CN102937625B - Cement-based material early-stage elasticity modulus measuring method and measuring device - Google Patents

Abstract

The invention discloses a cement-based material early-stage elasticity modulus measuring device. The method comprises that the blended cement-based material to be measured is filled and packaged in a equal-section straight hollow pipe; the hollow pipe is fixed horizontally through one end of the hollow pipe, and a combined cantilever beam composed of the cement-based material to be measured and the hollow pipe; the natural vibration frequency of the combined cantilever beam can be monitored continuously through a vibration sensor which is arranged at a free end of the combined cantilever beam; and finally, the elasticity modulus of the cement-based material to be measured is calculated when the age is t according to the natural vibration frequency. The invention also discloses a cement-based material early-stage elasticity modulus measuring method. The method comprises an equal-section straight hollow pipe, a fixing device and a vibration measuring device. The process that the cement-based material early-stage elasticity modulus changes along with the age under different curing temperatures can be detected continuously without demolding after the cement-based material enters into a mold, the structure is simple, and the cost is low.

Description

A kind of early stage elastic modulus measuring method of cement-based material and measurement mechanism

Technical field

The present invention relates to a kind of method of testing of Mechanical Properties of Cement-based Materials, particularly relate to the early stage elastic modulus measuring method of a kind of cement-based material and measurement mechanism.

Background technology

Question synthesis involved by the early-age crack of xoncrete structure and complicated, covers the every aspect of the early stage calorifics of cement-based material, mechanics and deformation performance, and mineral admixture and additive application also considerably increase the complicacy of its Early-age behavior.Domestic and international researcher has carried out a large amount of experimental studies to the early stage macro property of concrete, attempts to illustrate concrete bracing mechanism, Early-age behavior Changing Pattern and technical parameter problems of value.Wherein early stage elastic modulus is one of hot issue of being concerned about of researchist with the development and change process in the length of time, but traditional method of being tried to achieve elastic modulus by load-deformation, at least to carry out after form removal in a day built by test specimen, therefore be difficult to record the more early stage elastic modulus of cement-based material by traditional method.

Summary of the invention

Technical matters to be solved by this invention is to overcome the deficiencies in the prior art, the early stage elastic modulus measuring method of a kind of cement-based material and measurement mechanism are provided, can be implemented in from entering the commitment of mould to sclerosis, nondestructively the elastic modulus of cement-based material is monitored continuously with development of age, thus for the early stage mechanics of cement-based material, deformation performance research and Numerical Simulation Analysis elastic modulus parameter is accurately provided.

The present invention specifically solves the problems of the technologies described above by the following technical solutions:

The early stage elastic modulus measuring method of a kind of cement-based material, is first full of the cement-based material to be measured mixed and stirred and is packaged in the straight hollow tubular of a uniform cross section; Then by one end of hollow tubular, this hollow tubular level is fixed, form the combination semi-girder be made up of cement-based material to be measured and hollow tubular; The natural frequency of vibration of combination semi-girder is continued to monitor by the vibration transducer being arranged at combination semi-girder free end; The elastic modulus of cement-based material to be measured when the length of time is t is calculated by following formula:

$E_c\left(t\right)=[\mathrm{EI}\left(t\right)-E_a{I}_a]\frac{64}{{\mathrm{\πd}}_i^4}$

In formula, E _ct () represents the elastic modulus of the to be measured cement-based material of length of time when being t; E _ai _afor the rigidity of hollow tubular; d _ifor hollow tubular internal diameter; Combining the rigidity of semi-girder when EI (t) represents that the length of time is t, obtaining by solving following equation:

$A^3[\cosh \left(\mathrm{AL}\right)\cos \left(\mathrm{AL}\right)+1]+\frac{w^2{m}_1}{\mathrm{EI}\left(t\right)}[\cos \left(\mathrm{AL}\right)\sinh \left(\mathrm{AL}\right)-\cosh \left(\mathrm{AL}\right)\sin \left(\mathrm{AL}\right)]=0$

Wherein, L is the length of combination semi-girder; ω is combination semi-girder circular frequency, first natural frequency of vibration of the combination semi-girder that ω=2 π f, f are the length of time when being t, the length of time t from cement-based material water be filled with hollow tubular after count; for the uniform quality of unit length combination semi-girder; m ₁the vibration transducer of combination semi-girder free end and the lumped mass of tube sealing cock body is arranged on for described.

Further, the method also comprises by adjusting the early stage elastic modulus of described hollow tubular temperature survey cement-based material to be measured under different curing.Thus realize providing elastic modulus parameter accurately to the early stage mechanics of cement-based material under different curing, deformation performance research and Numerical Simulation Analysis.

For the ease of pouring into the cement-based material to be measured that mixes and stirs, described hollow tubular can at one end or arrange can folding and closed lid or plug at two ends; Also can both ends open, first close one end with tube sealing cock body, then after hollow tubular being filled the cement-based material to be measured that mixes and stirs, utilize tube sealing cock body to be closed by another openend.

Use the early stage elastic modulus measurement mechanism of the cement-based material of above-mentioned measuring method, comprising:

The straight hollow tubular of one uniform cross section, for pouring into cement-based material to be measured;

Stationary installation, fixes this hollow tubular level for the one end by hollow tubular, forms the combination semi-girder be made up of cement-based material to be measured and hollow tubular;

Vibration measurement device, comprises the vibration transducer being arranged at described combination semi-girder free end, and the vibration signals collecting treating apparatus be connected with vibration transducer.

Preferably, described measurement mechanism also comprises the temperature control equipment for adjusting described hollow tubular temperature.

Preferably, the cross section of described hollow tubular is circular or rectangle.The cross sectional dimensions of described hollow tubular is less than 100mm, and length is 600-1000mm.The material of described hollow tubular is plastics or alloy material.

Compared to existing technology, the present invention has following beneficial effect:

One, the present invention is nondestructive test method, tests before can advanceing to initial set the length of time.Owing to also not hardening completely before cement-based material condensation, be difficult to carry out load test by form removal and obtain elastic modulus, the inventive method does not need form removal, therefore namely can be able to test after device installation in position, and mixture pouring and device are installed whole process and can be completed in 30 minutes.

Two, the present invention is a kind of monitoring method of active Received signal strength, do not need artificial excitation, whole observation process is automatic and continuous print, can curing temperature be set simultaneously, after device installation, namely can monitor the process that the early stage elastic modulus of different curing cement-based material changed with the length of time continuously.

Three, apparatus of the present invention structure is simple, and with low cost, measuring method is easy to implement.

Accompanying drawing explanation

Fig. 1 is the structural representation of the early stage elastic modulus measurement mechanism of cement-based material of the present invention in embodiment; In figure, 1 is hollow tubular, and 2 is geometrical clamp, and 3 is vibration transducer, and 4 is data collecting instrument, and 5 is computing machine, and 6 is worktable, and 7 is tube sealing cock body, and 8 is power supply, and 9 is power regulating switch;

The cement paste elastic modulus progress curve that Fig. 2 is water cement ratio is 0.35, curing temperature is 25.0 DEG C.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in detail:

Thinking of the present invention cement-based material to be measured and hollow tubular is formed to combine semi-girder, continued to monitor the natural frequency of vibration of combination semi-girder by the vibration transducer being arranged at combination semi-girder free end, then try to achieve the early stage elastic modulus of cement-based material to be measured according to the mechanical characteristic of combination semi-girder.The derivation of computing formula is as follows:

Semi-girder line of deflection approximate differential equation is as the formula (1):

$\frac{{\∂}^{2}f(x,t)}{{\∂x}^2}=-\frac{M(x,t)}{\mathrm{EI}\left(t\right)}---\left(1\right)$

In formula, the amount of deflection that f (x, t) is semi-girder, for about beam length direction x and the length of time t function; M (x, t) is for semi-girder is in the moment of flexure in t x cross section; EI (t) is combination semi-girder rigidity, is the function of t in the length of time.

Can be obtained by formula (1):

$\mathrm{EI}\left(t\right)\frac{{\∂}^{4}f(x,t)}{{\∂x}^4}=-q(x,t)---\left(2\right)$

In formula, q (x, t) is the load intensity perpendicular to beam length directional spreding, calculates by formula (3):

$q(x,t)=\stackrel{\‾}{m}a(x,t)=\stackrel{\‾}{m}\frac{{\∂}^{2}f(x,t)}{{\∂t}^2}---\left(3\right)$

In formula, a (x, t) is for beam is along the self-vibration acceleration in self-vibration direction; for combination beam linear mass.Formula (3) is substituted into formula (2), can obtain:

$\mathrm{EI}\left(t\right)\frac{{\∂}^{4}f(x,t)}{{\∂x}^4}=-\stackrel{\‾}{m}\frac{{\∂}^{2}f(x,t)}{{\∂t}^2}---\left(4\right)$

Namely $\mathrm{EI}\left(t\right)\frac{{\∂}^{4}f(x,t)}{{\∂x}^4}=+\stackrel{\‾}{m}\frac{{\∂}^{2}f(x,t)}{{\∂t}^2}=0---\left(5\right)$

Adopt the separation of variable, if f (x, t)=φ (x) Y (t), formula (5) turns to formula (6):

$\mathrm{EI}\left(t\right)\frac{{\∂}^4\left[\mathrm{\φ}\left(x\right)Y\left(t\right)\right]}{{\∂x}^4}+\stackrel{\‾}{m}\frac{{\∂}^2\left[\mathrm{\φ}\left(x\right)Y\left(t\right)\right]}{{\∂t}^2}=0---\left(6\right)$

In formula, Y (t) is the function about t in the length of time; φ (x) is the function about beam length x.

Can be obtained by formula (6):

$-\frac{1}{\mathrm{\φ}\left(x\right)}\frac{d^4\mathrm{\φ}\left(x\right)}{{\mathrm{dx}}^4}=\frac{\stackrel{\‾}{m}}{\mathrm{EI}}\frac{1}{Y\left(t\right)}\frac{d^{2}Y\left(t\right)}{{\mathrm{dt}}^2}---\left(7\right)$

The equation left side is the function of x, and the right is the function of t, therefore equation can only equal constant, is set to λ, that is:

$-\frac{1}{\mathrm{\φ}\left(x\right)}\frac{d^4\mathrm{\φ}\left(x\right)}{{\mathrm{dx}}^4}=\frac{\stackrel{\‾}{m}}{\mathrm{EI}}\frac{1}{Y\left(t\right)}\frac{d^{2}Y\left(t\right)}{{\mathrm{dt}}^2}=\mathrm{\λ}---\left(8\right)$

Therefore,

$\left\{\begin{array}{c}\frac{{\∂}^4\mathrm{\φ}\left(x\right)}{{\mathrm{dx}}^4}+\mathrm{\λ\φ}\left(x\right)=0\\ \frac{d^{2}Y\left(t\right)}{{\mathrm{dt}}^2}-\frac{\mathrm{\λEI}}{\stackrel{\‾}{m}}Y\left(t\right)=0\end{array}\right.$

Can be established by (9a):

φ(x)=A ₁cos(Ax)+A ₂sin(Ax)+A ₃cosh(Ax)+A ₄sinh(Ax) （10）

In formula, ω is combination semi-girder circular frequency, i.e. first natural frequency of vibration of the combination semi-girder that ω=2 π f, f are the length of time when being t, and t is counted after cement-based material is poured into hollow tubular; A ₁, A ₂, A ₃, A ₄for undetermined constant.During x=0: f (x, t)=φ (x) Y (t)=0,

φ(0)=0 （11）

$\frac{\∂f(x,t)}{\∂x}=Y\left(t\right)\frac{\mathrm{d\φ}\left(x\right)}{\mathrm{dx}}=0,$ ?

$\frac{\mathrm{d\φ}\left(x\right)}{\mathrm{dx}}{|}_{x=0}=0---\left(12\right)$

During x=L: $F=\mathrm{EI}\left(t\right)\frac{{\∂}^{3}f(x,t)}{{\∂x}^3}=-m_{1}a(x,t)=-m_1{\mathrm{\ω}}^{2}f(x,t)$

In formula, L is the length of combination semi-girder, and F is semi-girder free end load, m ₁the vibration transducer of combination semi-girder free end and the lumped mass of tube sealing cock body is arranged on for described.

Namely $\mathrm{EI}\left(t\right)\frac{{\∂}^3\left[\mathrm{\φ}\left(x\right)Y\left(t\right)\right]}{{\∂x}^3}=-m_1{\mathrm{\ω}}^2\mathrm{\φ}\left(x\right)Y\left(t\right)$

?

$\frac{d^3\mathrm{\φ}\left(x\right)}{d{x}^3}{|}_{x=L}=-\frac{m_1{\mathrm{\ω}}^2}{\mathrm{EI}\left(t\right)}\mathrm{\φ}\left(L\right)---\left(13\right)$

Have again during x=L: $M(x,t)=\mathrm{EI}\left(t\right)\frac{{\∂}^{2}f(x,t)}{\∂x^2}=0$

Namely $\mathrm{EI}\left(t\right)\frac{{\∂}^2\left[\mathrm{\φ}\left(x\right)Y\left(t\right)\right]}{\∂x^2}=0$

?

$\frac{d^2\mathrm{\φ}\left(x\right)}{d{x}^2}{|}_{x=L}=0---\left(14\right)$

Undetermined constant A is solved to (14) by formula (11) ₁, A ₂, A ₃, A ₄, draw φ (x), substitute into formula (9a) and draw λ, then (9b) formula that substitutes into solve Y (t).The φ (x) solved, Y (t) are substituted into formula (7) to obtain:

$A^3[\cosh \left(\mathrm{AL}\right)\cos \left(\mathrm{AL}\right)+1]+\frac{w^2{m}_1}{\mathrm{EI}\left(t\right)}[\cos \left(\mathrm{AL}\right)\sinh \left(\mathrm{AL}\right)-\cosh \left(\mathrm{AL}\right)\sin \left(\mathrm{AL}\right)]=0---\left(15\right)$

Solve formula (15) by Newton iteration method, can EI (t) be obtained.

Again

$\mathrm{EI}\left(t\right)=E_a{I}_a+E_c{I}_c\left(t\right)=E_a{I}_a+E_c\left(t\right)\frac{\mathrm{\π}{d}_i^4}{64}---\left(16\right)$

In formula, E _ai _afor hollow tubular rigidity; E _ci _ct () is rigidity when cement-based material to be measured length of time is t; E _ct () is elastic modulus when water material length of time is t; d _ifor the internal diameter of hollow tubular.

Therefore, elastic modulus when cement-based material length of time is t is:

$E_c\left(t\right)=[\mathrm{EI}\left(t\right)-E_a{I}_a]\frac{64}{\mathrm{\π}{d}_i^4}---\left(17\right)$

The early stage elastic modulus measurement mechanism of cement-based material of the present invention, as shown in Figure 1, the data collecting instrument 4, the computing machine 5 that comprise hollow tubular 1, geometrical clamp 2, vibration transducer 3 and be connected successively with vibration transducer 3.Measurement mechanism of the present invention also comprises the temperature control equipment for adjusting described hollow tubular 1 temperature, a kind of easy hollow tubular temperature control equipment is have employed: outside the tube wall of hollow tubular 1, be wound with resistive heater in this embodiment, outer layer covers one layer of heat preservation material, resistive heater is connected with power supply 8 by power regulating switch 9, to switch on power after 8 by regulating power switch 9, the tube wall of hollow tubular 1 can be made to be heated to predetermined curing temperature.In this embodiment, hollow tubular 1 is xsect is the straight hollow tubular of circular uniform cross section, both ends open, and cross-sectional diameter is no more than 100mm, the preferred plastics of material (such as polystyrene) or alloy material, and length is 600-1000mm.Vibration transducer 3 can adopt the sensor such as accelerometer or strainometer, and data collecting instrument 4 is the data acquiring and recording equipment of same sensor 3 adaptation.

When carrying out the early stage elastic modulus of cement-based material, specifically in accordance with the following methods:

Step 1, need regulating power switch 9 according to test, hollow tubular 1 is heated to predetermined curing temperature;

Step 2, according to test objective according to match ratio mix cement mixture;

Step 3, to close with tube sealing cock body 7 one end by hollow tubular 1, poured into by the mixture stirred in hollow tubular 1, pouring is slight concussion simultaneously, bubble in vent pipe;

Step 4, to stop when cement mixture is about to fill, leave about 10mm highly not casting cement mixture, by another openend wiped clean of hollow tubular 1, use tube sealing cock body 7 to be enclosed in hollow tubular 1 by cement mixture;

Step 5, using filling have any one end of the hollow tubular 1 of cement mixture as stiff end, by geometrical clamp 2, hollow tubular 1 level is fixed on worktable 6, as shown in Figure 1, the other end is free end, thus forms the combination cantilever beam structure be made up of cement mixture and hollow tubular 1;

Step 6, to install at the free end of hollow tubular 1 and gather the sensor 3 of vibration signal, and be connected with data collecting instrument 4;

Step 7, startup data collecting instrument 4, by the vibration signal under sensor 3 continuous collecting combination semi-girder around environmental interference, and record preservation by data collecting instrument 4;

The vibration signal that step 8, computing machine 5 pairs of data collecting instruments 4 record obtains combining the natural frequency of vibration of semi-girder through fast time domain and frequency domain conversion process, and according to the first calculation of natural vibration frequency combination semi-girder rigidity; Calculation combination semi-girder rigidity obtains especially by solving following equation:

$A^3[\cosh \left(\mathrm{AL}\right)\cos \left(\mathrm{AL}\right)+1]+\frac{w^2{m}_1}{\mathrm{EI}\left(t\right)}[\cos \left(\mathrm{AL}\right)\sinh \left(\mathrm{AL}\right)-\cosh \left(\mathrm{AL}\right)\sin \left(\mathrm{AL}\right)]=0$

Wherein, L is the length of combination semi-girder; ω is combination semi-girder circular frequency, first natural frequency of vibration of the combination semi-girder that ω=2 π f, f are the length of time when being t, the length of time t from cement-based material water be filled with hollow tubular after count; for the uniform quality of unit length combination semi-girder; m ₁the vibration transducer of combination semi-girder free end and the lumped mass of tube sealing cock body is arranged on for described;

Step 9, calculate different larval instar cement mixture elastic modulus by following formula:

$E_c\left(t\right)=[\mathrm{EI}\left(t\right)-E_a{I}_a]\frac{64}{\mathrm{\π}{d}_i^4}$

In formula, E _ct () represents the elastic modulus of the to be measured cement-based material of length of time when being t; E _ai _afor the rigidity of hollow tubular; d _ifor hollow tubular internal diameter; The rigidity of semi-girder is combined when EI (t) represents that the length of time is t;

Step 10, draw cement-based material early stage elastic modulus progress curve by result of calculation;

Step 11, adopt different match ratios, admixture variety classes and the additive of volume and the cement mixture of mineral admixture, repeat step 2 ~ step 10, obtain different mixture ratio and admixture cement-based material elastic modulus progress curve under this curing temperature; By adjusting different curing temperatures, different mixture ratio and admixture cement-based material elastic modulus progress curve under different curing can be obtained.Fig. 2 shows the cement paste elastic modulus progress curve that water cement ratio is 0.35, curing temperature is 25.0 DEG C.

Claims (9)

1. the early stage elastic modulus measuring method of cement-based material, is characterized in that, is first full of by the cement-based material to be measured mixed and stirred and is packaged in the straight hollow tubular of a uniform cross section; Then by one end of hollow tubular, this hollow tubular level is fixed, form the combination semi-girder be made up of cement-based material to be measured and hollow tubular; The natural frequency of vibration of combination semi-girder is continued to monitor by the vibration transducer being arranged at combination semi-girder free end; The elastic modulus of cement-based material to be measured when the length of time is t is calculated by following formula:

$E_c\left(t\right)=[\mathrm{EI}\left(t\right)-E_a{I}_a]\frac{64}{{\mathrm{\πd}}_i^4}$

In formula, E _ct () represents the elastic modulus of the to be measured cement-based material of length of time when being t; E _ai _afor the rigidity of hollow tubular; d _ifor hollow tubular internal diameter; Combining the rigidity of semi-girder when EI (t) represents that the length of time is t, obtaining by solving following equation:

$A^3[\cosh \left(\mathrm{AL}\right)\cos \left(\mathrm{AL}\right)+1]\frac{{\mathrm{\ω}}^2{m}_1}{\mathrm{EI}\left(t\right)}[\cos \left(\mathrm{AL}\right)\sinh \left(\mathrm{AL}\right)-\cosh \left(\mathrm{AL}\right)\sin \left(\mathrm{AL}\right)]=0$

Wherein, L is the length of combination semi-girder; ω is combination semi-girder circular frequency, first natural frequency of vibration of the combination semi-girder that ω=2 π f, f are the length of time when being t, the length of time t from cement-based material water be filled with hollow tubular after count; for the uniform quality of unit length combination semi-girder; m ₁the vibration transducer of combination semi-girder free end and the lumped mass of tube sealing cock body is arranged on for described.

2. the early stage elastic modulus measuring method of cement-based material as claimed in claim 1, it is characterized in that, the method also comprises by adjusting the early stage elastic modulus of described hollow tubular temperature survey cement-based material to be measured under different curing.

3. the early stage elastic modulus measuring method of cement-based material as claimed in claim 1, is characterized in that, the cross section of described hollow tubular is circular.

4. the early stage elastic modulus measuring method of cement-based material as claimed in claim 1, is characterized in that, the natural frequency of vibration of described combination semi-girder is by carrying out time domain and frequency domain conversion obtains to the vibration signal of vibration transducer collection.

5. use the early stage elastic modulus measurement mechanism of the cement-based material of measuring method described in claim 1, it is characterized in that, comprising:

The straight hollow tubular of one uniform cross section, for pouring into cement-based material to be measured;

Stationary installation, fixes this hollow tubular level for the one end by hollow tubular, forms the combination semi-girder be made up of cement-based material to be measured and hollow tubular;

Vibration measurement device, comprises the vibration transducer being arranged at described combination semi-girder free end, and the vibration signals collecting treating apparatus be connected with vibration transducer.

6. the early stage elastic modulus measurement mechanism of cement-based material as claimed in claim 5, is characterized in that, also comprising the temperature control equipment for adjusting described hollow tubular temperature.

7. the early stage elastic modulus measurement mechanism of cement-based material as claimed in claim 5, is characterized in that, the cross section of described hollow tubular is circular.

8. the early stage elastic modulus measurement mechanism of cement-based material as claimed in claim 5, it is characterized in that, the cross sectional dimensions of described hollow tubular is less than 100mm, and length is 600-1000mm.

9. the early stage elastic modulus measurement mechanism of cement-based material as claimed in claim 5, it is characterized in that, the material of described hollow tubular is plastics or alloy material.