CN107894311B - The model test method of earth and rockfill dam eaerthquake damage - Google Patents

The model test method of earth and rockfill dam eaerthquake damage Download PDF

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CN107894311B
CN107894311B CN201711081214.6A CN201711081214A CN107894311B CN 107894311 B CN107894311 B CN 107894311B CN 201711081214 A CN201711081214 A CN 201711081214A CN 107894311 B CN107894311 B CN 107894311B
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dam
model
earth
acceleration
test
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CN107894311A (en
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刘小生
赵剑明
刘启旺
杨玉生
杨正权
陈宁
李红军
梁文杰
朱凯斌
王龙
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China Institute of Water Resources and Hydropower Research
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China Institute of Water Resources and Hydropower Research
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01MTESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M7/00Vibration-testing of structures; Shock-testing of structures
    • G01M7/02Vibration-testing by means of a shake table

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Abstract

The present invention relates to earth structure dynamic model test technical fields, disclose a kind of model test method of earth and rockfill dam eaerthquake damage.The present invention includes: to carry out model similar Design according to earth and rockfill dam model test likelihood requirement;Make test model;Model dam is subjected to white noise microseism test, determines the natural frequency of vibration on model dam;Then one group of time similar scale is selected, the design rules in place are compressed, obtains the seismic wave of identical amplitude, different spectral characteristic under different time similar scale;Then vibration test is carried out, the time similar scale of seismic wave in earthquake failure test is selected;Again under the conditions of different acceleration amplitudes, the eaerthquake damage vibration test on model dam is carried out, arrives the earth seismic wave acceleration amplitude that increases from childhood, tests dam acceleration responsive and dynamic respond, until dam earthquake destroys.The present invention is that high the collapsing property of earth and rockfill dam structural earthquake that cannot achieve originally destroys Study on Problems, provides a kind of feasible model test method of science.

Description

The model test method of earth and rockfill dam eaerthquake damage
Technical field
The present invention relates to earth structure dynamic model test technical fields, more particularly to a kind of earth and rockfill dam eaerthquake damage Model test method.
Background technique
High earth and rockfill dam is the main body dam type in hydroelectric development since it is to the adaptable of landform.Western China collection The hydroelectric resources for having suffered 80% or more the whole nation in the big Hydropower Base in the 13 of national planning, has 7 big Hydropower Bases to be located at western ground Area, a collection of 200m grades high earth and rockfill dam even 300m grades of superelevation earth and rockfill dams are being built or will put into operation.
But since west area seismic activity is frequent, intensity is big, earthquake intensity is high, to the safety effects pole of high earth and rockfill dam Greatly, earthquake load often becomes the controlling operating condition for building dam feasibility, these are located at the high earth and rockfill dam of highly seismic region, once because of ground Dam-break accident occurs for shake, and consequence and secondary disaster will be catastrophic.
Therefore, it is broken to reinforce high earth and rockfill dam eaerthquake damage mechanism study, high earth and rockfill dam earthquake resistant construction study on the efficiency and earthquake Bad model study is very necessary.Earth and rockfill dam shaking table model can be under certain control condition, with studying earth and rockfill dam The basic laws such as the influence for answering character, failure mechanism and each major parameter to dam body Dynamic response to earthquake are rung, evaluation structure is whole Body shock resistance, therefore always by the attention of domestic and international earthquake research worker.But it has problems in that, due to high earth and rockfill dam Geometric dimension is huge, and dam body section is more than 1000m, and length reaches thousands of rice, and 1g shake table and ng centrifugation making machine vibration table are limited to set The limitation of standby bearing capacity and the attainable acceleration maximum value of equipment, it is difficult to carry out eaerthquake damage test, soil can not be reproduced Earthquake the collapsing property eaerthquake damage situation of masonry dam, it is difficult to carry out eaerthquake damage model study.
Summary of the invention
The present invention provides a kind of using shaking table model, simulation limit earthquake, the native stone that implementation model destroys completely The model test method of dam eaerthquake damage.
The technical issues of solution is: high earth and rockfill dam geometric dimension is huge, and 1g shake table and ng centrifugation making machine vibration table are due to setting The limitation of standby self-condition, bearing capacity and the attainable acceleration maximum value of institute are limited, can not accurate recreation earth and rockfill dam The modelling mode of the eaerthquake damage situation for the collapsing property that collapses, the current high earth and rockfill dam about 200m or more is also immature, with Actual conditions deviation is larger, it is difficult to carry out eaerthquake damage model study.
In order to solve the above technical problems, the present invention adopts the following technical scheme:
2, the model test method of earth and rockfill dam eaerthquake damage of the present invention, comprising the following steps:
Step 1: requiring to carry out model similar Design according to earth and rockfill dam model test likelihood;
Step 2: requiring production test model according to model similar Design;
Step 3: model dam is carried out white noise microseism test, the natural frequency of vibration on model dam is determined;
Step 4: selecting one according to the seismic wave frequency spectrum characteristic of the model dam natural frequency of vibration and prototype earth and rockfill dam Site Design Group time similar scale, compresses the design rules in place, obtains identical amplitude, difference under different time similar scale The seismic wave of spectral characteristic;
Step 5: carrying out vibration test, really according to seismic wave under the conditions of identical amplitude, different time similar scale Acceleration responsive and dam surface dynamic respond of the cover half type dam under the ground seismic wave function of different time similar scale, in conjunction with adding The time similar scale of seismic wave in speed responsive and dam surface dynamic respond selection earthquake failure test;
Step 6: under the conditions of different acceleration amplitudes, carrying out the earthquake on model dam according to determining time similar scale Vibration test is destroyed, since design earthquake peak acceleration, arrives the earth seismic wave acceleration amplitude that increases from childhood, test dam adds Speed responsive and dynamic respond, until dam earthquake destroys.
The model test method of earth and rockfill dam eaerthquake damage of the present invention, further, model similar Design is specific in step 1 The following steps are included:
B, the geometric similarity constant C of model is determinedl
The geometric similarity constant C of model is determined according to formula (1)l,
In formula: ClFor the geometric similarity constant of model;
HpFor the height on prototype dam, m;
HmFor the height on model dam, m;
B, the density affinity constant C of model is determinedρ
Respectively by triaxial compression test, the prototype dam earth and stone material under certain stress state, different dry density conditions is determined With the effective angle of inner friction of model dam earth and stone material, then determine that model dam fills dry density ρ according to effective angle of inner frictionm, then root Density affinity constant C is determined according to formula (3)ρ
Cρpm (3)
In formula: CρFor density affinity constant;
ρpFor the design dry density of prototype dam earth and stone material, g/cm3
ρmDry density, g/cm are filled for model dam earth and stone material3
C, modulus coefficient affinity constant C is determinedc
It is tested respectively according to dynamic deformation, determines the dynamic shear modulus system of prototype dam earth and stone material and model dam earth and stone material Number, then
Modulus coefficient affinity constant C is determined according to formula (6)c
CC=Cp/Cm (6)
In formula: CcFor modulus coefficient affinity constant;
CpFor dynamic shear modulus coefficient related with prototype dam earth and stone material design dry density;
CmFor dynamic shear modulus coefficient related with model dam earth and stone material design dry density;
D, remaining affinity constant, including stress similitude constant, modulus of shearing affinity constant, strain ratio, speed are determined It is similar often to spend affinity constant, time affinity constant, frequency affinity constant, soil body damping ratio affinity constant, the effective cohesiveness of the soil body Number, soil body effective friction coefficient affinity constant and acceleration affinity constant;
E, the crucial control section on model dam is determined, to carry out real-time acceleration test and displacement measurement.
The model test method of earth and rockfill dam eaerthquake damage of the present invention, further, model dam earth and stone material fills in step B Dry density ρmDetermination method, specifically includes the following steps:
A), to prototype dam earth and stone material, the triaxial compression test under the conditions of prototype dam stress state, design dry density is carried out, Determine effective angle of inner friction φ ' of prototype dam earth and stone material under the conditions of design dry densityp
B), to model dam earth and stone material, the triaxial compression test under low-stress state, different dry density conditions is carried out, is determined Difference fills the effective angle of inner friction φ ' of the model dam earth and stone material under dry densitym
C), angle of friction affinity constant C is enabledφ'It is 1, according to formula (2), corresponding model dam is selected to fill dry density ρm
Cφ'=φ 'p/φ'm (2)
In formula: Cφ'For angle of friction affinity constant;
φ'pFor the effective angle of inner friction of prototype dam earth and stone material;
φ'mFor the effective angle of inner friction of model dam earth and stone material.
The model test method of earth and rockfill dam eaerthquake damage of the present invention, further, step C mesarcs dam earth and stone material and model The determination method of the dynamic shear modulus coefficient of dam earth and stone material, specifically includes the following steps:
3. carrying out the dynamic deformation examination under the conditions of prototype dam stress state, design dry density to prototype dam earth and stone material It tests, obtains modulus and damping parameter of the prototype dam earth and stone material under the conditions of design dry density, determine prototype dam earth and stone material according to this The functional relation of maximum shear modulus and mean effective stress, as formula (4), thus to obtain the dynamic cut-off-die of prototype dam earth and stone material Coefficient of discharge Cp
In formula: GmaxFor maximum shear modulus, i.e. modulus of shearing of the soil body unit in small strain;
CpFor dynamic shear modulus coefficient related with prototype dam earth and stone material design dry density;
PaIt is 98kPa for atmospheric pressure;
σ0' it is mean effective stress;
npFor zero dimension index;
4. carrying out low-stress state to model dam earth and stone material, model dam fills the dynamic deformation under the conditions of dry density Test obtains modulus and damping parameter of the model dam earth and stone material under the conditions of model dam fills dry density, determines model dam according to this The maximum shear modulus of earth and stone material and the functional relation of mean effective stress, as formula (5), thus to obtain model dam earth and stone material Dynamic shear modulus coefficient Cm
In formula: GmaxFor maximum shear modulus, i.e. modulus of shearing of the soil body unit in small strain;
CmFor dynamic shear modulus coefficient related with model dam earth and stone material design dry density;
PaFor atmospheric pressure, 98kPa;
σ0' it is mean effective stress;
nmFor zero dimension index.
The model test method of earth and rockfill dam eaerthquake damage of the present invention, further, the crucial control on model dam is disconnected in step E The determination method in face, specifically includes the following steps:
First according to the size of landform and prototype dam, the crucial control section on prototype dam is selected, then according to geometric similarity Compare ClReduced scale is carried out, the section after reduced scale is the crucial control section on model dam;The key control section includes measuring master Control section and auxiliary measurement control section, the main control section that measures is the maximum section by dam bottom or riverbed center, The auxiliary measurement control section is to change the section acutely located close to riverbed and bank slope;Auxiliary measurement control section quantity be 2-5.
The model test method of earth and rockfill dam eaerthquake damage of the present invention, further, the production side of test model in step 2 Method, specifically includes the following steps:
I, model casing is made;According to the size selection key control section on prototype dam, by crucial control section according to geometry Than ruler ClIt is reduced, determines the shape and size of model casing;The cabinet of model casing is welded to form with steel plate, solid on steel plate side wall Surely there is reinforcing steel bar shelf;
II, basement rock is poured;Install basement rock template, casting concrete;The basement rock template controls disconnected according to prototype dam key The basement rock shape in face, according to geometric proportion ruler ClDiminution is made;
III, dam body is filled;
The filling height graticule of each layer is drawn in model casing first;Then along dam slope carry out formwork erection, then be layered into Row dam embankment, the earth and stone material that the template installed along dam slope carries out this layer fill, and every layer of flatness for filling material is from dam crest axis Line horizontal direction and suitable river horizontal direction both direction are controlled;
IV, dam slope is filled;
Upstream template and downstream template are installed, dam slope is filled, dam slope is consistent with prototype dam.
The model test method of earth and rockfill dam eaerthquake damage of the present invention, further, the step 3 model dam natural frequency of vibration is really Determine method, specifically includes the following steps:
(1), white noise microseism test is carried out;
To the white noise of the small amplitude of mode input, white noise microseism test is carried out, white noise acoustic amplitude is 0.03-0.05g, By the accelerometer and control section of table top and the accelerometer of dam crest, table top acceleration excitation X (t) and dam body are obtained not With the acceleration responsive Y (t) at position;
(2), the acceleration frequence responses function H (ω) on model dam is determined;
The auto-power spectrum of X (t) and the acceleration responsive Y (t) and X (t) of dam body different parts are motivated according to table top acceleration Crosspower spectrum, the acceleration frequence responses function H (ω) on model dam is determined according to formula (7);
In formula: GXX(ω) is the auto-power spectrum that table top acceleration motivates X (t);
GXY(ω) is dam body point acceleration responsive Y (t) and responds the crosspower spectrum that table top acceleration motivates X (t);
(3), the natural frequency of vibration on model dam is determined;
Model analysis is carried out to acceleration frequence responses function H (ω) using Modal Parameter Identification technology, determines model dam Natural frequency of vibration fm
The model test method of earth and rockfill dam eaerthquake damage of the present invention, further, in step 4 time similar scale is really Determine method, specifically includes the following steps:
(Ⅹ) according to seismic wave excellent frequency feWith determining model dam natural frequency of vibration fm, it is determined to make according to formula (8) Compressed seismic wave excellent frequency frequency compression identical with the model dam natural frequency of vibration compares ruler;
In formula: CfrCompare ruler for frequency compression;
fmFor the model dam natural frequency of vibration;
feFor seismic wave excellent frequency;
(Ⅺ) according to frequency of seismic wave compression ratio ruler C maximum in x, y, z directionfr, determine that its is corresponding according to formula (9) Time compression ratio ruler Ctr, and thereby determine that one group of time similar scale Ct
In formula: CtrFor the time compression ratio ruler of seismic wave;
CfrCompare ruler for frequency compression;
(Ⅻ) according to one group of determining time similar scale, design rules is compressed, it is similar to obtain different time Than the seismic wave of amplitude identical under ruler, different spectral characteristic.
The model test method of earth and rockfill dam eaerthquake damage of the present invention, further, in step 5 in eaerthquake damage test The selection method of the time similar scale of seismic wave, specifically includes following steps;
(5-1) is for statistical analysis by the acceleration of the dam crest measuring point under the conditions of different time similar scale, according to acceleration The height of degree divides the distributed areas of acceleration, therefrom the higher one group of acceleration of Response to selection;
(5-2) determines the sample standard deviation of one group of acceleration of selection;
(5-3) illustrates that this group of acceleration responsive is close when the sample standard deviation of acceleration is not more than 0.01;Comparison respectively adds Dam crest surface displacement response under the conditions of the corresponding different time similar scale of speed responsive determines that wherein dam crest surface displacement is most Time compression ratio ruler of the big time similar scale as seismic wave in eaerthquake damage test;
(5-4) is repeated step (5-1), when the acceleration samples standard deviation of selection is greater than 0.01 according to the height of acceleration It is low, repartition the distributed areas of acceleration, the higher one group of acceleration of Response to selection, then repeatedly step (5-2) to (5- 3), until when the acceleration samples standard deviation of selection is not more than 0.01, the time compression of seismic wave in earthquake failure test is determined Compare ruler.
The model test method of earth and rockfill dam eaerthquake damage of the present invention, further, eaerthquake damage vibration test in step 6 The seismic wave acceleration amplitude of middle input determines in accordance with the following methods:
(6-1) determines initial acceleration amplitude ad
According to the earthquake motion peak acceleration of the Probability level of 100 Annual exceeding probability 2% of dam site place, initial acceleration is determined Spend amplitude ad
(6-2) determines the seismic wave acceleration target value a inputted in eaerthquake damage vibration testimax,
aimax=ad+(i-1)×Δa (10)
In formula, aimaxI-th input acceleration target value is tested for eaerthquake damage;
I is eaerthquake damage operating condition of test serial number;
Δ a is acceleration increment, generally takes 0.05~0.2;
adFor the initial acceleration amplitude in eaerthquake damage vibration test.
The model test method of earth and rockfill dam eaerthquake damage of the present invention compared with prior art, has the following beneficial effects:
The model test method of earth and rockfill dam eaerthquake damage of the present invention is from model dam, structural dynamic characteristic and input-to-state stabilization Spectrum signature is started with, and using the seismic wave with suitable spectral characteristic, simulates limit earthquake by shaking table model, real The complete shake on existing model dam is ruined, the eaerthquake damage mechanism of high earth and rockfill dam under research limit geological process, failure mode and ultimately Shake acts on the validation verification of lower earthquake resistant construction.
The model test method of earth and rockfill dam eaerthquake damage of the present invention requires progress model similar according to model test likelihood Design determines basic affinity constant, and then remaining determining affinity constant by triaxial compression test and dynamic deformation test, Modelling and production are carried out, modelling is more reasonable, and simulation accuracy is high, and the natural frequency of vibration on model dam is suitable for selected The complete shake of seismic wave, implementation model dam is ruined.
The model test method of earth and rockfill dam eaerthquake damage of the present invention is applicable not only to the eaerthquake damage mould of general earth and rockfill dam Type test applies also for the eaerthquake damage model examination of the high earth and rockfill dam of height 200m or more and the superelevation earth and rockfill dam of 300m or more It tests, the complete shake that high earth and rockfill dam model may be implemented is ruined, and avoids shake table by the attainable limit of self performance limitation institute Experimental condition is not able to satisfy model dam and shakes the case where ruining completely, provides section for the Aseismic Design and Evaluation of Seismic of high earth and rockfill dam Learn foundation.
The model test method of earth and rockfill dam eaerthquake damage of the invention is described further with reference to the accompanying drawing.
Detailed description of the invention
Fig. 1 is the control section distribution schematic diagram of high earth and rockfill dam in embodiment;
Fig. 2 is the Acceleration time course example that main control section center line measuring point is measured in embodiment;
Fig. 3 is the auto-power spectrum example that the acceleration excitation of main control section center line measuring point is measured in embodiment;
Fig. 4 is that main control section center line measuring point acceleration frequence responses examples of functions is measured in embodiment.
Specific embodiment
Now by taking the model failure test of the high earth and rockfill dam of some hydropower station as an example, illustrate model test method of the present invention.
The Dam Site basic earthquake intensity of some hydropower station is VII degree, and hinge water retaining structure is the panel enrockment of 211m high Dam, earthquake resistance of a dam set up defences classification as Class A, and seismic fortification intensity is VIII degree.
The model test method of specific earth and rockfill dam eaerthquake damage, comprising the following steps:
Step 1: requiring to carry out model similar Design according to earth and rockfill dam model test likelihood;
Shake table used in simulation test can be centrifuged making machine vibration table for 1g shake table or ng;In the test of the present embodiment Select the 1g shake table of 6m × 6m.
C, the geometric similarity constant C of model is determinedl
According to the performance parameter of shake table, determine that the height of dam of model is 1.50m;According to information it is found that prototype height of dam For 211m, then the geometric similarity constant C of model is determined by formula (1)lIt is 140.7;
In formula: ClFor the geometric similarity constant of model;
HpFor the height on prototype dam, m;
HmFor the height on model dam, m.
D, the density affinity constant C of model is determinedρ
By triaxial compression test, prototype dam earth and stone material and mould under certain stress state, different dry density conditions are determined Then the effective angle of inner friction of type dam earth and stone material determines density affinity constant C according to effective angle of inner frictionρ, specifically include following Step:
A), to prototype dam earth and stone material, the triaxial compression test under the conditions of prototype dam stress state, design dry density is carried out, Determine prototype dam earth and stone material in design dry density ρpUnder the conditions of effective angle of inner friction φ 'p
The design dry density ρ of its mesarcs dam earth and stone materialpFor 2.15g/cm3;In practical dam body, determine that dam body power is special Property mainly determined by being located at compared with the soil body under high confining pressure power, build a dam earth and stone material to prototype, progress is under 98kPa stress state Triaxial compression test, determine that prototype is built a dam the effective angle of inner friction φ ' of earth and stone materialpIt is 47 °;
B), to model dam earth and stone material, the triaxial compression test under low-stress state, different dry density conditions is carried out, is determined Difference fills the effective angle of inner friction φ ' of the model dam earth and stone material under dry densitym
In model dam, resistance to shear of soil is lower in dam body, to the model dam of 1.5m high in this present embodiment, section centroid The confining pressure power of position is about 20kPa;To the model dam dam material after reduced scale, carry out under low-stress state, different dry densities Triaxial compression test determines that difference fills effective angle of inner friction φ ' of the dry density drag dam earth and stone material under 20kPa confining pressurem, As shown in table 1;
The results of triaxial compressive test of 1 model dam earth and stone material of table
Model dam earth and stone material Dry density (g/cm3) φ'm(°)
1 group 1.79 44.4
2 groups 1.89 47.0
3 groups 1.99 50.1
4 groups 2.09 54.4
C), angle of friction affinity constant Cφ'It is 1, according to formula (2), corresponding model dam is selected to fill dry density ρm
Cφ'=φ 'p/φ'm (2)
In formula: Cφ'For angle of friction affinity constant;
φ'pFor the effective angle of inner friction of prototype dam earth and stone material;
φ'mFor the effective angle of inner friction of model dam earth and stone material;
Enable angle of friction affinity constant Cφ'=1, to ensure that prototype dam is equal with model dam average effective internal friction angle, i.e., really Determine φ 'm=φ 'p=47 °, according to the results of triaxial compressive test of step b), determine φ 'mCorresponding model dam fills at=47 ° Dry density ρmFor 1.89g/cm3
D), density affinity constant C is determined according to formula (3)ρIt is 1.14;
Cρpm (3)
In formula: CρFor density affinity constant;
ρpFor the design dry density of prototype dam earth and stone material, g/cm3
ρmDry density, g/cm are filled for model dam earth and stone material3
C, modulus coefficient affinity constant C is determinedc
It is tested according to dynamic deformation, determines modulus coefficient affinity constant Cc, specifically includes the following steps:
1. carrying out the dynamic deformation examination under the conditions of prototype dam stress state, design dry density to prototype dam earth and stone material It tests, obtains modulus and damping parameter of the prototype dam earth and stone material under the conditions of design dry density, determine prototype dam earth and stone material according to this The functional relation of maximum shear modulus and mean effective stress, for formula (4);
In formula: GmaxFor maximum shear modulus, i.e. modulus of shearing of the soil body unit in small strain;
CpFor dynamic shear modulus coefficient related with prototype dam earth and stone material design dry density;
PaIt is 98kPa for atmospheric pressure;
σ0' it is mean effective stress;
npFor zero dimension index;
The related modulus coefficient of the prototype dam earth and stone material thereby determined that is as shown in table 2.
The related modulus coefficient of 2 prototype dam earth and stone material of table
Dry density g/cm3 np Cp
Prototype dam earth and stone material 2.15 0.32 2400
2. carrying out low-stress state to model dam earth and stone material, model dam fills the dynamic deformation under the conditions of dry density Test obtains modulus and damping parameter of the model dam earth and stone material under the conditions of model dam fills dry density, determines model dam according to this The maximum shear modulus of earth and stone material and the functional relation of mean effective stress, as formula (5);
In formula: GmaxFor maximum shear modulus, i.e. modulus of shearing of the soil body unit in small strain;
CmFor dynamic shear modulus coefficient related with model dam earth and stone material design dry density;
PaFor atmospheric pressure, 98kPa;
σ0' it is mean effective stress;
nmFor zero dimension index;
The related modulus coefficient of the model dam earth and stone material thereby determined that is as shown in table 3.
The related modulus coefficient of 3 model dam earth and stone material of table
Dry density g/cm3 nm Cm
Model dam earth and stone material 1.89 0.573 1375
3. determining modulus coefficient affinity constant C according to formula (6)cIt is 1.745;
CC=Cp/Cm (6)
In formula: CcFor modulus coefficient affinity constant;
CpFor dynamic shear modulus coefficient related with prototype dam earth and stone material design dry density;
CmFor dynamic shear modulus coefficient related with model dam earth and stone material design dry density.
D, remaining affinity constant, including stress similitude constant, modulus of shearing affinity constant, strain ratio, speed are determined It is similar often to spend affinity constant, time affinity constant, frequency affinity constant, soil body damping ratio affinity constant, the effective cohesiveness of the soil body Number, soil body effective friction coefficient affinity constant and acceleration affinity constant;
According to the above-mentioned affinity constant obtained, geometric similarity constant ClIt is 140.7, density affinity constant CρIt is 1.04, Modulus coefficient affinity constant CcIt is 1.745, angle of friction affinity constant Cφ'Be 1, can the formula according to table 4 determine remaining it is similar often Number.
Remaining affinity constant of table 4
E, the crucial control section on model dam is determined, to carry out real-time acceleration test and displacement measurement;
First according to the size of landform and prototype dam, the crucial control section on prototype dam is selected, then according to geometric similarity Reduced scale is carried out than 140.7, the section after reduced scale is the crucial control section on model dam;Test is arranged on crucial control section Instrument;The main control section that measures of selection is the maximum section by dam bottom or riverbed center, then chooses 2-5 auxiliary quantity observing and controlling Section processed, auxiliary measurement control section, which is chosen, changes the section acutely located close to river valley and bank slope;
The Dam Site of high earth and rockfill dam described in the present embodiment is the Asymmetric V-type river valley that river valley is narrow, bank slope is precipitous, is passed through Vertical 9 sections of river valley bottom are maximum section, therefore select vertical 9 sections corresponding to prototype dam to measure main control section, together When choose to measure and correspond to vertical the 7 of prototype dam on the left of main control section (close to left bank) and indulge 5 two sections, and measure master control Vertical 11 sections that section right side (close to right bank) processed corresponds to prototype dam are to assist measurement control section, specific Latitudinal section, As shown in Figure 1.
Specific arrangement is as follows:
X, y, z is respectively indicated along river horizontal direction, along the axis of dam horizontally and vertically;
The measuring instrument that acceleration measuring point uses is the accelerometer of table top and the accelerometer of control section and dam crest; Accelerometer is directed along dam crest axis horizontal direction or suitable river horizontal direction, is arranged on each measurement control section, wherein Based on suitable river horizontal direction, the appropriate accelerometer arranging dam crest axis horizontal direction and vertical direction and being directed toward;The present embodiment 22 acceleration measuring points are arranged on measuring main control section, wherein 16, the direction x, 3, the direction y, 3, the direction z, in auxiliary The acceleration measuring point that 2 directions x are arranged on vertical 7 sections arranges the acceleration measuring point in 3 directions x, vertical 11 on vertical 5 sections The acceleration measuring point in 3 directions x is arranged on section;
The measuring instrument that strain and stress measuring point uses is foil gauge, is arranged on each measurement control section, to measure master Based on control section, and it is arranged on auxiliary measurement control section in right amount;
The measuring instrument that displacement measuring points use is fiber grating displacement sensor, fiber grating displacement sensor along dam crest and Dam slope surface layout is buried different depth, and is marked, and excavation inspection is carried out after the completion of vibration test, to be slided Slope depth monitoring.
Step 2: production test model is required according to model similar Design, specifically includes the following steps:
I, model casing is made;
According to the size selection key control section on prototype dam, crucial control section is carried out according to geometric proportion ruler 140.7 It reduces, determines the shape and size of model casing;Model cabinet is welded to form with steel plate, is welded with reinforced frame on steel plate side wall Body;It in the present embodiment, is distributed according to control section shown in FIG. 1, is successively reduced, make model casing;
II, basement rock is poured;
Basement rock template is installed, poured in place concrete forms the basement rock of reinforced concrete structure, to ensure basement rock structure The natural frequency of vibration is higher than 2 times of the first rank natural frequency of vibration of model, and the natural frequency of vibration of model is estimated at the beginning of using tangent-wedge method is cut;Basement rock template According to the basement rock shape of prototype dam key control section, it is made according to the diminution of geometric proportion ruler;
To guarantee formwork precision, 3 d geometric modeling is carried out to the basement rock after reduced scale with AUTOcad and ANSYS, has been used in combination To assist production basement rock cast template;
III, dam body is filled;
The filling height graticule of each layer is drawn in model casing first, it is ensured that every layer of filling height is no more than 20cm, together When according to the design density of prototype above and below the dam rockfill area determine that each layer fills the weight of earth and stone material, be to realize to be compacted design The strict control of density has carried out Geometric Modeling to each layering of three dimensional solid model, to obtain each placement in layers earth and stone material Volume, and then determine that each layer fills the weight of earth and stone material by the design density of each subregion in model dam;Then it is carried out along dam slope Formwork erection, then be layered carry out dam embankment, 10 layers of progress dam embankment of the present embodiment point, every layer when being filled, according to mould Dry density ρ is filled in the design of type dammFor 1.89g/cm3, the earth and stone material that the template installed along dam slope carries out this layer fills, and every layer The flatness of material is filled to be controlled from dam crest axis horizontal direction and along river horizontal direction both direction;
IV, dam slope is filled;
It makes upstream template and downstream template, upstream template and downstream template first to make by practical lofting Design, mould Plate is plank, and falsework is welded with angle steel;Then upstream template and downstream template are installed, then fills dam slope, dam slope with Prototype dam is consistent.
Step 3: model dam is carried out white noise microseism test, determines the natural frequency of vibration on model dam, specifically include following step It is rapid:
(1), white noise microseism test is carried out;
To the white noise of the small amplitude of mode input, white noise microseism test is carried out, white noise acoustic amplitude is 0.03-0.05g, The white noise acoustic amplitude for making a reservation for input in the present embodiment is 0.05g, passes through the accelerometer and control section of table top and dam crest Accelerometer obtains the acceleration responsive Y (t) of table top acceleration excitation X (t) and dam body different parts;
In the present embodiment, the center line measuring point that main control section indulges 9 sections is measured, what Acceleration time course and acceleration motivated Auto-power spectrum difference is as shown in Figures 2 and 3;
(2), the acceleration frequence responses function H (ω) on model dam is determined;
The auto-power spectrum of X (t) and the acceleration responsive Y (t) and X (t) of dam body different parts are motivated according to table top acceleration Crosspower spectrum, the acceleration frequence responses function H (ω) on model dam is determined according to formula (7);
In formula: GXX(ω) is the auto-power spectrum that table top acceleration motivates X (t);
GXY(ω) is dam body point acceleration responsive Y (t) and responds the crosspower spectrum that table top acceleration motivates X (t);
Citing, the center line measuring point for measuring main control section and indulging 9 sections of the present embodiment, i.e. the acceleration frequency in the direction x One of example of rate receptance function is as shown in Figure 4;
(3), the natural frequency of vibration on model dam is determined;
Model analysis is carried out to acceleration frequence responses function H (ω) using Modal Parameter Identification technology, determines model dam Natural frequency of vibration fm, the natural frequency of vibration average value in the direction x is 33.6Hz, and y is about 38.0Hz to the natural frequency of vibration, and z is to the natural frequency of vibration About 43.4Hz.
Step 4: selecting one according to the seismic wave frequency spectrum characteristic of the model dam natural frequency of vibration and prototype earth and rockfill dam Site Design Group time similar scale, compresses the design rules in place, obtains identical amplitude, different spectral under different compression ratio rulers The seismic wave of characteristic;Specifically includes the following steps:
(Ⅹ) according to seismic wave excellent frequency feWith determining model dam natural frequency of vibration fm, it is determined to make according to formula (8) Compressed seismic wave excellent frequency frequency compression identical with the model dam natural frequency of vibration than ruler, the dam site place of the present embodiment Seismic wave excellent frequency feFor 4.8Hz, Site Design seismic wave vibration time is 26s, thereby determines that the frequency of the direction x seismic wave Compression ratio ruler is that the frequency compression of the direction 0.143, y seismic wave is than ruler than the frequency compression that ruler is the direction 0.126, z seismic wave 0.111。
In formula: CfrCompare ruler for frequency compression;
fmFor the model dam natural frequency of vibration;
feFor seismic wave excellent frequency;
(Ⅺ) according to frequency of seismic wave compression ratio ruler C maximum in x, y, z directionfr, determine that its is corresponding according to formula (9) Time compression ratio ruler CtrIt is 7, thereby determines that one group of time similar scale CtIt is 7,6,5,4,3;
In formula: CtrFor the time compression ratio ruler of seismic wave;
CfrCompare ruler for frequency compression;
(Ⅻ) according to one group of determining time similar scale, design rules is compressed, it is similar to obtain different time Than the seismic wave of amplitude identical under ruler, different spectral characteristic.
Step 5: carrying out vibration test, really according to seismic wave under the conditions of identical amplitude, different time similar scale Acceleration responsive and dam surface dynamic respond of the cover half type dam under the ground seismic wave function of different time similar scale, in conjunction with adding The time compression ratio ruler of seismic wave in speed responsive and dam surface dynamic respond selection earthquake failure test;
The selection method of the time similar scale of seismic wave in eaerthquake damage test, specific as follows:
(5-1) is for statistical analysis by the acceleration of the dam crest measuring point under the conditions of different time similar scale, according to acceleration The height of degree divides the distributed areas of acceleration, therefrom the higher one group of acceleration of Response to selection;
(5-2) determines the sample standard deviation of one group of acceleration of selection;
(5-3) illustrates that this group of acceleration responsive is close when the sample standard deviation of acceleration is not more than 0.01;Comparison respectively adds Dam crest surface displacement response under the conditions of the corresponding different time similar scale of speed responsive determines that wherein dam crest surface displacement is most Time compression ratio ruler of the big time similar scale as seismic wave in eaerthquake damage test;
Wherein, dam surface dynamic respond is judged in combination with the duration of seismic wave, Duration time of seismic wave with Deformation accumulation correlation caused by it;
(5-4) is repeated step (5-1), when the acceleration samples standard deviation of selection is greater than 0.01 according to the height of acceleration Low, distributed areas that are more dense, repartitioning acceleration reselect the higher one group of acceleration of response, then repeat to walk Suddenly (5-2) to (5-3), until determining earthquake in earthquake failure test when the acceleration samples standard deviation of selection is not more than 0.01 The time compression ratio ruler of wave;
Vibration test in the present embodiment is shown, as time similar scale CtWhen=4~7, the acceleration responsive on model dam It is not much different, sample data standard deviation is 0.078, but is apparently higher than CtThe acceleration responsive on model dam when=3;Each time pressure Under the conditions of shrinkage scale the duration of seismic wave and its caused by the dam crest amount of collapsing such as table 5.
5 Duration time of seismic wave of table and its dam crest amount of collapsing
Time similar scale Ct 7 6 5 4 3
Duration time of seismic wave/s 3.7 4.3 5.2 6.5 8.7
Dam crest is averaged Loess deposits/mm 1.2 1.8 2.5 3.2 2.6
As shown in Table 5, the time similar scale C being not much different for the acceleration responsive on model damt=4~7, time phase Like than ruler CtWhen=4 the duration of seismic wave be 6.5s, caused by dam crest be averaged Loess deposits maximum, be 3.2mm, therefore combine add Speed responsive and the response of dam crest surface displacement, select Ct=4 time similar scale as seismic wave in eaerthquake damage test.
Step 6: under the conditions of different acceleration amplitudes, carrying out the earthquake on model dam according to determining time similar scale Vibration test is destroyed, since design earthquake peak acceleration, arrives the earth seismic wave acceleration amplitude that increases from childhood, test dam adds Speed responsive and dynamic respond, until dam earthquake destroys;
The seismic wave acceleration amplitude inputted in eaerthquake damage vibration test determines in accordance with the following methods:
(6-1) determines initial acceleration amplitude ad
According to the earthquake motion peak acceleration of the Probability level of 100 Annual exceeding probability 2% of dam site place, initial acceleration is determined Spend amplitude ad, initial acceleration amplitude a is determined in the present embodimentdIt is 0.299;
(6-2) determines the seismic wave acceleration target value a inputted in eaerthquake damage vibration testimax,
aimax=ad+(i-1)×Δa (10)
In formula, aimaxI-th input acceleration target value is tested for eaerthquake damage;
I is eaerthquake damage operating condition of test serial number;
Δ a is acceleration increment, generally takes 0.05~0.2, and the value of Δ a is 0.072 in the present embodiment;
adFor the initial acceleration amplitude in eaerthquake damage vibration test;
The seismic wave acceleration amplitude of eaerthquake damage vibration test in the present embodiment, input is as shown in table 5, ascending It is stepped up.
The seismic wave acceleration amplitude inputted in 5 eaerthquake damage vibration test of table
Operating condition serial number Seismic wave acceleration amplitude
1 0.299g
2 0.371g
3 0.443g
4 0.515g
5 0.587g
6 0.659g
7 0.731g
8 0.803g
9 0.875g
Test process is shown, in the case where seismic wave acceleration amplitude is the effect of vibration of 0.299g, the deformation very little on model dam; With the increase of seismic wave acceleration amplitude, under the effect of vibration of 0.371g, it is equivalent to and checks the acceleration of earthquake motion basement rock peak value Degree, that is, the range of the Probability level earthquake conditions of 100 Annual exceeding probabilities 1%, model dam Rolling Stone or failure by leaking is gradually Expand;During the acceleration amplitude of 0.443g~0.731g is stepped up, effect of vibration is gradually strong, and dam body destroys model It encloses and gradually increases with degree.Under the consumingly shock effect that experience earthquake motion peak acceleration is 0.515g, dam body downstream The sliding of globality can occur for slope, there is the possibility that larger landslide occurs, and dam crest and dam body are sternly serious damaged;It is arrived in 0.803g During the high vibration of 0.875g, the collapsing and destruction of globality occur for downstream dam slope, and unrepairable occurs for entire model dam Completeness it is damaged.
In eaerthquake damage vibration test, the data of each measuring point record can be used as analysis and research limit geological process The basic data of lower high earth and rockfill dam eaerthquake damage mechanism and failure mode are the high earth and rockfill dam Aseismic Design in highly seismic region and antidetonation Performance evaluation provides a kind of effectively research critical support means and scientific basis.
Embodiment described above only describe the preferred embodiments of the invention, not to model of the invention It encloses and is defined, without departing from the spirit of the design of the present invention, those of ordinary skill in the art are to technical side of the invention The various changes and improvements that case is made should all be fallen into the protection scope that claims of the present invention determines.

Claims (10)

1. the model test method of earth and rockfill dam eaerthquake damage, it is characterised in that: the following steps are included:
Step 1: requiring to carry out model similar Design according to earth and rockfill dam model test likelihood;
Step 2: requiring production test model according to model similar Design;
Step 3: model dam is carried out white noise microseism test, the natural frequency of vibration on model dam is determined;
Step 4: according to the seismic wave frequency spectrum characteristic of the model dam natural frequency of vibration and prototype earth and rockfill dam Site Design, when selecting one group Between similar scale, the design rules in place are compressed, obtain different time similar scale under identical amplitude, different spectral The seismic wave of characteristic;
Step 5: carrying out vibration test according to seismic wave under the conditions of identical amplitude, different time similar scale, determining mould Acceleration responsive and dam surface dynamic respond of the type dam under the ground seismic wave function of different time similar scale, in conjunction with acceleration The time similar scale of seismic wave in response and dam surface dynamic respond selection eaerthquake damage vibration test;
Step 6: under the conditions of different acceleration amplitudes, carrying out the eaerthquake damage on model dam according to determining time similar scale Vibration test arrives the earth seismic wave acceleration amplitude that increases since site ground motion peak accelerator from childhood, and test model dam adds Speed responsive and dynamic respond, until model dam eaerthquake damage.
2. the model test method of earth and rockfill dam eaerthquake damage according to claim 1, it is characterised in that: model in step 1 Similar Design specifically includes the following steps:
A, the geometric similarity constant C of model is determinedl
The geometric similarity constant C of model is determined according to formula (1)l,
In formula: ClFor the geometric similarity constant of model;
HpFor the height on prototype dam, m;
HmFor the height on model dam, m;
B, the density affinity constant C of model is determinedρ
Respectively by triaxial compression test, prototype dam earth and stone material and mould under certain stress state, different dry density conditions are determined Then the effective angle of inner friction of type dam earth and stone material determines that model dam fills dry density ρ according to effective angle of inner frictionm, further according to public affairs Formula (3) determines density affinity constant Cρ
Cρpm (3)
In formula: CρFor density affinity constant;
ρpFor the design dry density of prototype dam earth and stone material, g/cm3
ρmDry density, g/cm are filled for model dam earth and stone material3
C, modulus coefficient affinity constant C is determinedc
It is tested respectively according to dynamic deformation, determines the dynamic shear modulus coefficient of prototype dam earth and stone material and model dam earth and stone material, so Modulus coefficient affinity constant C is determined according to formula (6) afterwardsc
CC=Cp/Cm (6)
In formula: CcFor modulus coefficient affinity constant;
CpFor dynamic shear modulus coefficient related with prototype dam earth and stone material design dry density;
CmFor dynamic shear modulus coefficient related with model dam earth and stone material design dry density;
D, remaining affinity constant, including stress similitude constant, modulus of shearing affinity constant, strain ratio, speed phase are determined Like constant, time affinity constant, frequency affinity constant, soil body damping ratio affinity constant, the effective cohesiveness affinity constant of the soil body, soil Body effective friction coefficient affinity constant and acceleration affinity constant;
E, the crucial control section on model dam is determined, to carry out real-time acceleration test and displacement measurement.
3. the model test method of earth and rockfill dam eaerthquake damage according to claim 2, it is characterised in that: model in step B Dam earth and stone material fills dry density ρmDetermination method, specifically includes the following steps:
A), to prototype dam earth and stone material, the triaxial compression test under the conditions of prototype dam stress state, design dry density is carried out, is determined Effective angle of inner friction φ ' of prototype dam earth and stone material under the conditions of design dry densityp
B), to model dam earth and stone material, the triaxial compression test under low-stress state, different dry density conditions is carried out, is determined different Fill the effective angle of inner friction φ ' of the model dam earth and stone material under dry densitym
C), angle of friction affinity constant C is enabledφ'It is 1, according to formula (2), corresponding model dam is selected to fill dry density ρm
Cφ'=φ 'p/φ'm (2)
In formula: Cφ'For angle of friction affinity constant;
φ'pFor the effective angle of inner friction of prototype dam earth and stone material;
φ'mFor the effective angle of inner friction of model dam earth and stone material.
4. the model test method of earth and rockfill dam eaerthquake damage according to claim 2, it is characterised in that: step C mesarcs The determination method of the dynamic shear modulus coefficient of dam earth and stone material and model dam earth and stone material, specifically includes the following steps:
1. prototype dam earth and stone material is carried out the dynamic deformation test under the conditions of prototype dam stress state, design dry density, is obtained Modulus and damping parameter of the prototype dam earth and stone material under the conditions of design dry density are obtained, determines that the maximum of prototype dam earth and stone material is cut according to this The functional relation of shear modulu and mean effective stress, as formula (4), thus to obtain the dynamic shear modulus coefficient of prototype dam earth and stone material Cp
In formula: GmaxFor maximum shear modulus, i.e. modulus of shearing of the soil body unit in small strain;
CpFor dynamic shear modulus coefficient related with prototype dam earth and stone material design dry density;
PaIt is 98kPa for atmospheric pressure;
σ0' it is mean effective stress;
npFor zero dimension index;
2. to model dam earth and stone material, progress low-stress state, model dam fill the dynamic deformation test under the conditions of dry density, Modulus and damping parameter of the model dam earth and stone material under the conditions of model dam fills dry density are obtained, determines model dam earth and stone material according to this Maximum shear modulus and mean effective stress functional relation, as formula (5), thus to obtain dynamic the cutting of model dam earth and stone material Modulus coefficient Cm
In formula: GmaxFor maximum shear modulus, i.e. modulus of shearing of the soil body unit in small strain;
CmFor dynamic shear modulus coefficient related with model dam earth and stone material design dry density;
PaFor atmospheric pressure, 98kPa;
σ0' it is mean effective stress;
nmFor zero dimension index.
5. the model test method of earth and rockfill dam eaerthquake damage according to claim 2, it is characterised in that: model in step E The determination method of the crucial control section on dam, specifically includes the following steps:
First according to the size of landform and prototype dam, the crucial control section on prototype dam is selected, then according to geometric similarity constant Cl Reduced scale is carried out, the section after reduced scale is the crucial control section on model dam;The key control section includes measuring main control Section and auxiliary measurement control section, the main control section that measures is the maximum section by dam bottom or riverbed center, described Auxiliary measurement control section is to change the section acutely located close to riverbed and bank slope;The quantity for assisting measurement control section is 2-5 It is a.
6. the model test method of earth and rockfill dam eaerthquake damage according to claim 1, it is characterised in that: tested in step 2 The production method of model, specifically includes the following steps:
I, model casing is made;According to the size selection key control section on prototype dam, by crucial control section according to geometric similarity Constant ClIt is reduced, determines the shape and size of model casing;The cabinet of model casing is welded to form with steel plate, solid on steel plate side wall Surely there is reinforcing steel bar shelf;
II, basement rock is poured;Install basement rock template, casting concrete;The basement rock template is according to prototype dam key control section Basement rock shape, according to geometric similarity constant ClDiminution is made;
III, dam body is filled;
The filling height graticule of each layer is drawn in model casing first;Then formwork erection is carried out along dam slope, then is layered carry out dam Body fills, and the earth and stone material that the template installed along dam slope carries out this layer fills, and every layer of flatness for filling material is from dam crest axis water Square to controlled along river horizontal direction both direction;
IV, dam slope is filled;
Upstream template and downstream template are installed, dam slope is filled, dam slope is consistent with prototype dam.
7. the model test method of earth and rockfill dam eaerthquake damage according to claim 1, it is characterised in that: step 3 model dam The determination method of the natural frequency of vibration, specifically includes the following steps:
(1), white noise microseism test is carried out;
To the white noise of the small amplitude of mode input, white noise microseism test is carried out, white noise acoustic amplitude is 0.03-0.05g, is passed through The accelerometer and control section of table top and the accelerometer of dam crest obtain table top acceleration excitation X (t) portion different with dam body The acceleration responsive Y (t) of position;
(2), the acceleration frequence responses function H (ω) on model dam is determined;
According to the mutual of the acceleration responsive Y (t) and X (t) of the auto-power spectrum of table top acceleration excitation X (t) and dam body different parts Power spectrum determines the acceleration frequence responses function H (ω) on model dam according to formula (7);
In formula: GXX(ω) is the auto-power spectrum that table top acceleration motivates X (t);
GXY(ω) is the crosspower spectrum that dam body point acceleration responsive Y (t) and table top acceleration motivate X (t);
(3), the natural frequency of vibration on model dam is determined;
Model analysis is carried out to acceleration frequence responses function H (ω) using Modal Parameter Identification technology, determines model dam oneself Vibration frequency fm
8. the model test method of earth and rockfill dam eaerthquake damage according to claim 1, it is characterised in that: the time in step 4 The determination method of similar scale, specifically includes the following steps:
(Ⅹ) according to seismic wave excellent frequency feWith determining model dam natural frequency of vibration fm, it is determined to make to compress according to formula (8) The frequency compression identical with the model dam natural frequency of vibration of seismic wave excellent frequency afterwards compares ruler;
In formula: CfrCompare ruler for frequency compression;
fmFor the model dam natural frequency of vibration;
feFor seismic wave excellent frequency;
(Ⅺ) according to frequency of seismic wave compression ratio ruler C maximum in x, y, z directionfr, its corresponding time is determined according to formula (9) Compression ratio ruler Ctr, and thereby determine that one group of time similar scale Ct
In formula: CtrFor the time compression ratio ruler of seismic wave;
CfrCompare ruler for frequency compression;
(Ⅻ) according to one group of determining time similar scale, design rules is compressed, different time similar scale is obtained Under identical amplitude, different spectral characteristic seismic wave.
9. the model test method of earth and rockfill dam eaerthquake damage according to claim 1, it is characterised in that: earthquake in step 5 The selection method for destroying the time similar scale of seismic wave in vibration test, specifically includes following steps;
(5-1) is for statistical analysis by the acceleration of the dam crest measuring point under the conditions of different time similar scale, according to acceleration Height divides the distributed areas of acceleration, therefrom the higher one group of acceleration of Response to selection;
(5-2) determines the sample standard deviation of one group of acceleration of selection;
(5-3) illustrates that this group of acceleration responsive is close when the sample standard deviation of acceleration is not more than 0.01;Compare each acceleration The dam crest surface displacement response under the conditions of corresponding different time similar scale is responded, determines that wherein dam crest surface displacement is maximum Time compression ratio ruler of the time similar scale as seismic wave in eaerthquake damage vibration test;
(5-4) is repeated step (5-1) when the acceleration samples standard deviation of selection is greater than 0.01, according to the height of acceleration, weight The new distributed areas for dividing acceleration, the higher one group of acceleration of Response to selection, then repeatedly step (5-2) to (5-3), until When the acceleration samples standard deviation of selection is not more than 0.01, the time compression ratio of seismic wave in eaerthquake damage vibration test is determined Ruler.
10. the model test method of earth and rockfill dam eaerthquake damage according to claim 1, it is characterised in that: in step 6 Shake destroys the seismic wave acceleration amplitude inputted in vibration test and determines in accordance with the following methods:
(6-1) determines initial acceleration amplitude ad
According to the earthquake motion peak acceleration of the Probability level of 100 Annual exceeding probability 2% of dam site place, initial acceleration width is determined Value ad
(6-2) determines the seismic wave acceleration target value a inputted in eaerthquake damage vibration testi max,
ai max=ad+(i-1)×Δa (10)
In formula, ai maxFor eaerthquake damage vibration test i-th input acceleration target value;
I is eaerthquake damage vibration test operating condition serial number;
Δ a is acceleration increment, takes 0.05~0.2;
adFor the initial acceleration amplitude in eaerthquake damage vibration test.
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