CN103728436A - Seismic dynamic centrifugal model test extension analysis method - Google Patents
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Abstract
The invention provides a seismic dynamic centrifugal model test extension analysis method which aims at researching a seismic destructive mechanism and the disaster prevention and decrease of large-scale projects such as a high earth-rock dam by using an unequal stress small-scale dynamic centrifugal model test. The technical thought is as follows: an equal stress scale test result is obtained by fitting extension through a method that model stress gradually approaches prototype stress by adopting n unequal stress small-scale dynamic centrifugal model tests. The seismic dynamic centrifugal model test extension analysis method provided by the invention can be used for simulating the large-scale project through a relatively small scale and applying the centrifugal machine vibration table to the effective test research of the seismic destructive mechanism and disaster preventing and decreasing measures of large-scale projects such as the high earth-rock dam, a scientific and feasible way is provided for the model test research of the problem of seism of the large-scale projects, which can not be originally carried out, and the reasonability of the effective test result of the seismic destructive mechanism and disaster preventing and decreasing measures of large-scale projects such as the high earth-rock dam can be obviously promoted.
Description
Technical field
The invention belongs to test theory technical field, be specifically related to a kind of earthquake motive force centrifugal model test extension analytical approach.Be specially adapted to high earth and rockfill dam eaerthquake damage mechanism and the experimental study of earthquake disaster prevention hazard mitigation measure validation verification, the eaerthquake damage mechanism test research that simultaneously also can be applicable to large geotechnical structures and earth and stone material and works problem, makes the Dynamic Centrifugal Model Test of little guide can be applied to the earthquake disaster prevention disaster reduction research of heavy construction.
Background technology
China has more than 9.8 ten thousand of reservoir dam, wherein the high earth and rockfill dam of 100m level exceedes hundred, along with the propelling of water resources development and utilization and development of the West Regions process, the a collection of 100m level even high earth and rockfill dam of 200-300m level is being built or is being about to and putting into operation, the large storehouse of these high dams is positioned at high seismic intensity area mostly, once even have an accident because earthquake is in danger, consequence will be catastrophic, therefore strengthen high earth and rockfill dam eaerthquake damage mechanism and earthquake resistant construction study on the efficiency and seem very necessary.
Conventional model test method can be divided into two classes both at home and abroad at present:
(1) surface vibration platform model test method routinely.This method is also referred to as 1g gravity field test method.Because earth and stone material stress-deformation characteristic has significantly non-linearly, under 1g gravity field condition, model stress level and prototype have big difference, and have departed from the requirement of similarity theory, and the test findings drawing does not often conform to the actual conditions, even contrary.
(2) centrifugal model test method.Centrifugal model is the best physical experiments method of dynamic similarity in theory, and the core of its technology is that the stress of centrifugal model equates with prototype stress, is the model test method such as guide " authentic type " such as grade that a model stress equates with prototype stress.It meets main crucial simulated condition, can carry out until the overall process equal stress mechanical simulation test destroying can directly adopt former shaped material, realizes more quickly and easily " entirely similar ".Therefore, centrifugal model test method is considered to one of best Mechanical Model Test method of similarity up to now.
2002, the Zhang Weimin of Nanjing Hydraulic Research Institute etc. succeeded in developing China's first desk centrifuge shaking table model system.Although it is pointed out that centrifugal model test theoretical method basic science is reasonable, similarity is good, because high earth and rockfill dam physical dimension is huge, cross dimensions is greater than 1000 meters, and length number km, even if the current hydro-extractor of maximum in the world also can not be realized " entirely similar " simulation of congruent stress.In predictable future, build up 15 meters of mesa dimensions, centrifugal acceleration 100g, oscillating mass 3000t, the hydro-extractor shaking table of gyrating mass 30000t, cannot imagine, its development costs is greater than 5,000,000,000 yuan, the possibility of almost not building.
Meaning of the present invention is, studies eaerthquake damage mechanism and the Problems of Disaster Preparedness And Reduction of the large scale engineerings such as high earth and rockfill dam by the little guide Dynamic Centrifugal Model Test means of unequal stress.
Summary of the invention
The invention reside in a kind of earthquake motive force centrifugal model test extension analytical approach is provided, object of the present invention is studied eaerthquake damage mechanism and the Problems of Disaster Preparedness And Reduction of the large scale engineerings such as high earth and rockfill dam with the little guide Dynamic Centrifugal Model Test of unequal stress.Technical thought of the present invention is, with the little guide Dynamic Centrifugal Model Test of n unequal stress, the method matching extension of approaching gradually prototype stress by model stress obtains the test findings of equal stress guide.
Technical scheme of the present invention is:
A kind of earthquake motive force centrifugal model test extension analytical approach, comprises the following steps:
Step 1) designs a model according to the requirement of geometric similarity, determines geometric similarity constant η
l=1/N;
Step 2) according to the technical capability of hydro-extractor shaking table, select n gravity similarity constant, as η
1 g, η
2 g, η
3 g, η
4 g... η
n gcarry out the test of n group model, wherein η
1 g, η
2 g, η
3 g, η
4 g... η
n gall be less than N, and be to increase gradually, approach gradually N's;
Step 3), according to similarity theory, is worked as η
gincrease gradually while approaching N, model stress also approaches prototype stress gradually, and the result of test also increases and approaches true value gradually, when η g=N, the result of test equals true value, and the method matching extension of approaching gradually prototype stress by model stress obtains the test findings of equal stress guide.
Described step 1 comprises the step of the geometric similarity guide designing a model:
According to formula η
l=l
m/ l
p=1/N, determines the geometric similarity guide of model according to the size of the physical dimension of the structures such as dam and vibration table surface size, wherein, and l
mfor model length, l
pfor prototype length, η
lgeometric similarity constant, η
gbe gravity similarity constant, g is gravity, and l is length, and subscript m represents model, and subscript p represents prototype.N is model scale, represents the multiple that model dwindles, and also represents the multiple that model acceleration of gravity increases;
Described step 2 comprises the following steps:
1) the similar guide of design weight acceleration:
According to the maximum functional acceleration level of hydro-extractor shaking table and the maximum ability that impulses, determine the similar guide η of maximum acceleration of gravity
g, by η
gbe equally divided into n(n>=4) equal portions, obtain η
1 g, η
2 g, η
3 g, η
4 g... η
n gthe similar guide of acceleration of gravity of n test, η
i gcan be calculated as follows:
η
i g=i·η
g/n
Wherein, i=1,2,3 ..n;
2) carry out the centrifugal model test of n group.
According to geometric similarity guide, be η
l, gravity similarity guide is respectively η
1 g, η
2 g, η
3 g, η
4 g... η
n g, carry out the centrifugal model test of n group, can obtain the result of n group test.As v
1, v
2, v
3, v
4... v
nthe sedimentation of the group of n group displacement, and n altogether, n group pore water pressure, n group stress, the acceleration response of n group etc., in Table 1:
Table 1 no-load voltage ratio chi centrifugal model test design table
Described step 3 comprises the following steps:
1) by model value, ask for former offset:
According to the similarity criterion of table 2, the model value of the physical quantitys such as the n group displacement in table 1, the sedimentation of n group, n group pore water pressure, n group stress, the acceleration response of n group is deduced respectively as former offset;
Table 2 Dynamic Centrifugal Model Test similarity criterion
| Symbol | Project | Dimension | Hydro-extractor shaking table |
| L | Size | L | η l |
| ρ | Density | ML -3 | η ρ |
| g | Acceleration | LT -2 | η g |
| C | Modulus coefficient | η C | |
| σ | Stress | ML -1T -2 | η σ=η lη ρη g |
| E | Elastic modulus | ML -1T -2 | η E=η l 1/2η ρ 1/2η g 1/2η C |
| c | Cohesiveness | ML -1T -2 | η c′=η lη ρη g |
| φ | Angle of friction | η φ′=1 | |
| ε | Strain | η ε=η l 1/2η ρ 1/2η g 1/2η C -1 |
| u | Displacement | L | η u=η l 3/2η ρ 1/2η g 1/2η C -1 |
| v | Speed | LT -1 | η v=η l 3/4η ρ 1/4η g 3/4η C -1/2 |
| k | Infiltration coefficient | LT -1 | η k=η l 3/4η ρ -3/4η g -1/4η C -1/2 |
| EI | Bendind rigidity | ML 3T -2 | η EI=η l 7/2η ρ 1/2η g 1/2η C |
| EA | Tension (pressure) rigidity | MLT -2 | η EAε=η l 3/2η ρ 1/2η g 1/2η C |
| T | Time | T | η T=η l 3/4η ρ 1/4η g -1/4η C -1/2 |
| f | Frequency | T -1 | η f=η l -3/4η ρ -1/4η g 1/4η C 1/2 |
| ξ | Soil body damping ratio | η ξ=1 |
2) the deduction analysis of prototype true value:
Take approximation theory gradually as basis, the principle equal according to gravity, according to the variation relation of physical quantity and gravity similarity guide, by analyzing the method for extension, the final prototype true value of the displacement of exporting prototype, sedimentation, acceleration response, pore water pressure, stress and so on physical quantities respectively, test combinations is counted n and is more than or equal to 4.
The invention has the beneficial effects as follows:
Earthquake motive force centrifugal model test extension analytical approach of the present invention has the following advantages:
(1) earthquake motive force centrifugal model test extension analytical approach of the present invention can be with less guide simulation heavy construction, makes hydro-extractor shaking table can be applied to the eaerthquake damage mechanism and the measure efficiency assay research of preventing and reducing natural disasters of the heavy constructions such as high earth and rockfill dam.
(2) earthquake motive force centrifugal model test extension analytical approach of the present invention provides the feasible way of a science for the heavy construction Seismic Problems model investigation that originally cannot carry out.
(3) earthquake motive force centrifugal model test extension analytical approach of the present invention has effectively overcome current conventional vibration platform model test (1g gravitational acceleration field) model and prototype stress level has big difference, the deficiency that test findings does not conform to the actual conditions, has significantly promoted the eaerthquake damage mechanism of the heavy constructions such as high earth and rockfill dam and the rationality of the measure efficiency assay result of preventing and reducing natural disasters.Several model test methods are relatively shown in Table 3:
Several model test method comparisons of table 3
Accompanying drawing explanation
Fig. 1 is the dam earthquake maximum settlement amount test findings figure of embodiments of the invention.
Embodiment
Below in conjunction with accompanying drawing, the invention will be further described:
(1) ultimate principle of the inventive method.
Centrifugal model test under normal conditions, gravity similarity constant η
gwith geometric similarity constant η
lrelation be:
η
g×η
l=1 (1)
η
l=l
m/l
p=1/N (2)
η
g=g
m/g
p=N (3)
In formula, (1) is the similarity criterion of centrifugal model, the η in (2) (3)
lgeometric similarity constant, η
gbe gravity similarity constant, g is gravity, and l is length, and subscript m represents model, and subscript p represents prototype.N is model scale, represents the multiple that model dwindles, and also represents the multiple that model acceleration of gravity increases.
Centrifugal model test method, by model being dwindled to N doubly, increases N method doubly by the gravitational acceleration field of model, carrys out implementation model and equates with the stress of prototype.According to the principle of similitude, meeting under the condition of (1), the test findings of centrifugal model meets requirement of similarity, and result is true value.
The problem to be solved in the present invention is when (1) formula cannot meet, and, under the condition of unequal stress, how to utilize centrifugal model research heavy construction problem.
Technical thought of the present invention is, first according to the requirement of geometric similarity, designs a model, and determines geometric similarity constant η
l=1/N, then selects n gravity similarity constant according to the technical capability of hydro-extractor shaking table, as η
1 g, η
2 g, η
3 g, η
4 g... η
n gcarry out the test of n group model, wherein η
1 g, η
2 g, η
3 g, η
4 g... η
n gall be less than N, and be to increase gradually, approach gradually N's.According to similarity theory, work as η
gincrease while approaching N gradually, model stress also approaches prototype stress gradually, and the result of test also increases and approaches true value gradually, works as η
gduring=N, the result of test equals true value.
For example, first the centrifugal model dynamic test of certain dam, can determine the similar guide η of model geometric according to the size of dam and the size of shaking table
l=1/N=1/200, then according to the technical capability of hydro-extractor shaking table, determines gravity similarity constant η
g, the maximum functional acceleration level of supposing this hydro-extractor shaking table is 100g, η
g=N=100, and plan to carry out 4 groups of tests, can be by η
g4 equal portions, obtain 4 gravity similarity constants, are respectively: η
1 g=25, η
2 g=50, η
3 g=75, η
4 g=100.According to similarity theory, in 4 groups of tests, η
4 g=100 test findings is to approach true value most.And work as η
g=200 o'clock, test findings was true value.So just can, on the basis of four groups of test figures, according to the theory of approaching gradually, carry out the analysis of internal relation, by matching extension, obtain final test findings.
(2) main technical step:
1) the geometric similarity guide designing a model.
According to formula (2), according to the size of the physical dimension of the structures such as dam and vibration table surface size, determine the geometric similarity guide of model.Wherein, l
mfor model length, l
pfor prototype length
2) the similar guide of design weight acceleration.
According to the maximum functional acceleration level of hydro-extractor shaking table and the maximum ability that impulses, determine the similar guide η of maximum acceleration of gravity
g, by η
gbe equally divided into n(n>=4) equal portions, obtain η
1 g, η
2 g, η
3 g, η
4 g... η
n gthe similar guide of acceleration of gravity of n test, η
i gcan be calculated as follows:
η
i g=i·η
g/n （4）
Wherein, i=1,2,3 ..n.
3) carry out the centrifugal model test of n group.
According to geometric similarity guide, be η
l, gravity similarity guide is respectively η
1 g, η
2 g, η
3 g, η
4 g... η
n g, carry out the centrifugal model test of n group, can obtain the result of n group test.As v
1, v
2, v
3, v
4... v
nthe sedimentation of the group of n group displacement, and n altogether, n group pore water pressure, n group stress, the acceleration response of n group etc.In Table 1.
Table 1 no-load voltage ratio chi centrifugal model test design table
4) by model value, ask for former offset.
Table 2 is Dynamic Centrifugal Model Test similarity criterions, similarity criterion is the basis of model test, and it is generally similar from (1) material, (2) geometric similarity, (3) kinematic similarity, several aspects such as (4) kinematic similarity have stipulated the similarity relation of model and prototype.It is at the beginning of model test, and the basis of carrying out modelling, after being also off-test, deduces model test result the foundation of prototype.
According to the similarity criterion of table 2, the model value of the physical quantitys such as the n group displacement in table 1, the sedimentation of n group, n group pore water pressure, n group stress, the acceleration response of n group is deduced respectively as former offset.
Table 2 Dynamic Centrifugal Model Test similarity criterion
| Symbol | Project | Dimension | Hydro-extractor shaking table |
| L | Size | L | η l |
| ρ | Density | ML -3 | η ρ |
| g | Acceleration | LT -2 | η g |
| C | Modulus coefficient | η C | |
| σ | Stress | ML -1T -2 | η σ=η lη ρη g |
| E | Elastic modulus | ML -1T -2 | η E=η l 1/2η ρ 1/2η g 1/2η C |
| c | Cohesiveness | ML -1T -2 | η c′=η lη ρη g |
| φ | Angle of friction | η φ′=1 | |
| ε | Strain | η ε=η l 1/2η ρ 1/2η g 1/2η C -1 | |
| u | Displacement | L | η u=η l 3/2η ρ 1/2η g 1/2η C -1 |
| v | Speed | LT -1 | η v=η l 3/4η ρ 1/4η g 3/4η C -1/2 |
| k | Infiltration coefficient | LT -1 | η k=η l 3/4η ρ -3/4η g -1/4η C -1/2 |
| EI | Bendind rigidity | ML 3T -2 | η EI=η l 7/2η ρ 1/2η g 1/2η C |
| EA | Tension (pressure) rigidity | MLT -2 | η EAε=η l 3/2η ρ 1/2η g 1/2η C |
| T | Time | T | η T=η l 3/4η ρ 1/4η g -1/4η C -1/2 |
| f | Frequency | T -1 | η f=η l -3/4η ρ -1/4η g 1/4η C 1/2 |
| ξ | Soil body damping ratio | η ξ=1 |
5) the deduction analysis of prototype true value.
Above-mentioned step is basic identical with general centrifugal model test method, there is no difference in principle.Difference is, waits guide centrifugal model test ((1) satisfies condition) to only have a trial value, by unique trial value, can obtain a former offset (due to the restriction of condition, the method cannot realize).And method of the present invention completes after test, corresponding same prototype physical quantity can obtain n the test findings obtaining under different gravity similarity guide conditions.As, earthquake sedimentation S, just has S
1, S
2, S
3... .S
n, in Table 1.According to similarity theory, this n test findings is to approach gradually true value, when gravity similarity guide=1, (being equivalent to the common ground shaking table of 1g), trial value apart from true value farthest, the difference of trial value and true value reduces with the increase of gravity similarity guide, when gravity similarity guide=N, trial value=true value.Take approximation theory gradually as basis, the principle equal according to gravity, according to the variation relation of physical quantity and gravity similarity guide, by analyzing the method for extension, can distinguish displacement, sedimentation, acceleration response, the pore water pressure of exporting prototype, the final prototype true value of stress and so on physical quantities.
Because earth and stone material stress-deformation characteristic has significantly non-linearly, the variation relation of different physical quantities and gravity similarity guide, is not unique funtcional relationship, and the key of extension precision is the selection of function and the selection of experimental group number.According to the result of research, displacement, sedimentation type variable are logarithmic relationship, are suitable for semilog method extension.Test combinations is counted n should be more than or equal to 4.
Case study on implementation---dam, long river earthquake safety evaluation and earthquake resistant construction centrifugal model test.
As Fig. 1, some hydropower station is sandy gravel core wall rockfill dam, maximum height of dam 240m, crest length 497.94m, width at dam crest 16.00m, bottom width 500m, upstream and downstream dam slope is 1:2.0, power centrifugal model theory routinely, at present all hydro-extractor shaking table all cannot be to its Experimental Study on Seismic Behavior research in the world.According to the test method of applicant's invention, how much guides of preference pattern are 1/750, and gravity guide is 10,20,30,40, and the Dynamic Centrifugal Model Test of this dam is carried out smoothly.The reaction of dam body seismic acceleration, cut-pff wall dynamic stress and dam body earthquake residual deformation result that test has obtained, and the validity of multiple strengthening measure for earthquake resistance is checked.Wherein, the dam earthquake residual deformation maximal value that test draws appears near dam crest, under design earthquake condition, dam maximum settlement amount is about 122-125cm, maximum horizontal displacement is about 25cm, substantially conform to current domestic and international high earth and rockfill dam seimic disaster census data, thereby proved the reliability of institute's invention test method.The earthquake resistant construction centrifugal model test of dam, long river is in Table 4:
The earthquake resistant construction centrifugal model test of dam, table 4 long river
By gravity guide η
gas horizontal ordinate, S is as vertical coordinate in earthquake sedimentation, draw in semilog coordinate, and by (10,184), (20,172), and (30,166), (40,161) four points connect a straight line, are extended to η
g=750, corresponding S value is earthquake sedimentation, can obtain S=122cm from figure.
Embodiment recited above is described the preferred embodiment of the present invention; not the spirit and scope of the present invention are limited; do not departing under design concept prerequisite of the present invention; various modification and improvement that in this area, common engineering technical personnel make technical scheme of the present invention; all should fall into protection scope of the present invention, the technology contents of request protection of the present invention has all been documented in claims.
Claims (4)
1. an earthquake motive force centrifugal model test extension analytical approach, is characterized in that comprising the following steps:
Step 1) designs a model according to the requirement of geometric similarity, determines geometric similarity constant η
l=1/N;
Step 2) according to the technical capability of hydro-extractor shaking table, select n gravity similarity constant, as η
1 g, η
2 g, η
3 g, η
4 g... η
n gcarry out the test of n group model, wherein η
1 g, η
2 g, η
3 g, η
4 g... η
n gall be less than N, and be to increase gradually, approach gradually N's;
Step 3), according to similarity theory, is worked as η
gincrease while approaching N gradually, model stress also approaches prototype stress gradually, and the result of test also increases and approaches true value gradually, works as η
gduring=N, the result of test equals true value.The method matching extension of approaching gradually prototype stress by model stress obtains the test findings of equal stress guide.
2. earthquake motive force centrifugal model test extension analytical approach according to claim 1, is characterized in that described step 1 comprises the step of the geometric similarity guide designing a model:
According to formula η
l=l
m/ l
p=1/N, determines the geometric similarity guide of model according to the size of the physical dimension of the structures such as dam and vibration table surface size, wherein, and l
mfor model length, l
pfor prototype length, η
lgeometric similarity constant, η
gbe gravity similarity constant, g is gravity, and l is length, and subscript m represents model, and subscript p represents prototype.N is model scale, represents the multiple that model dwindles, and also represents the multiple that model acceleration of gravity increases.
3. earthquake motive force centrifugal model test extension analytical approach according to claim 1, is characterized in that described step 2 comprises the following steps:
1) the similar guide of design weight acceleration:
According to the maximum functional acceleration level of hydro-extractor shaking table and the maximum ability that impulses, determine the similar guide η of maximum acceleration of gravity
g, by η
gbe equally divided into n(n>=4) equal portions, obtain η
1 g, η
2 g, η
3 g, η
4 g... η
n gthe similar guide of acceleration of gravity of n test, η
i gcan be calculated as follows:
η
i g=i·η
g/n
Wherein, i=1,2,3 ..n;
2) carry out the centrifugal model test of n group.
According to geometric similarity guide, be η
l, gravity similarity guide is respectively η
1 g, η
2 g, η
3 g, η
4 g... η
n g, carry out the centrifugal model test of n group, can obtain the result of n group test.As v
1, v
2, v
3, v
4... v
nthe sedimentation of the group of n group displacement, and n altogether, n group pore water pressure, n group stress, the acceleration response of n group etc., in Table 1:
Table 1 no-load voltage ratio chi centrifugal model test design table
4. earthquake motive force centrifugal model test extension analytical approach according to claim 1, is characterized in that described step 3 comprises the following steps:
1) by model value, ask for former offset:
According to the similarity criterion of table 2, the model value of the physical quantitys such as the n group displacement in table 1, the sedimentation of n group, n group pore water pressure, n group stress, the acceleration response of n group is deduced respectively as former offset;
Table 2 Dynamic Centrifugal Model Test similarity criterion
2) the deduction analysis of prototype true value:
Take approximation theory gradually as basis, the principle equal according to gravity, according to the variation relation of physical quantity and gravity similarity guide, by analyzing the method for extension, the final prototype true value of the displacement of exporting prototype, sedimentation, acceleration response, pore water pressure, stress and so on physical quantities respectively, test combinations is counted n and is more than or equal to 4.
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| CN107894311A (en) * | 2017-11-06 | 2018-04-10 | 中国水利水电科学研究院 | The model test method of earth and rockfill dam eaerthquake damage |
| CN110243413A (en) * | 2019-06-27 | 2019-09-17 | 浙江大学 | A kind of monitoring device and monitoring method of hypergravity centrifugal model physical state |
| CN110258435A (en) * | 2019-06-25 | 2019-09-20 | 中国水利水电科学研究院 | A kind of true stress high earth and rockfill dam dynamic test method of hundred meter levels off field |
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| CN112964587A (en) * | 2021-02-08 | 2021-06-15 | 水利部交通运输部国家能源局南京水利科学研究院 | Centrifugal model test device and method for simulating dam break of concrete panel dam |
| CN115201450A (en) * | 2022-06-23 | 2022-10-18 | 水利部交通运输部国家能源局南京水利科学研究院 | Prototype time and deformation calculation method for geotechnical centrifugal model test |
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