CN106501853A - Either direction plane of incidence bulk wave excitation method in side slope seismic response numerical simulation - Google Patents
Either direction plane of incidence bulk wave excitation method in side slope seismic response numerical simulation Download PDFInfo
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- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
- G01V1/282—Application of seismic models, synthetic seismograms
Abstract
The invention provides either direction plane of incidence bulk wave excitation method in side slope seismic response numerical simulation, belongs to geological disasters analysis and prevention and control field.The method mainly includes six steps：Side slope is modeled；Either direction incident seismic bulk wave encourages the startup Time-Series analyses of each node on the exciting border of side slope bottom；The components of stress time-histories that different seismic phase bulk wave incentive actions are produced at each node in side slope bottom is calculated；The superposition time-histories of side slope bottom exciting boundary node difference bulk wave seismic phase fluctuating stress component is calculated；The exciting boundary node bulk wave exciting input of side slope bottom；In side slope model, each node dynamic response result is extracted.The present invention can solve a difficult problem for either direction incident seismic ripple input in side slope seismic response numerical simulation, realize the incidence of earthquake plane bulk wave either direction, including oblique incidence and vertical incidence, the multiformity of the impact and seismic slope destruction of different incident direction earthquake plane bulk wave side slope Dynamic response to earthquake is disclosed, significant.
Description
Technical field
The present invention relates in side slope seismic response and stability analyses field, more particularly to side slope seismic response numerical simulation
Either direction plane of incidence bulk wave excitation method.
Background technology
China is the country of earthquake more than, and the slope instability of earthquake-induced can directly threaten the people's lives and property pacifies
Entirely, therefore seismic stability of slopes Research Significance is great.However, earthquake-induced slope instability has very big uncertainty, this
Uncertainty acts on two aspects essentially from side slope itself character and potential complications, and side slope itself character belongs to seismic slope mistake
Steady easy clockwork spring part, including slope ground body structure and physico-mechanical properties and side slope geometry；Potential complications effect category
Risk factor in slope instability.For a specific side slope, it is believed that itself character of side slope is relative to be determined, main
Uncertainty comes from the geological process in future, that is, risk factor.Dynamic seismic effect is concluded by Traditional project seismology
For the intensity of earthquake motion, frequency and persistent period, i.e., so-called " three essential of earthquake motions ", to earthquake motive force model of action (that is, ground
Vibrations forced direction and interaction property) this key element consideration is enough.
At present, in the seismic response analysis of general site soil layers or structure, often assume that seismic wave vertically enters for S ripples
Penetrate, on underground horizontal exciting border, the incident seismic fluctuation of each point is identical and level of synchronization is vibrated on the spot.This is for hypocentral distance
Nearer site seismic response problem is rational, but for focus (particularly shallow-focus earthquake and focus and engineering farther out
When there is certain distance in place) site seismic response problem for, seismic wave non-normal incidence, but with certain orientation and
Incident angular place is incident, and each point starting of oscillation of place exciting border is asynchronous, so as to cause place diverse location earthquake motion to present
Significant phase difference and the change of dynamic seismic effect property.When object of study is large scale structure engineering or high slope,
The Dynamic response to earthquake that oblique incidence causes can be very different compared with vertical incidence.At present, the earthquake motion that oblique incidence brings
Force-responsive problem is not given sufficient attention.
In sum, in current side slope Dynamic response to earthquake research, the input method of earthquake load is single, seldom consideration ground
The problem of seismic wave oblique incidence from different directions, while also seldom consider the effect of different seismic phase seismic waves.Meanwhile, input-to-state stabilization
Frequency, select when holding and different seismic phase seismic wave overlap-add procedure considerations are not perfect enough.Therefore, in side slope Dynamic response to earthquake point
In analysis, it is badly in need of the analogue technique of a set of either direction plane bulk wave incidence exciting.
Content of the invention
Present invention aims to the deficiencies in the prior art, there is provided arbitrary in a kind of side slope seismic response numerical simulation
The point source superposed simulation technical method of direction plane of incidence bulk wave exciting, sets up the exciting of a set of either direction plane of incidence bulk wave
Scheme.
For achieving the above object, based on the Huygen's principle that the present invention is propagated by ripple, there is provided ring to a kind of side slope
Either direction plane of incidence bulk wave excitation method in numerical simulation is answered, is comprised the following steps：
(1) side slope modeling；
(2) according to each node difference bulk wave seismic phase fluctuating stress on Huygen's principle analysis of slope model bottom exciting border
The startup sequential of time-histories, determines the startup time difference of each node, calculates the Startup time of each node；
(3) displacement vector of each seismic phase bulk wave, according to the propagating characteristic and polarization characteristic of different seismic phase bulk waves, is obtained, by ripple
Dynamic displacement vector brings geometric equation, physical equation into, draws each seismic phase seismic wave incentive action on side slope model bottom exciting side
The each components of stress time-histories expression formula produced at each node in boundary；
(4) practical situation that consideration ripple is propagated, by different seismic phase fluctuations on each for side slope model bottom exciting border node
Stress time-histories component is chronologically superimposed, and obtains the supercoated stress time-histories of each components of stress；
(5) it is each to each node input on side slope model bottom exciting border that node startup sequential is pressed in numerical simulation software
The supercoated stress time-histories of the components of stress；
(6) the Dynamic response to earthquake result of side slope model, acquisition side slope Dynamic response to earthquake cloud atlas and monitoring point are extracted
Dynamic response to earthquake acceleration, speed and displacement time-histories.
Further, step (1) is specifically included：Side slope model bottom exciting border is traditionally arranged to be horizontal plane and (referred to as " swashs
Shake face "), by certain mesh-density subdivision exciting border (hexahedral mesh subdivision pressed by side slope model bottom, size of mesh opening big
Little satisfaction：The hexahedron length of side less than incident seismic ripple highest frequency corresponding wavelength 1/10 to 1/8), subdivision grid lines intersection point structure
Into the node on exciting border, so as to swash spatially continuous earthquake wave excitation effect discrete for each node on exciting border
Bestir oneself use.
Further, step (2) specifically include：When seismic wave vertical incidence, on side slope model bottom exciting border
All nodes start simultaneously, and this Startup time is called side slope first arrival, is set to t0；When inclined seismic wave, by side
It is subject to the node of earthquake wave disturbance to be referred to as side slope just moving point on the model bottom exciting border of slope at first, the Startup time of the point is referred to as
Side slope first arrival, is likewise provided as t0, arbitrary grid node p on exciting borderijThe starting of oscillation moment be designated as tij, asked by following formula
?：
In formula：tijFor arbitrary grid node p on side slope model bottom exciting borderijStartup time, i=0,1 ..., n-
1, the sequence number of the local coordinate system X-direction that to be the node set up in exciting face, i=0 is the sequence number of just moving point, and X-axis forward direction refers to
To the direction that node ID increases, origin is overlapped with first moving point；J=0,1 ..., m-1 are that the node is set up in exciting face
The sequence number of local coordinate system Y-direction, j=0 is the sequence number of just moving point, and Y-axis is positive to point to the direction that node ID increases, origin with
Just moving point overlaps；t0For side slope first arrival；lijSide slope model bottom is reached by first moving point for seismic wave wavefront incident direction
Any node p on exciting borderijThe distance that is passed through, when seismic wave vertical incidence, lij=0, now, according to side slope exciting
The concrete condition in face, can be arranged on local coordinate system origin on certain angle point in exciting face, exciting face is placed in the local and is sat
The first quartile of mark system；Elastic wave velocities of the c for the following medium in side slope exciting border, compressional wave take cP, shear wave takes cS；No matter seismic wave
Vertical incidence or oblique incidence, side slope first arrival t0It is functionally identical to the moment that seismic wave reaches side slope.
Further, in step (3), each bulk wave seismic phase includes：(P, caused particle vibration direction of displacement are passed compressional wave with ripple
Broadcast direction consistent), shear wave (S, caused particle vibration direction of displacement are orthogonal with direction of wave travel)；Consideration shear wave vibration vector
With the relation of the bulk wave plane of incidence (plane that bulk wave ray is determined with side slope bottom exciting face normal, be vertical guide), can be by shear wave
Vibration vector is further broken into the oscillating component SV ripples in the plane of incidence and the oscillating component SH ripples perpendicular to the plane of incidence；Consider further that
The first motion direction of each bulk wave seismic phase (P, SV, SH) undulatory displacements, P ripples can be divided into first motion compressional wave P forward+With first motion backward
Tensile wave P-；Along direction of wave travel eyes front, SV ripples are observed in the plane of incidence, observes SH ripples, SV and SH ripples perpendicular to the plane of incidence
The first motion right side to the right can be divided into and cut ripple SV+、SH+Ripple SV is cut with a first motion left side to the left-、SH-.
Further, in step (4), on side slope model bottom exciting border during the stress of each node difference bulk wave seismic phase fluctuation
Journey presses component superposition includes (12 kinds of the superposition of two kinds of seismic phases：P++SV+、P++SV-、P-+SV+、P-+SV-、P++SH+、P++SH-、P-+
SH+、P-+SH-、SV++SH+、SV++SH-、SV-+SH+、SV-+SH-) and three kinds of seismic phases (8 kinds of superposition：P++SV++SH+、P++SV++
SH-、P++SV-+SH+、P++SV-+SH-、P-+SV++SH+、P-+SV++SH-、P-+SV-+SH+、P-+SV-+SH-) amount to 20 kinds of situations,
Superposition Formula is further derived according to step (3)；When different bulk wave seismic phase components of stress time-histories superpositions are carried out, should be first
Determine the due in of each seismic phase and persistent period on each node, then side is completed by the startup sequential of each seismic phase on node
On the model bottom exciting border of slope, different bulk wave seismic phase fluctuating stress component time-histories superpositions at each node, obtain body at each node
Ripple seismic phase fluctuating stress component is superimposed time-histories.
Further, in step (5), time-histories will be superimposed by startup through the bulk wave seismic phase fluctuating stress component that step (4) obtain
Sequential is loaded on each node in exciting face.
Further, in step (6), from side slope first arrival t0Rise, numerical simulation system is in start recording side slope model
The Dynamic response to earthquake process of each node, and according to research need to extract side slope Dynamic response to earthquake cloud atlas not in the same time with
And the Dynamic response to earthquake acceleration of the arbitrary monitoring point of side slope model, speed and displacement time-histories.
Compared with prior art, the invention has the beneficial effects as follows：Can be in side slope seismic response Numerical-Mode by providing one kind
The method for realizing either direction plane of incidence bulk wave exciting in plan, sets up a set of side slope and is encouraged by either direction plane of incidence bulk wave
Numerical simulation scheme, to disclose the multiformity of certain edges thereof slope eaerthquake damage, and then estimate the possibility of ad hoc fashion slope failure
Property.
Description of the drawings
Fig. 1 is the flow process of either direction oblique incidence plane body wave excitation method in side slope seismic response numerical simulation of the present invention
Figure.
Fig. 2 is that the Huygen's principle of vertical incidence plane body wave excitation in side slope seismic response numerical simulation of the present invention is illustrated
Figure.
Fig. 3 is that the Huygen's principle of oblique incidence plane body wave excitation in side slope seismic response numerical simulation of the present invention is illustrated
Figure.
Fig. 4 is either direction oblique incidence plane body wave excitation side slope bottom section in side slope seismic response numerical simulation of the present invention
Point starts Time-Series analyses schematic diagram.
Fig. 5 is either direction oblique incidence plane body wave ray and undulatory displacements in side slope seismic response numerical simulation of the present invention
Vector and spatial relationship schematic diagram of the side slope bottom level exciting border in the plane of incidence.
Fig. 6 is either direction oblique incidence plane body wave ray and displacement vector in side slope seismic response numerical simulation of the present invention
Projection relation schematic diagram in side slope bottom level exciting face.
Fig. 7 is the P ripple displacements of either direction oblique incidence plane body wave excitation in side slope seismic response numerical simulation of the present invention
Component (uP,vP,wP) and displacement vector mould (SP) relation schematic diagram.
Fig. 8 is the SV ripple displacements of either direction oblique incidence plane body wave excitation in side slope seismic response numerical simulation of the present invention
Component (uV,vV,wV) and displacement vector mould (SV) relation schematic diagram.
Fig. 9 is the SH ripple displacements of either direction oblique incidence plane body wave excitation in side slope seismic response numerical simulation of the present invention
Component (uH,vH,wH) and displacement vector mould (SH) relation schematic diagram.
Figure 10 is vertical incidence transverse wave displacement component (u in side slope seismic response numerical simulation of the present inventionS,vS,wS=
0) with displacement vector mould (SS) relation schematic diagram.
Specific embodiment
The specific embodiment of the present invention will be described in detail below, but it should explanation, these embodiments
Not limitation of the present invention, those of ordinary skill in the art are according to these embodiment institute work energy, method or structures
On equivalent transformation or replacement, belong within protection scope of the present invention.
As shown in Figures 1 to 10：Fig. 1 is either direction oblique incidence plane body in side slope seismic response numerical simulation of the present invention
The flow chart of wave excitation method；Fig. 2 is the favour of vertical incidence plane body wave excitation in side slope seismic response numerical simulation of the present invention
More this principle schematic；Fig. 3 is that the Huygens of oblique incidence plane body wave excitation in side slope seismic response numerical simulation of the present invention is former
Reason schematic diagram；Fig. 4 is either direction oblique incidence plane body wave excitation side slope bottom in side slope seismic response numerical simulation of the present invention
Node starts Time-Series analyses schematic diagram；Fig. 5 is either direction oblique incidence plane body in side slope seismic response numerical simulation of the present invention
Wave ray and undulatory displacements vector and spatial relationship schematic diagram of the side slope bottom level exciting border in the plane of incidence；Fig. 6 is this
In invention side slope seismic response numerical simulation, either direction oblique incidence plane body wave ray and displacement vector are in side slope bottom level
Projection relation schematic diagram in exciting face；Fig. 7 is either direction oblique incidence plane in side slope seismic response numerical simulation of the present invention
The P ripple displacement component (u of bulk wave excitingP,vP,wP) and displacement vector mould (SP) relation schematic diagram；Fig. 8 is side slope of the present invention ground
Ring the SV ripple displacement component (u for answering either direction oblique incidence plane body wave excitation in numerical simulationV,vV,wV) and displacement vector mould
(SV) relation schematic diagram；Fig. 9 is either direction oblique incidence plane body wave excitation in side slope seismic response numerical simulation of the present invention
SH ripple displacement component (uH,vH,wH) and displacement vector mould (SH) relation schematic diagram；Figure 10 is side slope seismic response of the present invention
Vertical incidence transverse wave displacement component (u in numerical simulationS,vS,wS=0) with displacement vector mould (SS) relation schematic diagram.
Present embodiments provide for either direction plane of incidence bulk wave excitation method in a kind of side slope earthquake numerical simulation, tool
Body step is as follows：
Step S1, side slope are modeled
Side slope modeling can utilize multi-modeling software and instrument, can build up solid threedimensional model or the letter of complexity
Single two dimensional model, but should be noted in modeling process：The side slope bottom exciting border of numerical model is set to horizontal plane,
Referred to as " exciting face ", by certain requirement, exciting border carries out subdivision by certain mesh-density, and (side slope model bottom is by hexahedro
Volume mesh subdivision, the size of size of mesh opening meet：The hexahedron length of side less than incident seismic ripple highest frequency corresponding wavelength 1/10
To 1/8), subdivision grid lines intersection point constitutes the node on exciting border, so as to will spatially continuous earthquake wave excitation effect discrete
Exciting effect for each node on exciting border.
Step S2, either direction incident seismic plane body wave excitation each node on the side slope model bottom exciting border are opened
Dynamic sequential is calculated.
The theoretical basiss of this step are the Huygen's principle that ripple is propagated.As shown in Figure 2 and Figure 3, Huygen's principle can be stated
For：Any time t in medium0Each point in wavefront surface, can all regard the wave source that can launch wavelet as, and these Source of Wavelets are in medium
Transmitting spherical wavelet, spherical wavelet is pushed ahead by the velocity of wave c of medium near Source of Wavelets, through the incremental time Δ of a very little
Subsequent time t after t0+ Δ t, it is Δ r=c Δ t that spherical wavelet wavefront leaves the distance of Source of Wavelets, now, in the wavefront side of entering
The enveloping surface of all wavelet wavefront is exactly moment t upwards0The corresponding new wavefront surface of+Δ t.
Fig. 2 can illustrate that seismic wave incides the situation in side slope model vertically upward.In t0Moment seismic wave vertically enters
When penetrating, all nodes of side slope model bottom vibrate simultaneously, and these nodes are considered as wavelet wave source, and seismic wave is in side slope mould
Upwardly propagate in type, in t0+ Δ t, wavefront pass to model meshes node layer second from the bottom, cause the second node layer of model
Vibrate simultaneously.So seismic wave is just spread in side slope vertically upward.
Equally, inclined seismic wave can be solved the problems, such as using Huygen's principle.As shown in figure 3, side slope first arrival is
t0, on the exciting border of side slope bottom, each node is considered as wavelet wave source, in numerical simulation software, can arrange side
On the model bottom exciting border of slope, by sequential starting of oscillation successively is started, the Induction Peried of two adjacent nodes is at intervals of Δ t ' for each node
(relevant with adjacent node spacing), due to side slope model bottom each node starting of oscillation moment different, through time Δ t after, new produce
Wavefront can in a certain angle with side slope bottom exciting face (when exciting face upper and lower medium velocity of wave is equal, this angle and bulk wave be incident
Angle is equal), it is achieved thereby that the oblique incidence exciting of seismic body wave.
As shown in figure 4, side slope bottom exciting surface grids subdivision line is parallel with coordinate axess x, y.One group of grid parallel with x-axis
Subdivision line sequence number is designated as i, i=0,1 ..., n-1, altogether n bars；One group of mesh generation line sequence number parallel with y-axis is designated as j, j=
0,1 ..., m-1, altogether m bars.Two groups of subdivision grid lines are crossed to form a series of node pij, interstitial content amounts to m × n, from ground
The incident earthquake plane bulk wave of lower either direction causes these nodes to start by certain sequential successively.As shown in figure 4, by side slope bottom
The node being disturbed on portion exciting border at first is set to x/y plane zero.Convenient for expression, the node is referred to as side also
The first moving point in slope, and remember that its starting of oscillation moment is t0；Arbitrary mess node p in note side slope bottom exciting borderijThe starting of oscillation moment be tij.
As shown in Figure 4, when incident orientation angle is α, wavefront surface reaches node p by first moving point o along incident directionijWhen, wave propagation away from
From as t0Moment and tijThe distance between two wavefront of moment lij：
lij=| oq | sin θs=(i Δ x cos α+j Δ y sin α) sin θ (a)
Therefore, arbitrary mess node pijStarting of oscillation moment tijFor：
In formula：I=0,1 ..., n-1；J=0,1 ..., m-1；t0For side slope, just moving point fluctuates then；C is side slope exciting side
The elastic wave velocity of the following medium in boundary, compressional wave take cP, shear wave takes cS.
As the propagation velocity of wave of bulk wave seismic phase is broadly divided into longitudinal wave velocity cPWith transverse wave speed cSTwo kinds, therefore from kinesiology
Angle considers, for the superposition of exciting boundary node seismic phase, as long as consideration compressional wave and the basic seismic phase of two kinds of shear wave can just expire
Sufficient overlay analysis need.
Consideration compressional wave (P ripples) is incident, and formula (b) can be written as：
In formula, tPijIt is P ripples seismic phase in node pijStartup time；tP0For side slope just moving point P wave disturbance then.
Consideration shear wave (S ripples, including SV and SH) is incident, and formula (b) can be written as：
In formula, tSijIt is S ripples seismic phase in node pijStartup time；tS0For side slope just moving point S wave disturbance then.
As perseverance has cP＞ cS, therefore for same node, perseverance has tPij＜ tSij.Equally, perseverance has tP0＜ tS0.
If focus is to side slope, and just the distance between moving point is R, then tP0And tS0Calculated by formula (c) and formula (d) respectively：
tP0=R/cP0(c)
tS0=R/cS0(d)
By formula (c) and formula (d), can be by elastic wave velocity cP0And cS0It is considered as earthquake source and side slope region medium of earth crust
Average eguivalent velocity of wave.From from the point of view of focus radiation wave field, from the position that macroscopically observes in the wave field of side slope region,
Then further can further investigate because side slope is in the change of the caused side slope Dynamic response to earthquake of wave field spatial location difference.
From formula (c) and formula (d), by side slope, just the compressional wave of moving point, shear wave then can be in the hope of calculating the distance between side slope and focus
R, as shown in formula (e)：
R=Δ tPS0·cΦ(e)
In formula, Δ tPS0=tS0-tP0, it is the arrival time difference of secondary wave and compressional wave arrival side slope；Referred to as
Side slope and the empty wave velocity of focus region medium of earth crust.
Step S3, when different seismic phase plane body wave excitations act on the components of stress produced at each node of side slope model bottom
Journey is calculated.
Step S3 can be specifically divided into following step to realize：
1) displacement solution of wave equation is sought
If any point (x, y, z) place causes the particle displacement as shown in formula (1) to earthquake wave disturbance in media as well
Wherein, u, v, w be respectively displacement component of the undulatory displacements on x, tri- directions of y, z, be space coordinatess (x, y,
Z) function with time t：
U=u (x, y, z, t)；V=v (x, y, z, t)；W=w (x, y, z, t)
If displacement vectorMould be S, i.e.,：
According to elastic wave prorogation theory, the seimic wave propagation in elastic fluid can be retouched with the wave equation shown in formula (2)
State：
In formula, ρ is Media density；μ is modulus of shearing；λ and μ synthesizes Lame constants, Lame constants and dielectric resilient modulus E
Relation with Poisson's ratio v is：
Arbitrary particle in for dielectric space, may certify that, the single-frequency simple harmoinic wave motion displacement shown in formula (3) is fluctuation side
One general solution of journey (2)：
In formula, Aω=AωThe amplitude of (x, y, z) for simple harmoinic wave motion, in certain model at a certain concrete medium point (x, y, z) place
Constant can be approximately in enclosing；I is empty unit, For fluctuate phase function, wherein
ω is ω=2 π f for the relation fluctuated between circular frequency, with frequency f；For the position vector of any point in medium (x, y, z), For wave vector, the direction of wave vector is identical with direction of wave travel, the mould of wave vectorClaim
For wave number, wherein c is fluctuation spread speed in media as well, is divided into longitudinal wave velocity cPWith transverse wave speed cS.Longitudinal wave velocity cP, horizontal
Ripple velocity of wave cSWith the relation between Media density ρ and Lame constants λ, μ it is：
According to Fourier principle, for arbitrarily non-simple harmoinic wave motion displacement S=S (x, y, z, t), can be by such as formula (3) Suo Shi
Different frequency simple harmoinic wave motion displacement superposed form.I.e.：
Because the direction of propagation of non-simple harmoinic wave motion identical with the direction of propagation of its simple harmonic quantity component fluctuation, therefore non-simple harmonic wave
Wave vectorWave vector with its each simple harmonic quantity component fluctuationSensing is identical, but non-simple harmoinic wave motion wave numberEach with which
The wave number of simple harmonic quantity component fluctuationNot necessarily equal.To not differentiate between in analysis belowWithBoth it is written as
Equally may certify that, the non-simple harmoinic wave motion displacement of the mixing shown in formula (4) is also a solution of wave equation (2).
2) the undulatory displacements weight expression of each bulk wave seismic phase is derived
In side slope earthquake response numerical simulation, the exciting border of side slope numerical model is generally arranged at side slope bottom, interface
For horizontal plane, exciting face is can be described as.The setting of side slope model local coordinate system (x, y, z)：Upwards, x, y-axis are located at and swash z-axis vertical
Shake in plane, x-axis is pointed to outside slope along side slope gradient maximum direction, and zero is placed in certain angle point in exciting face depending on concrete condition
On；The mutually orthogonal formation right hand rectangular coordinate system of three axle of x, y, z.
If side slope is subject to the earthquake plane body wave excitation incident from underground either direction, bulk wave seismic phase include P ripples, SV ripples and
Three kinds of SH ripples, the incident orientation of different seismic phases, first motion displacement vector relative to side slope model local coordinate system spatial relationship such as
Shown in Fig. 5, Fig. 6.
Fig. 5 show and observes the bulk wave oblique situation for being incident upon side slope bottom from bottom to top in the plane of incidence.Coordinate axess z with swash
Plane of shaking is perpendicularly oriented to, and coordinate axess r is exactly in exciting face, overlaps with the intersection of the plane of incidence and exciting face, and r axles are pointed to and entered
Projecting direction of the ejected wave directions of rays in exciting face is consistent.Angle theta between incident wave ray and exciting face normal is referred to as
Seismic wave angle of incidence.
As shown in fig. 6, in exciting face, projecting direction of the r direction of principal axis with wave ray in exciting face is consistent, radiation levels
Angle α between projecting direction and x-axis direction is referred to as layered halfspace azimuth.Throwings of any point r in x-axis and y-axis on r axles
Shadow is respectively x and y, on value, there is following relation between r and x, y：
The wave vector consistent with direction of wave travelK be can be analyzed in the side slope local coordinate system shown in Fig. 5, Fig. 6x,
ky,kzThree components, i.e.,Wherein：
The phase function of simple harmoinic wave motion displacement shown in formula (3)Specifically can expand into：
Shown in Fig. 5, Fig. 6, several bulk wave seismic phase vibration displacement vectors and wave ray indicate seismic wave direction of displacement and ripple
The geometrical relationship of the direction of propagation.
The direction that the particle vibration displacement that P ripples cause is propagated along ripple, propagates front medium and produces compression or stretch to ripple
Effect.P ripple displacement first motions can be divided into identical with direction of wave travel and contrary two kinds：With the first trend of direction of wave travel identical P ripple
Before push away, produce pressure to front medium, referred to as compressional wave is designated as P+；The P ripple first motions contrary with direction of wave travel are pulled back, right
Front medium generation pulling force, referred to as tensile wave, are designated as P-.
The particle vibration displacement that SV ripples cause in the plane of incidence, perpendicular to direction of wave travel, produces shearing to front medium and makees
With.Along direction of wave travel eyes front in the plane of incidence, SV ripple displacement first motions can be divided into two kinds of right and left：First motion SV to the right
Ripple may be simply referred to as the right side and cut SV ripples, be designated as SV+；First motion SV ripples to the left may be simply referred to as a left side and cut SV ripples, be designated as SV-.
Perpendicular to the plane of incidence and direction of wave travel, it is level that particle vibration direction is permanent for the particle vibration displacement that SH ripples cause,
Shear action is equally produced to front medium.Along direction of wave travel eyes front, SH ripple displacement first motions can be divided into level to the right and water
Flat two kinds to the left：First motion level SH ripples to the right may be simply referred to as the right side and cut SH ripples, be designated as SH+；First motion level SH ripples to the left are referred to as
SH ripples are cut for a left side, SH is designated as-.
Relation and wave ray according to different seismic phase undulatory displacements directions and direction of wave travel is sat with side slope model local
The relation of mark system, by the method for vector projection, can derive different seismic phase displacement components u, v, w and undulatory displacements Vector Mode S
Between relation.
P ripple displacement components
Fig. 7 show P ripple displacement components uP、vP、wPWith compressional wave P+Displacement vector mould SP +And tensile wave P-Displacement vector mould
SP -Between geometrical relationship schematic diagram.
If compressional wave P+With tensile wave P-Displacement vector equal in magnitude, in opposite direction, then P+Displacement vector mould SP +And P-
Displacement vector mould SP -Between relation be：
SP +=-SP -=SP
Accordingly, compressional wave P (compressional wave P+With tensile wave P-) displacement component uP、vP、wPWith displacement vector mould SPRelation
Not as shown in formula (7) and formula (8).
Compressional wave P+Displacement component：
Tensile wave P-Displacement component：
According to formula (3), formula (4), S in formula (7), formula (8)PThe P shown in Fig. 7 not only can be represented+And P-Seismic phase fluctuation
First motion Vector Mode, while can also represent the mould that first motion is respectively P ripple displacement vector time-histories forward or backward, is divided into single-frequency simple harmonic quantity
Two kinds of fluctuation and arbitrarily non-simple harmoinic wave motion, respectively as shown in formula (9) and formula (10)：
SP=SP(x,y,z,t) (10)
In formula, AP=AP(x, y, z) is the amplitude of simple harmoinic wave motion, in point (x, y, z) nearby certain limit can be considered normal
Number；For the wave vector of P ripples, wave numberWherein cPFor longitudinal wave velocity.
SV ripple displacement components
Fig. 8 show SV ripple displacement components uV、vV、wVSV ripple SV are cut with the right side+Displacement vector mould SV +And SV ripple SV are cut on a left side-
Displacement vector mould SV -Between geometrical relationship schematic diagram.
If SV ripple SV are cut on the right side+SV ripple SV are cut with a left side-Displacement vector equal in magnitude, in opposite direction, then SV+The displacement arrow of ripple
Amount mould SV +And SV-The displacement vector mould S of rippleV -Between relation be：
SV +=-SV -=SV
Accordingly, SV ripples (SV+And SV-) displacement component uV、vV、wVWith displacement vector mould SVRelation respectively such as formula (11) and
Shown in formula (12).
Cut ripple SV in the right side+Displacement component：
Cut ripple SV in a left side-The displacement component of ripple：
Similar with P ripples, in formula (11), formula (12) displacement vector mould SVThe first dynamic vector of SV ripples displacement not only can be represented
Mould, while can also representing, the right side is cut or the mould of SV ripple displacement vector time-histories is cut on a left side, is divided into single-frequency simple harmonic wave dynamic formula (13) and arbitrarily non-
Simple harmonic wave dynamic formula (14)：
SV=SV(x,y,z,t) (14)
In formula, AV=AV(x, y, z) is the amplitude of simple harmoinic wave motion, in point (x, y, z) nearby certain limit can be considered normal
Number；For the wave vector of shear wave (SV ripples), wave numberWherein cSFor transverse wave speed.
SH ripple displacement components
Fig. 9 show SH ripple displacement components uH、vH(wH0) ≡ cuts SH ripple SH with the right side+Displacement vector mould SH +And SH ripples are cut on a left side
SH-Displacement vector mould SH -Between geometrical relationship schematic diagram in the horizontal plane.
If SH ripple SH are cut on the right side+SH ripple SH are cut with a left side-Displacement vector equal in magnitude, in opposite direction, then SH+The displacement arrow of ripple
Amount mould SH +And SH-The displacement vector mould S of rippleH -Between relation be：
SH +=-SH -=SH
Accordingly, SH ripples (SH+And SH-) displacement component uH、vH(wH≡ 0) with displacement vector mould SHRelation respectively such as formula
(15) and shown in formula (16).
Cut ripple SH in the right side+Displacement component：
Cut ripple SH in a left side-Displacement component：
Equally, the displacement vector mould S in formula (15), formula (16)HThe mould of the first dynamic vector of SH ripples displacement not only can be represented, with
Shi Yeke represents the right side and cuts and the left mould for cutting SH ripple displacement vector time-histories, is divided into single-frequency simple harmonic wave dynamic formula (17) and arbitrarily non-simple harmonic wave
Dynamic formula (18)：
SH=SH(x,y,z,t) (18)
In formula, AH=AH(x, y, z) is the amplitude of simple harmoinic wave motion, in point (x, y, z) nearby certain limit can be considered normal
Number；For the wave vector of shear wave (SH ripples), wave numberWherein csFor transverse wave speed.
3) fluctuating stress of bulk wave seismic phase is solved
In side slope local coordinate system, exciting borderline fluctuating stress component in side slope bottom has three：σz、τzxAnd τzy.
According to geometric equation (strain-displacement relation) and physical equation (strain-stress relation) in Elasticity, can be fluctuated
Components of stress σz、τzx、τzyWith the relation between undulatory displacements component u, v, w, as shown in formula (19)：
The displacement component of each bulk wave seismic phase shown in formula (7)～formula (18) is substituted into above formula, you can obtain different bulk waves
Relational expression between the fluctuating stress component and undulatory displacements component of seismic phase.
From formula (19), fluctuating stress component σz、τzx、τzyThe displacement component partial derivative that is related to of calculating have These partial derivatives are sought to the displacement component of each bulk wave seismic phase, substitute into formula (19),
Expression formula each bulk wave seismic phase fluctuating stress component and undulatory displacements component between can determine that.
By formula (7)～formula (18) as can be seen that each bulk wave seismic phase displacement component is all represented by seismic phase motion vector and exists
The projection in tri- directions of x, y, z, after all, real command displacement component variation be displacement vector mould change.And it is different
The mould of bulk wave seismic phase displacement vector time-histories can be summarized as single-frequency simple harmoinic wave motion and arbitrarily non-two kinds of forms of simple harmoinic wave motion, and can unite
One is expressed as：
S=S (x, y, z, t) (21)
To P ripples, S=SP, A=AP,To SV ripples, S=SV, A=AV,To SH ripples, S=SH, A=AH,
Partial derivative to undulatory displacements Vector Mode can be all attributed to several partial derivatives of undulatory displacements component
First simple harmoinic wave motion is analyzed.
Formula (20) to space variable x, y, z derivation, has respectively：
Wushu (5) substitutes into formula (22), and considersWithHave：
In addition, the mould S of undulatory displacements (particle displacement) vector is velocity of wave motion (Particle Vibration Velocity) to the derivative of time
Mould V, i.e.,
Formula (20) is obtained to the derivation of time t：
In formula, V=V (x, y, z, t) is the Particle Vibration Velocity (velocity of wave motion) that seismic wave causes at point (x, y, z) place
The mould of vector time-histories.To P ripples, V=VP=VP(x, y, z, t), S=SP, A=AP,To SV ripples, V=VV=VV(x,y,z,
T), S=SV, A=AV,To SH ripples, V=VH=VH(x, y, z, t), S=SH, A=AH,
Wushu (23) substitutes into formula (22) and obtains：
In formula, speed of the c for seimic wave propagation, compressional wave (P ripples) c=cP, shear wave (SV, SH ripple) c=cS；V exists for seismic wave
The mould (referred to as vibration velocity time-histories) of the Particle Vibration Velocity vector time-histories that point (x, y, z) causes.Press formula (23), the mode of vibration of V
For simple harmonic oscillation, following form can be written as：
In formula, VmAmplitudes (vibration velocity maximum) of the=- ω A for particle vibration velocity, circular frequency of the wherein ω for particle vibration,
Displacement amplitudes (displacement maximum) of the A for particle vibration.For P ripples, Vm=VmP=-ω AP；For SV ripples, Vm=VmV=-
ω·AV；For SH ripples, Vm=VmH=-ω AH.
It is similar anharmonic vibration formula (4) can be extended to the simple harmonic oscillation formula (3) of undulatory displacements, according to Fourier principle,
Shown in formula (25), the simple harmonic oscillation process of velocity of wave motion can equally be extended to anharmonic vibration process, as shown in formula (26)：
V=V (x, y, z, t)=Vm·f(x,y,z,t) (26)
In formula, VmFor the maximum vibration velocity value of the non-simple harmonic quantity particle vibration velocity time-histories in point (x, y, z) place, or referred to as peak value vibration velocity；f
(x, y, z, t)=V/VmFor normalization (dimensionless) the particle vibration velocity time-histories that point (x, y, z) place maximum is 1.
P wave stress components
Compressional wave P+The components of stress
To P shown in formula (7)+The displacement component of ripple seeks partial derivative Again
The partial derivative of displacement Vector Mode is substituted into shown in formula (24)：
Above partial derivative is substituted into formula (19) and obtains compressional wave P+The components of stress, as shown in formula (27)：
Tensile wave P-The components of stress
To P shown in formula (8)-The displacement component of ripple seeks partial derivative Again
The partial derivative of displacement mould is substituted into shown in formula (24)：
Above partial derivative is substituted into formula (19) and obtains tensile wave P-The components of stress, as shown in formula (28)：
SV wave stress components
Cut ripple SV in the right side+The components of stress
To SV shown in formula (11)+The displacement component of ripple seeks partial derivative Again
The partial derivative of displacement Vector Mode is substituted into shown in formula (24)：
Above partial derivative substitution formula (19) is obtained the right side and cuts ripple SV+The components of stress, as shown in formula (29)：
Cut ripple SV in a left side-The components of stress
To SV shown in formula (12)-The displacement component of ripple seeks partial derivative Again
The partial derivative of displacement Vector Mode is substituted into shown in formula (24)：
Above partial derivative substitution formula (19) is obtained a left side and cuts ripple SV-The components of stress, as shown in formula (30)：
SH wave stress components
Cut ripple SH in the right side+The components of stress
To SH shown in formula (15)+The displacement component of ripple seeks partial derivative Again
The partial derivative of displacement Vector Mode is substituted into shown in wushu (24)：
Above partial derivative substitution formula (19) is obtained the right side and cuts ripple SH+The components of stress, as shown in formula (31)：
Cut ripple SH in a left side-The components of stress
To SH shown in formula (16)-The displacement component of ripple seeks partial derivative Again
The partial derivative of displacement Vector Mode is substituted into shown in formula (24)：
Above partial derivative substitution formula (19) is obtained a left side and cuts ripple SH-The components of stress, as shown in formula (32)：
Particularly, when seismic wave vertical incidence, incidence angle θ is that all nodes are same on 0 °, i.e. side slope bottom exciting border
Shi Qizhen.According to formula (27), formula (28), now P ripples only have z to the components of stress be not 0, i.e.,：
When S ripple vertical incidence, from the formula of above-mentioned expression S wave stress components, parameter alpha can not be vertical as P ripples
Incident stress formula is equally directly eliminated.And now, according to the definition of aforementioned azimuthal α, which can not express incidence wave
Ray and the true bearing relation of side slope.Therefore, components of stress formula during S ripples vertical incidence needs vertically to be entered according to S ripples
Polarization shift situation when penetrating is derived again.
If the displacement that certain point (x, y, z) causes in media as well of the polarization of shear wave isIts mould is SS.As shown in Figure 10, if
The angle for being rotated counterclockwise to shear wave vibration first motion direction by x-axis forward direction is β (360 ° of 0 °≤β ＜), then have：
From above formula and formula (11), the contrast of formula (12), during shear wave vertical incidence, its displacement component in form with horizontal stroke
During ripple oblique incidence, the displacement component formula of SV ripples is similar to.Using identical components of stress time-histories function derivation, the shear wave that is easy to get hangs down
Under straight condition of incidence, its components of stress is as follows：
Step S4, the superposition time-histories meter of each node difference bulk wave seismic phase fluctuating stress component in side slope model bottom exciting border
Calculate.
Consideration formula (b ') and formula (node p shown in b ")ijP ripples and S ripple Startup time tPijAnd tSij, formula (27)～formula (32)
Shown P (P+, P-)、SV(SV+, SV-) and SH (SH+, SH-) fluctuating stress time-histories expression formula can be written as formula (27 ')～formula
(32′).
1. P wave stresses component time-histories (t >=tPij)
Compressional wave P+Components of stress time-histories.
Tensile wave P-Components of stress time-histories.
2. SV wave stresses component time-histories (t >=tSij)
Cut ripple SV in the right side+Components of stress time-histories
Cut ripple SV in a left side-Components of stress time-histories
3. SH wave stresses component time-histories (t >=tSij)
Cut ripple SH in the right side+Components of stress time-histories
Cut ripple SH in a left side-Components of stress time-histories
The relation in undulatory displacements direction and wave ray is pressed, the bulk wave seismic phase for reaching exciting border has tri- kinds of P, SV and SH, enters
The first motion direction of displacement of one step consideration fluctuation, can be further divided into P again+, P-；SV+, SV-；SH+, SH-Six classes.From the thing that ripple is propagated
Reason is actual to be considered, reaching the fluctuation seismic phase combination that may occur at any node of exciting border includes two kinds of seismic phase combinations and three kinds
Seismic phase is combined.
1. two kinds of seismic phases combine (12 kinds)
P++SV+, P++SV-；P-+SV+, P-+SV-；
P++SH+, P++SH-；P-+SH+, P-+SH-；
SV++SH+, SV++SH-；SV-+SH+, SV-+SH-.
There are 12 kinds of combinations.
2. three kinds of seismic phases combine (8 kinds)
P++SV++SH+, P++SV++SH-；P++SV-+SH+, P++SV-+SH-；
P-+SV++SH+, P-+SV++SH-；P-+SV-+SH+, P-+SV-+SH-.
Consider above-mentioned possible seismic phase combination, select corresponding components of stress time-histories formula, take the algebraical sum of respective components,
Exciting face node p is obtainedijThe superposition time-histories expression formula of upper different bulk wave seismic phase fluctuating stress components.For example, two kinds of seismic phase
Combination P++SV+In node pijOn input fluctuating stress component σz P + +V +(pij)、τzx P + +V +(pij) and τzy P + +V +(pij) it is formula
The algebraical sum of the corresponding components of stress time-histories of (27 ') and formula (29 ')：
To σzP +(t-tPij), t >=tPij；To σzV +(t-tSij), t >=tSij.I.e.：
To VP(t-tPij), t >=tPij；To VV(t-tSij), t >=tSij.
Step S5, each node bulk wave seismic phase fluctuating stress component superposition time-histories input in side slope model bottom exciting border
By taking single-frequency simple harmoinic wave motion input as an example, can be by above-mentioned formula (27)～formula (32) Formula Input Technology.
Simple harmonic quantity P ripples, S ripple stack combinations numerical simulations are also adopted by saving the power input scheme that mentions.Determine P ripples, S first
The frequency of ripple, amplitude, then with the factor such as when holding.According to the action time of the P ripples and S ripples for calculating, each time period is input into
Stress time-histories.
With FLAC3DAs a example by software, simple harmonic quantity P ripples, the command stream example of SV ripples superposition incidence is now included：
Wherein, dingyi1x.txt, dingyi2y.txt, dingyi3z.txt, definition is P ripples and S ripples from certain side
Three-component wave function FISH linguistic expression to input.call shijia1.txt、call shijia2.txt、call
Shijia3.txt definition is P ripples, S ripples from the three-component stress time-histories expression formula of certain direction input.
Step S6, side slope model Dynamic response to earthquake analog result are extracted
From side slope model bottom exciting border bulk wave seismic phase fluctuating stress component superposition time-histories loading (side slope first arrival
t0) rise, numerical simulation system at once in start recording side slope model each node Dynamic response to earthquake process, and according to research
The Dynamic response to earthquake for extracting side slope Dynamic response to earthquake cloud atlas and the arbitrary monitoring point of side slope model not in the same time is needed to add
Speed, speed and displacement time-histories.
When the present invention is started by earthquake motive force load action by each node on calculating side slope model bottom exciting border
Sequence, the startup sequential that the vertical incidence of seismic wave and oblique incidence problem are converted into each node on the exciting border of side slope bottom is asked
Topic；The range site body equation of motion, geometric equation and physical equation (Hooke's law), derive the three-dimensional fluctuation represented with displacement
Equation；According to the propagating characteristic and polarization characteristic of different seismic phase seismic waves, the displacement vector of each seismic phase seismic wave is drawn, by displacement
Vector brings geometric equation and Hooke's law into, calculates each seismic phase earthquake wave excitation each node on the exciting border of side slope bottom
The components of stress time-histories expression formula that place produces, it is established that side slope of a set of side slope by either direction incident seismic plane body wave excitation
Exciting scheme, can reveal that the multiformity of certain edges thereof slope eaerthquake damage, and then estimates the probability of the slope failure of ad hoc fashion.
A series of detailed description in detail of those listed above is only for illustrating for feasibility embodiment of the invention,
They are simultaneously not used to limit the scope of the invention, all equivalent implementations that is made without departing from skill spirit of the present invention or change
More should be included within the scope of the present invention.
It is obvious to a person skilled in the art that the invention is not restricted to the details of above-mentioned one exemplary embodiment, Er Qie
In the case of spirit or essential attributes without departing substantially from the present invention, the present invention can be realized in other specific forms.Therefore, no matter
From the point of view of which point, embodiment all should be regarded as exemplary, and be nonrestrictive, the scope of the present invention is by appended power
Profit is required rather than described above is limited, it is intended that all in the implication and scope of the equivalency of claim by falling
Change is included in the present invention.
Claims (7)
1. either direction plane of incidence bulk wave excitation method in a kind of side slope seismic response numerical simulation, it is characterised in that include
Following steps：
(1) side slope modeling；
(2) according to each node difference bulk wave seismic phase fluctuating stress time-histories on Huygen's principle analysis of slope model bottom exciting border
Startup sequential, determine the startup time difference of each node, calculate the Startup time of each node；
(3) displacement vector of each seismic phase bulk wave, position of fluctuating, according to the propagating characteristic and polarization characteristic of different seismic phase bulk waves, are obtained
Move vector and bring geometric equation, physical equation into, show that each seismic phase seismic wave incentive action is each on side slope model bottom exciting border
The each components of stress time-histories expression formula produced at node；
(4) practical situation that consideration ripple is propagated, by the stress of different seismic phase fluctuations on each for side slope model bottom exciting border node
Time-histories component is chronologically superimposed, and obtains the supercoated stress time-histories of each components of stress；
(5) node is pressed in numerical simulation software starts sequential to each stress of each node input on side slope model bottom exciting border
The supercoated stress time-histories of component；
(6) the Dynamic response to earthquake result of side slope model is extracted, the earthquake of side slope Dynamic response to earthquake cloud atlas and monitoring point is obtained
Dynamic response acceleration, speed and displacement time-histories.
2. either direction plane of incidence bulk wave excitation method in side slope seismic response numerical simulation according to claim 1,
Characterized in that, step (1) specifically includes：Side slope model bottom exciting border is set to horizontal plane, by default net
Lattice density subdivision exciting border, subdivision grid lines intersection point constitute the node on exciting border, so that spatially continuous seismic wave swashs
Bestir oneself with the discrete exciting effect for each node on exciting border.
3. either direction plane of incidence bulk wave excitation method in side slope seismic response numerical simulation according to claim 2,
Characterized in that, step (2) specifically include：When seismic wave vertical incidence, own on side slope model bottom exciting border
Node starts simultaneously, and this Startup time is called side slope first arrival, is set to t0；When inclined seismic wave, by side slope mould
It is subject to the node of earthquake wave disturbance to be referred to as side slope just moving point on the exciting border of type bottom at first, the Startup time of the point is referred to as side slope
First arrival, is likewise provided as t0, arbitrary grid node p on exciting borderijThe starting of oscillation moment be designated as tij, tried to achieve by following formula：
In formula：tijFor arbitrary grid node p on side slope model bottom exciting borderijStartup time, i=0,1 ..., n-1 are
The sequence number of the local coordinate system X-direction that the node is set up in exciting plane, i=0 are the sequence number of just moving point, and X-axis is positive to be pointed to
The direction that node ID increases, origin are overlapped with first moving point；J=0,1 ..., m-1 are that the node is set up in exciting plane
The sequence number of local coordinate system Y-direction, j=0 is the sequence number of just moving point, and Y-axis is positive to point to the direction that node ID increases, origin with
Just moving point overlaps；t0For side slope first arrival；lijSide slope model bottom is reached by first moving point for seismic wave wavefront incident direction
Any node p on exciting borderijThe distance that is passed through, when seismic wave vertical incidence, lij=0, now, by local coordinate system
Origin is arranged on an angle point of exciting plane, the first quartile that side slope bottom exciting plane is placed in the local coordinate system；c
For the elastic wave velocity of the following medium in side slope exciting border, compressional wave takes cP, shear wave takes cS；No matter seismic wave vertical incidence or oblique
Penetrate, side slope first arrival t0It is functionally identical to the moment that seismic wave reaches side slope.
4. either direction incidence bulk wave excitation method in side slope seismic response numerical simulation according to claim 3, which is special
Levy and be, in step (3), each bulk wave seismic phase includes：Compressional wave, shear wave；According to shear wave vibration vector and bulk wave incidence relation of plane,
Shear wave vibration vector is further broken into the oscillating component SV ripples in the plane of incidence and the oscillating component SH ripples perpendicular to the plane of incidence；
According to P ripples, SV ripples, SH ripple seismic phase undulatory displacements first motion direction, by P wavelength-divisions be first motion compressional wave P forward+With first motion backward
Tensile wave P-；Along direction of wave travel eyes front, observe SV ripples in the plane of incidence, observe SH ripples perpendicular to the plane of incidence, by SV and
SH wavelength-divisions cut ripple SV for the first motion right side to the right+、SH+Ripple SV is cut with a first motion left side to the left-、SH-.
5. either direction incidence bulk wave excitation method in side slope seismic response numerical simulation according to claim 4, which is special
Levy and be, during step (4) is described, the stress time-histories of each node difference bulk wave seismic phase fluctuation is pressed on side slope model bottom exciting border
Component superposition includes the superposition and the superposition of three kinds of seismic phases of two kinds of seismic phases, and wherein, the superposition of two kinds of seismic phases includes：P++SV+、P++
SV-、P-+SV+、P-+SV-、P++SH+、P++SH-、P-+SH+、P-+SH-、SV++SH+、SV++SH-、SV-+SH+、SV-+SH-,, three kinds
The superposition of seismic phase includes：P++SV++SH+、P++SV++SH-、P++SV-+SH+、P++SV-+SH-、P-+SV++SH+、P-+SV++SH-、P-
+SV-+SH+、P-+SV-+SH-；When different bulk wave seismic phase components of stress time-histories superpositions are carried out, it is first determined each shake on each node
The due in of phase and persistent period, then the startup sequential by each seismic phase on node complete side slope model bottom exciting border
At each node upper, different bulk wave seismic phase fluctuating stress component time-histories superpositions, obtain bulk wave seismic phase fluctuating stress component at each node
Superposition time-histories.
6. either direction plane of incidence bulk wave excitation method in side slope seismic response numerical simulation according to claim 5,
Characterized in that, in step (5), time-histories will be superimposed by startup sequential through the bulk wave seismic phase fluctuating stress component that step (4) obtain
It is loaded on each node.
7. either direction incidence bulk wave excitation method in side slope seismic response numerical simulation according to claim 6, which is special
Levy and be, in step (6), from side slope first arrival t0Rise, by each section in numerical simulation system start recording side slope model
The Dynamic response to earthquake process of point, and extract side slope Dynamic response to earthquake cloud atlas not in the same time and the arbitrary monitoring of side slope model
The Dynamic response to earthquake acceleration of point, speed and displacement time-histories.
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| CN108254782A (en) * | 2018-02-09 | 2018-07-06 | 中国地质大学（北京） | A kind of acquisition methods and system of side slope eaerthquake damage failure probability |
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| CN109711110A (en) * | 2019-02-26 | 2019-05-03 | 中国地质大学（北京） | Either direction plane of incidence wave excitation side slope seismic response analogy method |
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