CN111563343A - A method for determining the elastic modulus of rockfill concrete - Google Patents

Abstract

The invention provides a method for determining the elastic modulus of rockfill concrete. First, the elastic modulus parameters and Poisson's ratio of rockfill and self-compacting concrete were obtained by experimental method, and the elastic modulus expression of self-compacting concrete was determined. Then, a meso-finite element model of the rockfill concrete specimen is constructed, and the rockfill concrete specimen is numerically loaded by the finite element method, and the stress field of the specimen at different ages is calculated. The volumes are averaged to obtain the average stress of the specimen. According to the physical equation in elastic mechanics, the macroscopic elastic modulus of the specimens of different ages is calculated. Finally, curve fitting is performed on the calculated macroscopic elastic modulus data, and the corresponding function expression is obtained. Compared with the empirical formula, the present invention has the advantage that it can reflect the hardening process of the rockfill concrete and provide more comprehensive and accurate results.

Description

A method for determining the elastic modulus of rockfill concrete

technical field

The invention relates to the technical field of water conservancy and hydropower engineering, in particular to a method for determining the elastic modulus of rockfill concrete.

Background technique

Rock-Filled Concrete (RFC for short) refers to the natural filling of the silo surface with boulders (or pebbles) that meet the requirements of a certain particle size, and then pouring self-compacting concrete (Self-Compacting) that meets the special requirements on the surface of the rockfill body. Concrete, referred to as SCC), does not need to vibrate, and only relies on its own weight to fill the voids of the rockfill body to form a complete and dense concrete, as shown in Figure 1.

Compared with normal concrete and roller compacted concrete commonly used in water conservancy and hydropower projects, rockfill concrete uses less cement and a larger amount of aggregate, and has the advantages of low carbon and environmental protection, low hydration heat, simple process, low cost, and construction The advantages of fast speed and so on. Rockfill concrete has great application potential in mass concrete engineering.

The elastic modulus is an important index to measure the difficulty of concrete deformation and an important basis for the design of concrete structures. It is generally measured directly by experiments. However, since the particle size of rockfill concrete can be as high as 1 m, it is difficult to directly test the elastic modulus of static compression. Therefore, the main method to obtain the elastic modulus of rockfill concrete is to use empirical formulas to directly The elastic modulus of compact concrete and the elastic modulus of rockfill are averaged according to the rockfill rate. This method of value selection relies too much on experience and cannot accurately reflect the hardening process of rockfill concrete, and the results are often biased.

SUMMARY OF THE INVENTION

Aiming at the defects of the prior art, the present invention provides a method for determining the elastic modulus of rockfill concrete, which solves the defects existing in the prior art.

In order to realize the above purpose of the invention, the technical scheme adopted by the present invention is as follows:

A method for determining elastic modulus of rockfill concrete, comprising the following steps:

S1: Obtain the values of the elastic modulus _{ER and Poisson's ratio ν R of} the rockfill through the static compression elastic modulus test.

S2: Obtain the elastic modulus parameters E ⁰ _scc , a , b and Poisson’s ratio ν _scc of the self-compacting concrete through the static compression elastic modulus test, and determine the composite exponential expression of its elastic modulus E _scc (τ _scc ) As shown in Equation 1, where τ _scc represents the age of the self-compacting concrete.

S3: Determine the rockfill rate n of the rockfill concrete.

S4: According to the rockfill rate n and the particle size distribution of the rockfill, in the Cartesian coordinate system, a meso-scale finite element model of the rockfill concrete specimen is established, and constraints are imposed on the model, so that the model is subject to displacement constraints in the z direction , which can be freely deformed in the xoy plane;

S5: Based on the calculation parameters obtained in steps S1 to S4 and the established model, apply a displacement load ΔL in the z-direction to the rockfill concrete specimen, and use the finite element method to calculate the stress field of the specimens with different ages τ _RFC .

如公式2所示。S6. Average the z-direction stress values of each element in the calculated stress field by volume to obtain the average z-direction stress of the rockfill concrete specimen

as shown in Equation 2.

表示龄期为τ_RFC的试件中点(x,y,z)处的z向应力值，△Ri表示模型中第i个单元的体积，V 为模型的总体积。In formula 2, x, y, z represent the coordinates of the Cartesian coordinate system in the model, τ _RFC represents the age of rockfill concrete, i represents the unit number in the model, m is the total number of units in the model,

represents the z-direction stress value at the midpoint (x, y, z) of the specimen with age τ _RFC , ΔRi represents the volume of the i-th element in the model, and V is the total volume of the model.

为S7: The z-direction strain of the rockfill concrete specimen under the action of the z-direction displacement load △L

for

S8: According to the constraints imposed on the model in S4, the rockfill concrete specimen can be freely deformed on the xoy plane. Therefore, the average normal stress of the rockfill concrete specimen in both the x and y directions is zero, namely:

S9: Based on the data obtained from S6 to S8, and according to the physical equation of elasticity, the macroscopic elastic modulus E _RFC (τ _RFC ) of rockfill concrete specimens of different ages is calculated, as shown in Equation 5:

where ν _RFC is the Poisson's ratio of rockfill concrete.

S10: perform data fitting on the calculated macroscopic elastic modulus E _RFC (τ _RFC ) of rockfill concrete at different ages, (the fitting method is the basic knowledge in the field), and obtain the macroscopic elastic modulus of rockfill concrete. A double exponential expression, as shown in Equation 6.

Among them, E ⁰ _RFC , A and B are elastic modulus parameters

S11: According to formula 6, the macroscopic elastic modulus value of rockfill concrete at any age is obtained.

Compared with the prior art, the advantages of the present invention are:

From the microscopic level, the macroscopic mechanical properties of rockfill concrete are deduced. Considering the elastic modulus of rockfill and the hardening process of self-compacting concrete respectively, the rockfill concrete specimens were numerically loaded by the finite element method, and the macroscopic elastic modulus of the specimens at different ages was calculated according to the physical equation of elastic mechanics. Curve fitting is performed on the obtained elastic modulus data to obtain the corresponding function expression. Using this expression, the elastic modulus value of rockfill concrete at any time can be accurately obtained, and accurate parameters can be provided for the design and numerical simulation of rockfill concrete structure.

Description of drawings

Fig. 1 is the composition schematic diagram of rockfill concrete;

Figure 2 shows the meso-scale finite element model of the rockfill concrete specimen;

Figure 3 is a schematic diagram of the stress field of a rockfill concrete specimen with an age of 0.5d to 3.5d calculated by the finite element method; Figure 3a is 0.5d, Figure 3b is 1.0d, Figure 3c is 1.5d, and Figure 3d is 2d, Fig. 3e is 2.5d, Fig. 3f is 3.5d;

Figure 4 is a schematic diagram of the stress field of the rockfill concrete specimens aged 5d to 30d calculated by the finite element method; Figure 4a is 5d, Figure 4b is 7.5d, Figure 4c is 10d, Figure 4d is 14d, Figure 4e is 20d, and Figure 4f is 30d;

Figure 5 is a schematic diagram of the stress field of rockfill concrete specimens aged 45d to 180d calculated by the finite element method; Figure 5a is 45d, Figure 5b is 90d, and Figure 5c is 180d.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below according to the accompanying drawings and examples.

A method for determining the elastic modulus of rockfill concrete disclosed in the present invention comprises the following steps:

S1: Through the static compression elastic modulus test (the test method is the basic knowledge in the field, and will not be described in detail here), the elastic modulus _{ER of the rockfill is obtained as 25GPa, and the Poisson's ratio ν R is} 0.25.

S2: Obtain the elastic modulus parameters of the self-compacting concrete through the static compression elastic modulus test, and determine the double exponential expression of its elastic modulus E _scc (τ _scc ) (as shown in Equation 1), where τ _scc represents the age of self-compacting concrete.

S3: The rockfill ratio n of the rockfill concrete is determined to be 0.53 (the determination method is the basic knowledge in the field).

S4: According to the rockfill ratio n and the particle size distribution of the rockfill, establish a mesoscopic finite element model of the rockfill concrete specimen, as shown in Figure 2, the model is a cube, and the side length L=4.5m. Apply z-direction constraints at the bottom of the model, x-direction constraints at points A and B, and y-direction constraints at points B and C,;

S5: Based on the calculation parameters obtained in steps S1 to S4 and the established model, apply a z-direction displacement load △L=0.01m to the rockfill concrete specimen, and use the finite element method to calculate the stress of the specimens of different ages τ _RFC field, as shown in Figure 3 (the calculation method is the basic knowledge in the field).

如表1所示。S6. Average the z-direction stress value of each element in the calculated stress field by volume (as shown in formula 2) to obtain the average z-direction stress of the rockfill concrete specimen

As shown in Table 1.

表示龄期为τ_RFC的试件中点(x,y,z)处的z向应力值，△Ri表示模型中第i个单元的体积，V 为模型的总体积。In formula 2, x, y, z represent the coordinates of the Cartesian coordinate system in the model, τ _RFC represents the age of rockfill concrete, i represents the unit number in the model, m is the total number of units in the model,

represents the z-direction stress value at the midpoint (x, y, z) of the specimen with age τ _RFC , ΔRi represents the volume of the i-th element in the model, and V is the total volume of the model.

Table 1

为0.00222。S7: Under the action of the z-direction displacement load △L, the z-direction strain of the rockfill concrete specimen is calculated by formula 3

is 0.00222.

S8: According to the constraints imposed on the model in S4, it can be determined that the rockfill concrete specimen can be freely deformed on the xoy plane. Therefore, the average normal stress of the rockfill concrete specimen in both the x and y directions is zero, that is, :

S9: Based on the data obtained from S6 to S8, according to the physical equation of elasticity (basic knowledge in the field), formula 5 can be used to calculate the macroscopic elastic modulus E _RFC (τ _RFC of rockfill concrete specimens of different ages) ),As shown in table 2,

where ν _RFC is the Poisson's ratio of rockfill concrete.

Table 2

S10: perform data fitting on the calculated macroscopic elastic modulus E _RFC (τ _RFC ) of rockfill concrete at different ages, (the fitting method is the basic knowledge in the field), and obtain the macroscopic elastic modulus of rockfill concrete. A double exponential expression (as shown in Equation 6).

E _RFC (τ _RFC )=27.35τ _RFC ^0.69 /(0.87+τ _RFC ^0.69 ) (6)

S11: According to formula 6, the macroscopic elastic modulus value of rockfill concrete at any age can be obtained.

Those of ordinary skill in the art will appreciate that the embodiments described herein are intended to help readers understand the implementation method of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations without departing from the essence of the present invention according to the technical teaching disclosed in the present invention, and these modifications and combinations still fall within the protection scope of the present invention.

Claims (1)

1. a determination method of rockfill concrete elastic modulus, is characterized in that, comprises the following steps: S1: Obtain the values of the elastic modulus E _R and Poisson’s ratio ν _R of the rockfill through the static compression elastic modulus test; S2: Obtain the elastic modulus parameters E ⁰ _scc , a, b and Poisson’s ratio ν _scc of the self-compacting concrete through the static compression elastic modulus test, and determine the double exponential expression of its elastic modulus E _scc (τ _scc ) , as shown in Equation 1, where τ _scc represents the age of the self-compacting concrete;

S3: measure the rockfill rate n of rockfill concrete; S4: According to the rockfill rate n and the particle size distribution of the rockfill, in the Cartesian coordinate system, a meso-scale finite element model of the rockfill concrete specimen is established, and constraints are imposed on the model, so that the model is subject to displacement constraints in the z direction , which can be freely deformed in the xoy plane; S5: Based on the calculation parameters obtained in steps S1-S4 and the established model, apply a displacement load ΔL in the z-direction to the rockfill concrete specimen, and use the finite element method to calculate the stress field of the specimens with different ages τ _RFC ; S6. Average the z-direction stress values of each element in the calculated stress field by volume to obtain the average z-direction stress of the rockfill concrete specimen

As shown in formula 2;

In formula 2, x, y, z represent the coordinates of the Cartesian coordinate system in the model, τ _RFC represents the age of rockfill concrete, i represents the unit number in the model, m is the total number of units in the model,

represents the z-direction stress value at the midpoint (x, y, z) of the specimen with age τ _RFC , ΔRi represents the volume of the i-th element in the model, and V is the total volume of the model; S7: The z-direction strain of the rockfill concrete specimen under the action of the z-direction displacement load ΔL

for

S8: According to the constraints imposed on the model in S4, the rockfill concrete specimen can be freely deformed on the xoy plane. Therefore, the average normal stress of the rockfill concrete specimen in both the x and y directions is zero, namely:

S9: Based on the data obtained from S6 to S8, and according to the physical equation of elasticity, the macroscopic elastic modulus E _RFC (τ _RFC ) of rockfill concrete specimens of different ages is calculated, as shown in Equation 5:

Among them, ν _RFC is the Poisson's ratio of rockfill concrete; S10: perform data fitting on the calculated macro-elastic modulus E _RFC (τ _RFC ) of different ages of rock-fill concrete, to obtain a double-exponential expression of the macro-elastic modulus of rock-fill concrete, as shown in formula 6;

Among them, E ⁰ _RFC , A and B are elastic modulus parameters S11: According to formula 6, the macroscopic elastic modulus value of rockfill concrete at any age is obtained.

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