CN111563343A - Method for determining elasticity modulus of rock-fill concrete - Google Patents
Method for determining elasticity modulus of rock-fill concrete Download PDFInfo
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- 239000004567 concrete Substances 0.000 title claims abstract description 70
- 238000000034 method Methods 0.000 title claims abstract description 26
- 238000012360 testing method Methods 0.000 claims abstract description 38
- 239000011376 self-consolidating concrete Substances 0.000 claims abstract description 13
- 238000004364 calculation method Methods 0.000 claims abstract description 5
- 238000012935 Averaging Methods 0.000 claims abstract description 3
- 239000011435 rock Substances 0.000 claims description 9
- 238000006073 displacement reaction Methods 0.000 claims description 8
- 230000006835 compression Effects 0.000 claims description 7
- 238000007906 compression Methods 0.000 claims description 7
- 230000003068 static effect Effects 0.000 claims description 7
- 239000002245 particle Substances 0.000 claims description 5
- 238000010998 test method Methods 0.000 abstract description 2
- 238000010586 diagram Methods 0.000 description 3
- 238000010276 construction Methods 0.000 description 2
- 230000007547 defect Effects 0.000 description 2
- OKTJSMMVPCPJKN-UHFFFAOYSA-N Carbon Chemical compound [C] OKTJSMMVPCPJKN-UHFFFAOYSA-N 0.000 description 1
- 229910052799 carbon Inorganic materials 0.000 description 1
- 239000004568 cement Substances 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
- 230000036571 hydration Effects 0.000 description 1
- 238000006703 hydration reaction Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000000691 measurement method Methods 0.000 description 1
- 239000011382 roller-compacted concrete Substances 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
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- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- G06F2111/00—Details relating to CAD techniques
- G06F2111/10—Numerical modelling
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
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Abstract
The invention provides a method for determining the elastic modulus of rock-fill concrete. Firstly, elastic modulus parameters and Poisson's ratio of the rockfill and the self-compacting concrete are respectively obtained through a test method, and an elastic modulus expression of the self-compacting concrete is determined. And then, constructing a microscopic finite element model of the rock-fill concrete test piece, carrying out numerical value loading on the rock-fill concrete test piece by using a finite element method, calculating to obtain stress fields of the test pieces in different ages, and averaging the stress values of all parts of the test piece according to the volume to obtain the average stress of the test piece. And calculating to obtain the macroscopic elastic modulus of the test pieces in different ages according to a physical equation in the elasticity mechanics. And finally, performing curve fitting on the macroscopic elastic modulus data obtained by calculation to obtain a corresponding function expression. Compared with an empirical formula, the method has the advantages that: can reflect the hardening process of the rock-fill concrete and provide more comprehensive and accurate results.
Description
Technical Field
The invention relates to the technical field of hydraulic and hydroelectric engineering, in particular to a method for determining the elastic modulus of rock-fill concrete.
Background
Rock-Filled Concrete (RFC for short) means that firstly, lump stones (or pebbles) meeting certain particle size requirements are naturally piled on a warehouse surface, then Self-Compacting Concrete (SCC for short) meeting special requirements is poured on the surface of a Rock-Filled body, vibration is not needed, and the gaps of the Rock-Filled body are Filled only by the Self weight of the Rock-Filled body, so that complete and compact Concrete is formed, as shown in fig. 1.
Compared with normal concrete and roller compacted concrete which are commonly used in hydraulic and hydroelectric engineering, the rock-filled concrete has the advantages of less cement consumption, larger aggregate consumption, low carbon, environmental protection, low heat of hydration, simple and convenient process, low manufacturing cost, high construction speed and the like. The rock-fill concrete has great application potential in large-volume concrete engineering.
The elastic modulus is an important index for measuring the deformation difficulty of concrete, is an important basis for designing a concrete structure, and is generally directly measured by tests. However, since the particle size of the rock-fill in the rock-fill concrete can be as high as 1m, it is difficult to directly perform a static compression elastic modulus test, so that the main method for obtaining the elastic modulus of the rock-fill concrete at present is to directly average the elastic modulus of the self-compacting concrete and the elastic modulus of the rock-fill according to the rock-fill rate by using an empirical formula. The value taking method is too dependent on experience, the hardening process of the rock-fill concrete cannot be accurately reflected, and the given result is prone to have deviation.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for determining the elasticity modulus of rock-fill concrete, and solves the defects in the prior art.
In order to realize the purpose, the technical scheme adopted by the invention is as follows:
a method for determining the elastic modulus of rock-fill concrete comprises the following steps:
s1 obtaining the elastic modulus E of the rockfill through a static compression elastic modulus testRAnd poisson ratio vRThe value of (c).
S2 obtaining elastic modulus parameter E of self-compacting concrete through static compression elastic modulus test0 sccA, b and Poisson's ratio vsccDetermining the modulus of elasticity Escc(τscc) Is shown in formula 1, wherein tausccIndicating the age of the self-compacting concrete.
And S3, measuring the rockfill rate n of the rockfill concrete.
S4, establishing a microscopic finite element model of the rock-fill concrete test piece in a Cartesian coordinate system according to the rock-fill rate n and the particle size distribution condition of the rock-fill, and applying constraint to the model to enable the model to be subjected to displacement constraint in the z direction and to be capable of freely deforming in the xoy plane;
s5, based on the calculation parameters obtained in the steps S1-S4 and the established model, applying a displacement load △ L in the z direction to the rock-fill concrete specimen, and calculating the tau in different ages by using a finite element methodRFCThe stress field of the test piece.
S6, calculating each unit in the obtained stress fieldThe z-direction stress value is averaged according to the volume to obtain the average z-direction stress of the rock-filled concrete test piece
As shown in equation 2.
In equation 2, x, y, z represent the coordinates of the cartesian coordinate system in the model, τRFCIndicates the age of the rock-fill concrete, i indicates the number of cells in the model, m is the total number of cells in the model,
an indication of age τRFCThe z-direction stress value at the midpoint (x, y, z) of the test piece, △ Ri represents the volume of the ith cell in the model, and V is the total volume of the model.
S7. the z-direction strain of the rock-fill concrete specimen under the action of the z-direction displacement load △ L
Is composed of
And S8, according to the constraint condition applied to the model in the S4, the rock-fill concrete test piece can be freely deformed on the xoy plane, so that the average normal stress of the rock-fill concrete test piece in the x direction and the y direction is zero, namely:
s9, calculating to obtain the macroscopic elastic modulus E of the rock-fill concrete test pieces of different ages according to the physical equation of elasticity mechanics based on the data obtained from S6-S8RFC(τRFC) As shown in formula 5:
wherein, vRFCIs the poisson's ratio of the rock-fill concrete.
S10, calculating the macroscopic elastic modulus E of the rock-fill concrete in different agesRFC(τRFC) And (4) performing data fitting, wherein the fitting method is basic knowledge in the field, and obtaining a double-exponential expression of the macroscopic elastic modulus of the rock-fill concrete, as shown in a formula 6.
Wherein E0 RFCA, B is the modulus of elasticity parameter
And S11, obtaining the macroscopic elastic modulus value of the rock-fill concrete at any age according to the formula 6.
Compared with the prior art, the invention has the advantages that:
from the aspect of mesoscopic level, the macroscopic mechanical properties of the rock-fill concrete are calculated. The method comprises the steps of respectively considering the elastic modulus of the rock pile and the hardening process of the self-compacting concrete, carrying out numerical value loading on the rock pile concrete test piece by using a finite element method, calculating the macroscopic elastic modulus of the test piece in different ages according to the physical equation of elasticity mechanics, and finally carrying out curve fitting on the obtained elastic modulus data to obtain a corresponding function expression. By applying the expression, the elastic modulus value of the rock-fill concrete at any moment can be accurately obtained, and accurate parameters are provided for the rock-fill concrete structure design and numerical simulation.
Drawings
FIG. 1 is a schematic view showing the construction of rock-fill concrete;
FIG. 2 is a microscopic finite element model of a rock-fill concrete specimen;
FIG. 3 is a stress field diagram of a 0.5 d-3.5 d age rock-filled concrete specimen calculated by a finite element method; wherein fig. 3a is 0.5d, fig. 3b is 1.0d, fig. 3c is 1.5d, fig. 3d is 2d, fig. 3e is 2.5d, and fig. 3f is 3.5 d;
FIG. 4 is a stress field diagram of a 5 d-30 d age rock-filled concrete specimen calculated by a finite element method; wherein fig. 4a is 5d, fig. 4b is 7.5d, fig. 4c is 10d, fig. 4d is 14d, fig. 4e is 20d, fig. 4f is 30 d;
FIG. 5 is a stress field diagram of a 45 d-180 d age rock-filled concrete specimen calculated by a finite element method; where fig. 5a is 45d, fig. 5b is 90d, and fig. 5c is 180 d.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail below with reference to the accompanying drawings by way of examples.
The invention discloses a method for determining the elastic modulus of rock-fill concrete, which comprises the following steps:
s1 obtaining elastic modulus E of the rockfill through static compression elastic modulus test (the test method is the basic knowledge in the field and is not explained in detail here)RIs 25GPa and the Poisson ratio vRIs 0.25.
S2, obtaining the elastic modulus parameter of the self-compacting concrete through a static compression elastic modulus test, and determining the elastic modulus E of the self-compacting concretescc(τscc) Is expressed as shown in formula 1, wherein tausccIndicating the age of the self-compacting concrete.
S3, the rockfill ratio n of the rockfill concrete is measured to be 0.53 (the measurement method is the basic knowledge in the field).
And S4, establishing a microscopic finite element model of the rock-fill concrete test piece according to the rock-fill rate n and the particle size distribution of the rock-fill, wherein the model is a cube with the side length L being 4.5m as shown in the attached figure 2. Applying a z-direction constraint at the bottom of the model, applying an x-direction constraint at the points A and B, and applying a y-direction constraint at the points B and C;
s5, based on the calculation parameters obtained in the steps S1-S4 and the established model, applying a displacement load △ L in the z direction to the rock-fill concrete specimen to be 0.01m, and calculating tau in different ages by using a finite element methodRFCThe stress field of the test piece of (2), as shown in FIG. 3(calculation methods are basic knowledge in the field).
S6, averaging the calculated z-direction stress values of all units in the stress field according to the volume (as shown in a formula 2), and obtaining the average z-direction stress of the rock-filled concrete test piece
As shown in table 1.
In equation 2, x, y, z represent the coordinates of the cartesian coordinate system in the model, τRFCIndicates the age of the rock-fill concrete, i indicates the number of cells in the model, m is the total number of cells in the model,
an indication of age τRFCThe z-direction stress value at the midpoint (x, y, z) of the test piece, △ Ri represents the volume of the ith cell in the model, and V is the total volume of the model.
TABLE 1
S7 calculating the z-direction strain of the rock-fill concrete specimen under the action of the z-direction displacement load △ L by using the formula 3
Is 0.00222.
And S8, according to the constraint condition applied to the model in S4, judging that the rock-fill concrete test piece can deform freely on the xoy plane, so that the average normal stress of the rock-fill concrete test piece in the x direction and the y direction is zero, namely:
s9, based on the data obtained from S6-S8, according to the physical equation of elasticity mechanics (basic knowledge in the field), the macroscopic elastic modulus E of the rock-fill concrete test pieces of different ages can be calculated and obtained by the formula 5RFC(τRFC) As shown in table 2, the results of,
wherein, vRFCIs the poisson's ratio of the rock-fill concrete.
TABLE 2
S10, calculating the macroscopic elastic modulus E of the rock-fill concrete in different agesRFC(τRFC) And (4) performing data fitting, wherein the fitting method is basic knowledge in the field, and obtaining a double-exponential expression (shown in an equation 6) of the macroscopic elastic modulus of the rock-fill concrete.
ERFC(τRFC)＝27.35τRFC 0.69/(0.87+τRFC 0.69) (6)
And S11, obtaining the macroscopic elastic modulus value of the rock-fill concrete at any age according to the formula 6.
It will be appreciated by those of ordinary skill in the art that the examples described herein are intended to assist the reader in understanding the manner in which the invention is practiced, and it is to be understood that the scope of the invention is not limited to such specifically recited statements and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (1)
1. A method for determining the elastic modulus of rock-fill concrete is characterized by comprising the following steps:
s1 obtaining the elastic modulus E of the rockfill through a static compression elastic modulus testRAnd poisson ratio vRA value of (d);
s2 obtaining elastic modulus parameter E of self-compacting concrete through static compression elastic modulus test0 sccA, b and Poisson's ratio vsccDetermining the modulus of elasticity Escc(τscc) Is expressed as shown in formula 1, wherein tausccIndicating the age of the self-compacting concrete;
s3, determining the rockfill rate n of the rockfill concrete;
s4, establishing a microscopic finite element model of the rock-fill concrete test piece in a Cartesian coordinate system according to the rock-fill rate n and the particle size distribution condition of the rock-fill, and applying constraint to the model to enable the model to be subjected to displacement constraint in the z direction and to be capable of freely deforming in the xoy plane;
s5, based on the calculation parameters obtained in the steps S1-S4 and the established model, applying z-direction displacement load delta L to the rock-fill concrete specimen, and calculating tau in different ages by using a finite element methodRFCThe stress field of the test piece;
s6, averaging the calculated z-direction stress values of all units in the stress field according to the volume to obtain the average z-direction stress of the rock-filled concrete test piece
As shown in equation 2;
in equation 2, x, y, z represent the coordinates of the cartesian coordinate system in the model, τRFCIndicates the age of the rock-fill concrete, i indicates the number of cells in the model, m is the total number of cells in the model,
an indication of age τRFCThe z-direction stress value at the midpoint (x, y, z) of the test piece, wherein delta Ri represents the volume of the ith unit in the model, and V is the total volume of the model;
s7. the z-direction strain generated by the rock-fill concrete test piece under the action of the z-direction displacement load Delta L
Is composed of
And S8, according to the constraint condition applied to the model in the S4, the rock-fill concrete test piece can be freely deformed on the xoy plane, so that the average normal stress of the rock-fill concrete test piece in the x direction and the y direction is zero, namely:
s9, calculating to obtain the macroscopic elastic modulus E of the rock-fill concrete test pieces of different ages according to the physical equation of elasticity mechanics based on the data obtained from S6-S8RFC(τRFC) As shown in formula 5:
wherein, vRFCIs the Poisson's ratio of the rock-fill concrete;
s10, calculating the macroscopic elastic modulus E of the rock-fill concrete in different agesRFC(τRFC) Fitting the data to obtain the rock-fill mixtureThe double-exponential expression of the macroscopic elastic modulus of the concrete is shown in formula 6;
wherein E0 RFCA, B is the modulus of elasticity parameter
And S11, obtaining the macroscopic elastic modulus value of the rock-fill concrete at any age according to the formula 6.
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Cited By (3)
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| CN112765871A (en) * | 2021-04-07 | 2021-05-07 | 中国人民解放军国防科技大学 | Parallel particle tracking method and device based on curve coordinates |
| CN113211649A (en) * | 2021-05-20 | 2021-08-06 | 李友彬 | Method for cutting, processing and forming rock-fill concrete large test piece |
| CN116644599A (en) * | 2023-06-05 | 2023-08-25 | 重庆大学 | Crack prediction method based on elastic modulus of concrete under capillary pore stress effect |
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