the power limit slope curve chart, and x can be obtained1＝5.4846；
FIG. 5 is a diagram of: when k isH0.1, 0.5 (i.e. k)V0.05) and a reduction factor F21.52, homogeneous slope seismic event glide slope field theory (Δ x 0.5, N)1＝50、N25) calculating the power limit slope curve chart, and x can be obtained1＝0；
FIG. 6 is a diagram of: when k isH0.1, 0.5 (i.e. k)V0.05) and a reduction factor F3When the value is 1.8, the sliding line field theory under the action of the homogeneous slope earthquake (delta x is 0.5, N)1＝50、N25) calculating the power limit slope curve chart, and x can be obtained1＝-9.4591；
FIG. 7 is a diagram of: and (4) calculating a result by a limit balance bar simulation static method (simplified bishop method).
Detailed Description
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings.
The invention relates to a quasi-static method for calculating the power safety coefficient of a homogeneous slope under the action of an earthquake, which comprises the following steps:
1. a quasi-static method for calculating the power safety coefficient of a homogeneous slope under the action of an earthquake is characterized by comprising the following steps:
1) and (3) reducing the strength parameter:
Figure BSA0000232852750000051
in the formula c0In order to be the initial cohesive force,
Figure BSA0000232852750000052
is an initial angle of friction, clIn order to reduce the cohesive force after the folding,
Figure BSA0000232852750000053
for the post-reduction friction angle, F is the reduction coefficient, Δ F is the increase in the reduction coefficient, and l is a natural number 1, 2, 3.
2) Formula for calculating slip line field by pseudo-static method
The schematic diagram of the slope curve of the theoretical calculation dynamic limit of the glide slope field under the action of the earthquake is shown in figure 1.
Under the action of earthquake, the stress balance equation set is as follows:
Figure BSA0000232852750000061
Figure BSA0000232852750000062
in the formula sigmaxAnd σyDenotes positive stress in x and y directions, respectively, τxyAnd τyxDenotes shear stress in x and y directions, respectively, fx＝γ·kH，fy＝γ·(1-kV) γ represents volume weight, kHAnd kVRepresenting horizontal and vertical seismic coefficients, k, respectivelyV＝ξ·kHAnd xi is a scaling factor.
To give an expression for the normal stress as well as the shear stress in the molar coulomb criterion, the formula for the characteristic stress σ is introduced:
Figure BSA0000232852750000063
the normal and shear stress expressions at this time are:
Figure BSA0000232852750000064
Figure BSA0000232852750000065
in which theta is the maximum principal stress sigma1Intersecting the x-axis at an angle.
And (3) simultaneously substituting the expressions (5) and (6) into the expressions (2) and (3), and obtaining characteristic line differential equations of two families (alpha and beta families) of the glide slope field theory under the action of the earthquake according to a characteristic line method:
Figure BSA0000232852750000066
Figure BSA0000232852750000067
in the formula
Figure BSA0000232852750000068
The mean value of the intersection angles of the two families of slip lines is obtained.
The differential method is adopted to approximately solve the characteristic line equations (7) and (8),
Figure BSA0000232852750000069
Figure BSA00002328527500000610
in the formula Mα(xα，yα，θα，σα) Is a point on the alpha group, Mβ(xβ，yβ，θβ，σβ) Is a point in the beta family, (x, y) are coordinate values,
Figure BSA0000232852750000071
and
Figure BSA0000232852750000072
calculating a point M (x, y, theta, sigma) to be found on the slip line simultaneously by the following equations (9) and (10):
Figure BSA0000232852750000073
Figure BSA0000232852750000074
Figure BSA0000232852750000075
Figure BSA0000232852750000076
the slope curve (power is called as limit slope curve for short) differential equation under the slope power limit state calculated by the slip line field theory under the action of earthquake is as follows:
Figure BSA0000232852750000077
coordinate point M of power limit slope curve can be solved by combining with beta family slip line equation formula (8)ij(xij，yij，θij，σij)：
Figure BSA0000232852750000078
Figure BSA0000232852750000079
Figure BSA00002328527500000710
Figure BSA00002328527500000711
In the formula Mb(xb，yb，θb，σb) And M'β(x′β，y′β，θ′β，σ′β) The known points of the power limit slope curve and the beta slip line are shown.
3) Pseudo-static method slip line field boundary condition
(1) Active region O1AB boundary conditions
Known calculation point M of alpha and beta families of active regionαAnd Mβ(x, y) is the crest O1A coordinate value, where x is Δ x · i, Δ x is a calculation step, i is a natural number, and i is 0 to N1，N1Step length is the number of steps, the vertical coordinate is the slope height, and the intersection angle of the maximum principal stress of the boundary of the active region and the x axis is as follows:
Figure BSA00002328527500000712
in the formula
Figure BSA0000232852750000081
For the stress deflection angle caused by earthquake dynamic force, according to the formula, the stress deflection angle and the friction angle must satisfy the relational expression
Figure BSA0000232852750000082
Characteristic stress of active zone boundary:
Figure BSA0000232852750000083
formula middle slope top power load
Figure BSA0000232852750000084
Dynamic positive stress sigma0＝P0·(1-kV) Dynamic shear stress tau0＝P0·kH，P0Is the static load of the top of the slope,
Figure BSA0000232852750000085
the intersection calculation formulas of the slip lines are (11) - (14);
(2) transition zone O1BC boundary condition
Known boundary point O of transition zone1And (x, y) is a slope shoulder coordinate value, and the characteristic stress is as follows:
Figure BSA0000232852750000086
in the formula
Figure BSA0000232852750000087
k is a natural number, k is 0 to N2，Δθ＝θIII-θI，N2The intersection calculation formula of the transition region sliding lines is (11) - (14) for the subdivision number of the transition region points;
(3) passive region O1CD boundary condition
MbThe first known point is the shoulder O1The (x, y) coordinate value of (c), but the characteristic stress value is
Figure BSA0000232852750000088
By substituting the formula (21)
Figure BSA0000232852750000089
To satisfy Δ θ ≧ 0, θ is necessaryIII≥θIThus minimum value of dynamic load on the top of the hill
Figure BSA00002328527500000810
In this case, Δ θ is 0, the passive region slip line intersection calculation formulas are (11) to (14), and the dynamic limit slope curve OD is calculated using formulas (15) to (18).
4) Dynamic safety coefficient calculated by instability criterion of pseudo-static method
The intersection point of the curve of the power limit slope and the slope bottom is (x)10), based on the abscissa value x1The instability criterion for analyzing the slope stability by the pseudo-static method under the action of positive and negative judgment earthquake comprises the following steps: when x is1When the slope is more than 0, the slope is judged to be in a stable state, the reduction coefficient F is increased, namely the increase value delta F is a positive value, and can be 0.01; when x is1When the power safety factor FS is equal to 0, the slope is judged to be in the power limit stateF; when x is1If the value is less than 0, the slope is judged to be in a destruction state, the reduction coefficient F is reduced, namely the increase value delta F is a negative value, and can be-0.01.
The technical process of the invention is shown in figure 3, and table 1 shows the geometric and physical parameter values of a homogeneous side slope with 9 degrees of seismic intensity, according to the technical specification GB50330-2013 of building side slope engineering, the seismic intensity is 9 degrees, and the horizontal seismic coefficient k isHThe calculation example can be used for comparing and verifying the correctness of the dynamic safety coefficient calculated by the pseudo-static method instability criterion.
TABLE 1 homogeneous slope examination question calculation parameters (seismic intensity 9 degree) in the embodiment of the invention
Figure BSA0000232852750000091
*Technical Specification of building slope engineering GB50330-2013
According to the calculation flow chart 3, the horizontal earthquake dynamic coefficient kH0.1, 0.5 (i.e. vertical seismic dynamics coefficient k)V0.05), the theoretical boundary condition of the sliding line field under the action of the homogeneous slope earthquake is that deltax is 0.5, and N is1＝50、N2When the reduction factor F is 51When the power limit slope curve chart is calculated as 1.3, x can be obtained15.4846 (see fig. 4); reduction factor F2When 1.52, x is obtained10 (see fig. 5); reduction factor F3When 1.8, x is obtained1-9.4591 (see fig. 6); according to the pseudo-static force instability criterion (shown in figure 2), the obtained dynamic safety coefficient is FS (1.52), and the obtained dynamic safety coefficient is 1.636 (shown in figure 7) together with the calculation result of the extreme balance bar quasi-static force method (simplified bishop quasi-static force method), and the error percentage is 6.7%.
According to examination questions, the instability criterion of the pseudo-static method can provide reliable power safety coefficients, and the calculation process shows that the instability criterion of the pseudo-static method provides an objective standard for judging the power limit state of a homogeneous slope under the action of an earthquake, namely the abscissa x of the intersection point between a power limit slope curve and a slope bottom calculated by a sliding line field theory1When equal to 0, the corresponding reduction parameter F is a power safety systemThe number FS is counted, the situation that characteristic points need to be selected and characteristic displacement curve mutation points need to be judged artificially and subjectively in the traditional dynamic instability criterion of the slope intensity reduction method is avoided, and compared with the existing extreme balance bar quasi-static method, the instability criterion does not need to assume and search a critical slip crack surface under the dynamic condition.
Finally, it should be noted that the above-mentioned embodiments are only used for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the above-mentioned embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made on the specific embodiments of the present invention without departing from the spirit and scope of the present invention, and all the modifications or equivalent substitutions should be covered in the claims of the present invention.

Claims (1)

1. A quasi-static method for calculating the power safety coefficient of a homogeneous slope under the action of an earthquake is characterized by comprising the following steps:
1) and (3) reducing the strength parameter:
Figure FSA0000232852740000011
in the formula c0In order to be the initial cohesive force,
Figure FSA0000232852740000012
is an initial angle of friction, clIn order to reduce the cohesive force after the folding,
Figure FSA0000232852740000013
for the post-reduction friction angle, F is the reduction coefficient, Δ F is the increase in the reduction coefficient, and l is a natural number 1, 2, 3.
2) Formula for calculating slip line field by pseudo-static method
Under the action of earthquake, the stress balance equation set is as follows:
Figure FSA0000232852740000014
Figure FSA0000232852740000015
in the formula sigmaxAnd σyDenotes positive stress in x and y directions, respectively, τxyAnd τyxDenotes shear stress in x and y directions, respectively, fx＝γ·kH，fy＝γ·(1-kV) γ represents volume weight, kHAnd kVRepresenting horizontal and vertical seismic coefficients, k, respectivelyV＝ξ·kHAnd xi is a scaling factor.
To give an expression for the normal stress as well as the shear stress in the molar coulomb criterion, the formula for the characteristic stress σ is introduced:
Figure FSA0000232852740000016
the normal and shear stress expressions at this time are:
Figure FSA0000232852740000017
Figure FSA0000232852740000018
in which theta is the maximum principal stress sigma1Intersecting the x-axis at an angle.
And (3) simultaneously substituting the expressions (5) and (6) into the expressions (2) and (3), and obtaining characteristic line differential equations of two families (alpha and beta families) of the glide slope field theory under the action of the earthquake according to a characteristic line method:
Figure FSA0000232852740000019
Figure FSA00002328527400000110
in the formula
Figure FSA0000232852740000021
The mean value of the intersection angles of the two families of slip lines is obtained.
The differential method is adopted to approximately solve the characteristic line equations (7) and (8),
Figure FSA0000232852740000022
Figure FSA0000232852740000023
in the formula Mα(xα，yα，θα，σα) Is a point on the alpha group, Mβ(xβ，yβ，θβ，σβ) Is a point in the beta family, (x, y) are coordinate values,
Figure FSA0000232852740000024
and
Figure FSA0000232852740000025
calculating a point M (x, y, theta, sigma) to be found on the slip line simultaneously by the following equations (9) and (10):
Figure FSA0000232852740000026
Figure FSA0000232852740000027
Figure FSA0000232852740000028
Figure FSA0000232852740000029
the slope curve under the slope dynamic limit state (called dynamic limit slope curve for short) differential equation obtained by the theoretical calculation of the slip line field under the action of earthquake is as follows:
Figure FSA00002328527400000210
the coordinate point M of the curve of the power limit slope can be solved by adopting a finite difference method in conjunction with the equation (8) of the slip line of the beta groupij(xij，yij，θij，σij)：
Figure FSA00002328527400000211
Figure FSA00002328527400000212
Figure FSA00002328527400000213
Figure FSA0000232852740000031
In the formula Mb(xb，yb，θb，σb) And M'β(xβ′，y′β，θ′β，σ′β) The known points of the power limit slope curve and the beta slip line are shown.
3) Pseudo-static method slip line field boundary condition
(1) Active region O1AB boundary conditions
Known calculation point M of alpha and beta families of active regionαAnd Mβ(x, y) is the crest O1A coordinate value, where x is Δ x · i, Δ x is a calculation step, i is a natural number, and i is 0 to N1，N1Step length is the number of steps, the vertical coordinate is the slope height, and the intersection angle of the maximum principal stress of the boundary of the active region and the x axis is as follows:
Figure FSA0000232852740000032
in the formula
Figure FSA0000232852740000033
For the stress deflection angle caused by earthquake dynamic force, according to the formula, the stress deflection angle and the friction angle must satisfy the relational expression
Figure FSA0000232852740000034
Characteristic stress of active zone boundary:
Figure FSA0000232852740000035
formula middle slope top power load
Figure FSA0000232852740000036
Dynamic positive stress sigma0＝P0·(1-kV) Dynamic shear stress tau0＝P0·kH，P0Is the static load of the top of the slope,
Figure FSA0000232852740000037
the intersection calculation formulas of the slip lines are (11) - (14);
(2) transition zone O1BC boundary condition
Known boundary point O of transition zone1And (x, y) is a slope shoulder coordinate value, and the characteristic stress is as follows:
Figure FSA0000232852740000038
in the formula
Figure FSA0000232852740000039
k is a natural number, k is 0 to N2，Δθ＝θIII-θI，N2The intersection calculation formula of the transition region sliding lines is (11) - (14) for the subdivision number of the transition region points;
(3) passive region O1CD boundary condition
MbThe first known point is the shoulder O1The (x, y) coordinate value of (c), but the characteristic stress value is
Figure FSA00002328527400000310
By substituting the formula (21)
Figure FSA00002328527400000311
To satisfy Δ θ ≧ 0, θ is necessaryIII≥θIThus minimum value of dynamic load on the top of the hill
Figure FSA00002328527400000312
In this case, Δ θ is 0, the passive region slip line intersection calculation formulas are (11) to (14), and the dynamic limit slope curve OD is calculated using formulas (15) to (18).
4) Dynamic safety coefficient calculated by instability criterion of pseudo-static method
The intersection point of the curve of the power limit slope and the slope bottom is (x)10), based on the abscissa value x1The instability criterion for analyzing the slope stability by the pseudo-static method under the action of positive and negative judgment earthquake comprises the following steps: when x is1When the slope is more than 0, the slope is judged to be in a stable state, the reduction coefficient F is increased, namely the increase value delta F is a positive value, and can be 0.01; when x is1When the speed is equal to 0, judging that the slope is in a power limit state, and at the moment, setting a power safety coefficient FS to be F; when x is1If less than 0, judging that the side slope is in a failure state, and changing the reduction coefficient F intoSmall, i.e., increasing the value of Δ F to a negative value, may take-0.01.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113722920A (en) * 2021-08-30 2021-11-30 河海大学 Rapid slope earthquake reliability calculation method based on FLAC3D-Python secondary development
CN114036794A (en) * 2021-11-12 2022-02-11 中国海洋大学 Method for analyzing stability of seabed slope after earthquake

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20130276175A1 (en) * 2011-08-15 2013-10-17 William P. King Magnetic Actuation and Thermal Cantilevers for Temperature and Frequency Dependent Atomic Force Microscopy
CN105044774A (en) * 2015-08-26 2015-11-11 长安大学 Side slope stability prediction method under earthquake effect
CN106709182A (en) * 2016-12-26 2017-05-24 华中科技大学 Safety assessment method for stable reliability of consequent bedding rock slope under earthquake action
CN106801422A (en) * 2017-01-09 2017-06-06 东北电力大学 A kind of open-pit slope Structural shape optimization
CN106874649A (en) * 2017-01-09 2017-06-20 东北电力大学 A kind of homogeneous slope stability_intensity reduction method INSTABILITY CRITERION
US20180164165A1 (en) * 2016-12-08 2018-06-14 Magcanica, Inc. Devices and methods to stimulate motion in magnetoelastic beams

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20130276175A1 (en) * 2011-08-15 2013-10-17 William P. King Magnetic Actuation and Thermal Cantilevers for Temperature and Frequency Dependent Atomic Force Microscopy
CN105044774A (en) * 2015-08-26 2015-11-11 长安大学 Side slope stability prediction method under earthquake effect
US20180164165A1 (en) * 2016-12-08 2018-06-14 Magcanica, Inc. Devices and methods to stimulate motion in magnetoelastic beams
CN106709182A (en) * 2016-12-26 2017-05-24 华中科技大学 Safety assessment method for stable reliability of consequent bedding rock slope under earthquake action
CN106801422A (en) * 2017-01-09 2017-06-06 东北电力大学 A kind of open-pit slope Structural shape optimization
CN106874649A (en) * 2017-01-09 2017-06-20 东北电力大学 A kind of homogeneous slope stability_intensity reduction method INSTABILITY CRITERION

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
C.-B. QIN ET AL.: "Kinematic analysis of seismic slope stability with a discretisation technique and pseudo-dynamic approach:a new perspective", GEOTECHNIQUE, vol. 68, no. 06, 9 May 2018 (2018-05-09), pages 492 - 503 *
方宏伟 等: "成层土质边坡稳定性极限曲线法", 长江科学院院报, vol. 32, no. 01, 15 January 2015 (2015-01-15), pages 97 - 101 *
李俊 等: "完全动力分析法在求解边坡动力稳定系数中的应用研究", 中国水运（下半月）, vol. 13, no. 08, 15 August 2013 (2013-08-15), pages 332 - 333 *
薛彦雨 等: "基于"锚杆框架梁+主动防护网"的裂隙岩质边坡治理措施研究", 石家庄铁道大学学报(自然科学版), vol. 33, no. 01, 25 March 2020 (2020-03-25), pages 44 - 48 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113722920A (en) * 2021-08-30 2021-11-30 河海大学 Rapid slope earthquake reliability calculation method based on FLAC3D-Python secondary development
CN113722920B (en) * 2021-08-30 2024-03-19 河海大学 Rapid calculation method for reliability of side slope earthquake based on FLAC3D-Python secondary development
CN114036794A (en) * 2021-11-12 2022-02-11 中国海洋大学 Method for analyzing stability of seabed slope after earthquake
CN114036794B (en) * 2021-11-12 2022-07-22 中国海洋大学 Method for analyzing stability of seabed slope after earthquake

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