CN103669317A - Method for measuring dynamic subgrade reaction coefficient of two-parameter foundation through rigid plate dynamic test - Google Patents
Method for measuring dynamic subgrade reaction coefficient of two-parameter foundation through rigid plate dynamic test Download PDFInfo
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- CN103669317A CN103669317A CN201210333942.2A CN201210333942A CN103669317A CN 103669317 A CN103669317 A CN 103669317A CN 201210333942 A CN201210333942 A CN 201210333942A CN 103669317 A CN103669317 A CN 103669317A
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- parameter foundation
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Abstract
The invention discloses a method for measuring the dynamic subgrade reaction coefficient of a two-parameter foundation through a rigid plate dynamic test. The method includes the steps of as can be seen in the first drawing, dividing the area of the foundation under the action of a rigid plate into an inter-plate area, a plate edge area and a plate corner area according to the characteristics of a two-parameter foundation model, solving an oscillation equation of the two-parameter foundation-rigid plate system, solving a system inherent frequency expression, setting up the relational expression of the inherent frequency of the two-parameter foundation-rigid plate system, the foundation subgrade reaction coefficient (k,G), the rigid plate size (a*b), the rigid plate mass Mb and the vibration soil unit area equivalent mass mf, conducting the test of the inherent frequency of the two-parameter foundation-rigid plate system through the dynamic test method according to the relational expression, setting up an equation set according to the frequency test result, and solving the equation set to obtain the dynamic subgrade reaction coefficient (k,G) of the two-parameter foundation. The concept that the dynamic subgrade reaction coefficient of the two-parameter foundation is obtained on the basis of theoretical analysis and by combining the method with dynamic test actual measurement is clear, the method can be implemented with the help of an existing frequently-used dynamic test device and method, and the method is convenient to apply and popularize.
Description
Technical field
The present invention relates to field of civil engineering, specifically refer to a kind of method of utilizing the moving coefficient of subgrade reaction of rigid slab dynamic test field survey Two_Parameter Foundation.
Background technology
The mechanical calculation theory of basic engineering method institute foundation is mainly the elastic foundation plate theory based under action of static load at present, and ground coefficient of subgrade reaction used is quiet coefficient of subgrade reaction.Yet the load that bear the building foundation under real road road surface, airfield runway, Power-equipment Foundation and geological process is generally dynamic load.A large amount of analysis and research show, under dynamic load function, between basis and ground, have dynamic interaction, and under dynamic loading, the dynamic response problem on basis is also more and more concerned in recent years.At present, due to the noncontinuity of foundation soil, definite existence of moving coefficient of subgrade reaction in Two_Parameter Foundation model is much difficult, there is no in the industry maturation or more universally recognized method, more there is no feasible field survey method.
Summary of the invention
For the moving coefficient of subgrade reaction of current Two_Parameter Foundation, determine difficult problem, the present invention provides a kind of method of utilizing the moving coefficient of subgrade reaction of Different Plane size rigid slab dynamic test field survey Two_Parameter Foundation on the basis of theory analysis, can effectively deal with problems and easy to utilize.
The technical scheme that the present invention adopted is for achieving the above object:
First according to the characteristic of Two_Parameter Foundation model, the foundation region under rigid slab effect is divided into plate inner region, edges of boards region and plate angular zone (Fig. 1), try to achieve Two_Parameter Foundation---the vibration equation of rigid slab system and the expression formula of system frequency, set up Two_Parameter Foundation---the intrinsic frequency of rigid slab system
, the moving coefficient of subgrade reaction of ground (
k,
g), rigid slab size (
a*
b), rigid slab quality
m band the ginseng native unit area equivalent mass m that shakes
fbetween relational expression.
By existing conventional Methods for Measuring Dynamic Characteristics, carry out dynamic test, measure Two_Parameter Foundation---the intrinsic frequency of rigid slab system, according to the intrinsic frequency of rigid slab system
, the moving coefficient of subgrade reaction of ground (
k,
g), rigid slab size (
a*
b), rigid slab quality
m band the ginseng native unit area equivalent mass m that shakes
fbetween relational expression, set up a moving coefficient of subgrade reaction with Two_Parameter Foundation (
k,
g) for the relation equation of unknown quantity to be asked.
Adopt two or more rigid slab to carry out dynamic test, according to preceding method, can set up moving coefficient of subgrade reaction about Two_Parameter Foundation (
k,
g) a prescription journey, solve this equation group, can obtain Two_Parameter Foundation moving coefficient of subgrade reaction (
k,
g).
Below in conjunction with accompanying drawing, the present invention is further described.
Accompanying drawing explanation
Fig. 1 is that schematic diagram is divided in elastic foundation plate plate Zhou Tuti region, and under plate, the soil body is plate inner region,
a 2,
a 4,
a 5,
a 7for edges of boards region,
a 1,
a 3,
a 6,
a 8for plate angular zone.
The specific embodiment
By reference to the accompanying drawings, specific embodiment of the invention step is as follows:
Plate is on Two_Parameter Foundation, and under plate, ground play supporting role, all grounds of plate also participate in work.For making problem reduction, during the rigid body mode of research Two_Parameter Foundation plate, suppose that in survey region, ground is evenly distributed, the moving coefficient of subgrade reaction of ground compression
kwith the moving coefficient of subgrade reaction of shearing
gfor normal value.
By ground under Rectangular Rigid Plate be divided into plate inner region, edges of boards region (
a 2,
a 4,
a 5,
a 7) and plate angular zone (
a 1,
a 3,
a 6,
a 8), in vibration processes, plate inner region amount of deflection is
.According to fringe conditions: each region soil body surface amount of deflection of infinite point is zero, with plate joint be edges of boards or plate angular deflection,
, determine each region soil body surface amount of deflection expression formula.
Region
a 1:
;
Region
a 2:
;
Region
a 3:
;
Region
a 4:
;
Region
a 5:
;
Region
a 6:
;
Region
a 7:
;
Region
a 8:
.
For obtaining the oscillatory differential equation of Rectangular Rigid Plate on Two_Parameter Foundation, first study the vibration kinetic energy of the Two_Parameter Foundation-rigid slab system shown in Fig. 1
tand potential energy
v.
Plate (planar dimension
a*
b, unit plane density
m, containing the ginseng soil body equivalent mass of shaking, longitudinal rigidity plate and the ginseng soil body equivalence gross mass of shaking is
m) amount of deflection be
w, the kinetic energy of plate
tfor:
(1)
Soil body compression potential energy under plate
v 1with shearing potential energy
v 2for:
(3)
Plate Zhou Tuti compresses potential energy
v 3with shearing potential energy
v 4for:
(5)
The potential energy of Eguivalent nodal loads on plate,
The total kinetic energy of Two_Parameter Foundation-rigid slab system
twith total potential energy
vbe respectively:
(7)
According to Hamiton's principle:
Will
twith
vexpression formula substitution above formula, obtain Two_Parameter Foundation-rigid slab system vibration equation:
Be able to thus system free vibration frequency expression formula
(10a)
For square plate,
, above formula becomes
(10b)
For simplifying, suppose that under unit area, soil body equivalence mass of vibration is
m f, the quality of pure rigid slab is designated as
m b,
System free vibration frequency expression formula
For square plate,
, above formula becomes
(12b)
(single order) intrinsic frequency of visible Two_Parameter Foundation-rigid slab system vibration
with ground coefficient of subgrade reaction
kwith
g, rigid slab planar dimension
awith
b, rigid slab quality
m band the ginseng soil body unit area equivalent mass m that shakes
frelevant.For on-the-spot test,
k,
g,
m funknown quantity,
a,
b,
m bbe known quantity, be test parameters.
By existing conventional Methods for Measuring Dynamic Characteristics, carry out dynamic test, the rigid slab of choosing Different Plane size or different quality is carried out the intrinsic frequency test of dynamic characteristics, can obtain a class frequency test result, utilize formula (12) can set up a prescription journey, by solving equation group, can obtain
k,
g,
m fvalue.
Based on formula (12), can consider to change different test parameters (
a,
b,
m b), obtain different unknown quantitys (
k,
g,
m f).Join the soil body unit area equivalent mass of shaking
m fto obtain by other method.Here provide by changing the bed-plate dimension of rigid slab
a*
b, obtain ground coefficient of subgrade reaction
k,
gmethod.
For solving, facilitate and guarantee precision, considering to have the plate of three kinds of Different Plane sizes:
a 1*
b 1,
a 2*
b 2,
a 3*
b 3, have respectively:
Above three formulas are subtracted each other and are obtained successively
Can obtain,
(16)
Wherein, coefficient
a,
bas follows:
(1) when adopting square rigid slab,
and
m b1≠
m b2≠
m b3time, formula (15), (16) and (17) become:
Wherein, coefficient
a,
bbecome:
(2) when each side's board size
a 1:
a 2:
a 3=1:2:3 and
m b1≠
m b2≠
m b3time, formula (15), (16) and (17) become:
Wherein, coefficient
a,
bbecome:
(23)
(3) when each side's board size
a 1:
a 2:
a 3=1:2:3 and
m b1:
m b2:
m b3it is identical that=1:4:9(is equivalent to each plate thickness) time, formula (15), (16) and (17) become:
(25)
Wherein, coefficient
a,
bbecome:
Join the soil body unit area equivalent mass of shaking
m fcan obtain by the following method:
The bottom surface of maintenance rigid slab (face of ground contact) size (
a*
b) constant, by changing counterweight, realize the quality of two or more rigid slab, might as well consider to get two kinds of quality of rigid slab
m b1with
m b2, can obtain:
(27)
Can obtain
When employing side's plate,
a=
b, and 2
m b1=
m b2time, (14) formula becomes
Change rigid slab be of a size of (
a 1 *
b 1 ), (
a 2 *
b 2 ), (
a 3 *
b 3 ) ..., according to said method, can obtain successively the required ginseng soil body unit area equivalent mass of shaking
m f1,
m f2,
m f3
In a word, the concrete condition of implementing according to test, there is different forms formula (15), (16) and (17), all can realize moving coefficient of subgrade reaction (
k,
g) field survey obtain.
Claims (3)
1. one kind is utilized rigid slab dynamic test to measure the method that Two_Parameter Foundation moves coefficient of subgrade reaction, it is characterized in that: according to the mechanical characteristic of Two_Parameter Foundation, foundation region under rigid slab effect is divided into plate inner region and plate exterior domain, try to achieve Two_Parameter Foundation---the vibration equation of rigid slab system and system frequency table reach formula, set up Two_Parameter Foundation---the intrinsic frequency of rigid slab system
, the moving coefficient of subgrade reaction of ground (
k,
g), rigid slab size (
a*
b), rigid slab quality
m band the ginseng native unit area equivalent mass m that shakes
fbetween relational expression; Utilize this relational expression, adopt dynamic test method to carry out Two_Parameter Foundation---the intrinsic frequency test of rigid slab system, utilize frequency test result to set up a prescription journey, solve the moving coefficient of subgrade reaction that this equation group obtains Two_Parameter Foundation (
k,
g).
2. the method for utilizing rigid slab dynamic test to measure the moving coefficient of subgrade reaction of Two_Parameter Foundation according to claim 1, is characterized in that: adopt Rectangular Rigid Plate, by Rectangular Rigid Plate plate exterior domain be divided into edges of boards region (
a 2,
a 4,
a 5,
a) and plate angular zone (
a 1,
a 3,
a 6,
a 8).
3. the method for utilizing rigid slab dynamic test to measure the moving coefficient of subgrade reaction of Two_Parameter Foundation according to claim 1, is characterized in that: adopt two or more rigid slab to carry out dynamic test, obtain one group of corresponding frequency test result.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104762945A (en) * | 2015-04-21 | 2015-07-08 | 中铁上海设计院集团有限公司 | Correction method for in-situ horizontal bedding coefficient test |
Citations (4)
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|---|---|---|---|---|
| JPH0755668A (en) * | 1993-08-06 | 1995-03-03 | Jiban Hoshiyou Kyokai:Kk | Measuring method for modulus of foundation |
| JP2004332400A (en) * | 2003-05-08 | 2004-11-25 | Shimizu Corp | Method of measuring coefficient of subgrade reaction, device for deriving coefficient of subgrade reaction, method of constructing subgrade, and program |
| CN101377079A (en) * | 2008-10-08 | 2009-03-04 | 上海市政工程设计研究总院 | Method for measuring foundation bed coefficient indoor |
| CN101650286A (en) * | 2009-08-26 | 2010-02-17 | 中冶集团武汉勘察研究院有限公司 | Bedding coefficient testing method |
-
2012
- 2012-09-11 CN CN201210333942.2A patent/CN103669317B/en not_active Expired - Fee Related
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH0755668A (en) * | 1993-08-06 | 1995-03-03 | Jiban Hoshiyou Kyokai:Kk | Measuring method for modulus of foundation |
| JP2004332400A (en) * | 2003-05-08 | 2004-11-25 | Shimizu Corp | Method of measuring coefficient of subgrade reaction, device for deriving coefficient of subgrade reaction, method of constructing subgrade, and program |
| CN101377079A (en) * | 2008-10-08 | 2009-03-04 | 上海市政工程设计研究总院 | Method for measuring foundation bed coefficient indoor |
| CN101650286A (en) * | 2009-08-26 | 2010-02-17 | 中冶集团武汉勘察研究院有限公司 | Bedding coefficient testing method |
Non-Patent Citations (1)
| Title |
|---|
| 张望喜: "混凝土地基板静、动力特性试验与研究", 《中国博士学位论文全文数据库工程科技2辑》, no. 1, 15 March 2004 (2004-03-15), pages 3 - 39 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104762945A (en) * | 2015-04-21 | 2015-07-08 | 中铁上海设计院集团有限公司 | Correction method for in-situ horizontal bedding coefficient test |
| CN104762945B (en) * | 2015-04-21 | 2016-07-06 | 中铁上海设计院集团有限公司 | A kind of modification method of original position horizontal foundation modulus test |
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