FATIGUE DEFORMATION EVOLUTION MODEL OF CONCRETE BASED ON WEIBULL FUNCTION

Abstract

The present invention discloses a fatigue deformation evolution model of concrete based on Weibull function. With the continuous development of modern civil engineering, the fatigue performance of concrete materials has become one of the focuses of concern. The accurate characterization of concrete fatigue performance evolution and prediction of fatigue life of concrete has become an important issue in the field of engineering construction. The model provided by the invention can be used to characterize the concrete deformation evolution law under the compressive, tensile and flexural fatigue loads, having the advantages of diverse applicable forms of loads, simple expression, simpleness to use and high accuracy, etc. During the use, it can greatly reduce the computations, and only two fatigue parameters of the number of fatigue load cycles n and the deformation corresponding to the stress of the n.sup.th cycle need to be measured, which simplifies the monitoring equipment. The model can provide an important technical support for engineering design, construction, monitoring and maintenance.

Claims

1. A fatigue deformation evolution model of concrete based on Weibull function, wherein the number of fatigue load cycles n of a concrete under the fatigue load at one certain stress level and the deformation corresponding to one of the stresses of the n.sup.th fatigue load cycle are expressed by the following equation:
n/N.sub.f=1exp(((.sub.0)/).sup.k) wherein, N.sub.f is fatigue life, .sub.0 is position parameter, is scale parameter, k is shape parameter.

2. The fatigue deformation evolution model of concrete based on Weibull function according to claim 1, wherein said one of the stresses is larger than or equal to zero, and smaller than or equal to the maximum stress of the fatigue load.

3. The fatigue deformation evolution model of concrete based on Weibull function according to claim 1, wherein the fatigue load may be a compressive fatigue load, a tensile fatigue load or a flexural fatigue load.

4. The fatigue deformation evolution model of concrete based on Weibull function according to claim 1, wherein the fatigue life N.sub.f, position parameter .sub.0, scale parameter , and shape parameter k can be obtained by fitting, on the basis of several of the measured deformations and the corresponding number of fatigue load cycles n.

5. The fatigue deformation evolution model of concrete based on Weibull function according to claim 1, wherein the deformation is a maximum deformation .sub.s when said one of the stresses is the maximum stress of the fatigue load; the number of fatigue load cycles n and the maximum deformation .sub.s of the n.sup.th fatigue load cycle of the concrete under the fatigue load at one certain stress level can be expressed as follows:
n/N.sub.f=1exp(((.sub.s.sub.s0)/.sub.s).sup.k.sup.s) wherein, N.sub.f is fatigue life, .sub.s0 is position parameter, .sub.s is scale parameter, k.sub.s is shape parameter.

6. The fatigue deformation evolution model of concrete based on Weibull function according to claim 5, wherein an optional value for the position parameter .sub.s0 is the deformation corresponding to the maximum stress of the first fatigue load cycle of the concrete.

7. The fatigue deformation evolution model of concrete based on Weibull function according to claim 1, wherein the deformation is a residual deformation .sub.p when said one of the stresses is 0; the number of fatigue load cycles n and the residual deformation .sub.p of the n.sup.th fatigue load cycle of the concrete under the fatigue load at one certain stress level can be expressed as follows:
n/N.sub.f=1exp(((.sub.p.sub.p0)/.sub.p).sup.k.sup.p) wherein, N.sub.f is fatigue life, .sub.p0 is position parameter, .sub.p is scale parameter, k.sub.p is shape parameter.

8. The fatigue deformation evolution model of concrete based on Weibull function according to claim 7, wherein an optional value of the position parameter .sub.p0 is 0, and another optional value is the residual deformation of the concrete after the first cycle of the fatigue load.

9. The fatigue deformation evolution model of concrete based on Weibull function according to claim 1, wherein the deformation is the maximum deformation .sub.s when said one of the stresses is the maximum stress of the fatigue load; the number of fatigue load cycles n and the maximum deformation .sub.s of the n.sup.th fatigue load cycle of the concrete under a fatigue load at one certain stress level can be expressed as follows:
n/N.sub.f=1exp(((.sub.s.sub.s0)/.sub.s).sup.k.sup.s) wherein, N.sub.f is fatigue life, .sub.s0 is position parameter, .sub.s is scale parameter, k.sub.s is shape parameter; The deformation is the residual deformation .sub.p when said one of the stresses is 0; the number of fatigue load cycles n and the residual deformation .sub.p of the n.sup.th fatigue load cycle of the concrete under a fatigue load at one certain stress level can be expressed as follows:
n/N.sub.f=1exp(((.sub.p.sub.p0)/.sub.p).sup.k.sup.p) wherein, N.sub.f is fatigue life, .sub.p0 is position parameter, .sub.p is scale parameter, k.sub.p is shape parameter; When one of the shape parameters k.sub.s and k.sub.p is a known value, the value of the other parameter may be equal to the known value.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] FIG. 1 shows the experimental results and model results of the maximum deformation and residual deformation evolution of concrete under the compressive fatigue load according to Example 1 of the present invention.

[0013] FIG. 2 shows the experimental results and model results of the maximum deformation and residual deformation evolution of concrete under the tensile fatigue load according to Example 2 of the present invention.

[0014] FIG. 3 shows the experimental results and model results of the maximum deformation and residual deformation evolution of concrete subjected to flexural fatigue load according to Example 3 of the present invention.

DETAILED DESCRIPTION

[0015] The present invention is further described in combination with drawings and specific embodiments. The embodiments are intended to illustrate the present invention, but not to limit the invention in any way.

Example 1

[0016] This example uses the fatigue deformation result of concrete compressive fatigue specimen D22 in FIG. 11 of the document Holmen J O. Fatigue of concrete by constant and variable amplitude loading. ACI Special Publication, 1982, 75: 71-110. The evolution law of the maximum deformation .sub.s and residual deformation .sub.p under the compressive fatigue load are shown in FIG. 1. It should be noted that, the maximum deformation .sub.s of the fatigue specimen is obtained directly from the document, and the residual deformation .sub.p is calculated from the fatigue deformation results in the document.

[0017] According to the experimental values of maximum deformation .sub.s shown in FIG. 1, the position parameter .sub.s0=0.09582, scale parameter .sub.s=0.11497, and shape parameter k.sub.s=3.16309 can be obtained by fitting, so as to obtain the following fatigue deformation evolution model.

n/N.sub.f=1exp(((.sub.s0.09582)/0.11497).sup.3.16309), (r.sup.2=0.9971)

[0018] According to the experimental values of residual deformation .sub.p shown in FIG. 1, the position parameter .sub.p0=0.01483, scale parameter .sub.p=0.09422, and shape parameter k.sub.p=3.27520 can be obtained by fitting, so as to obtain the following fatigue deformation evolution model.

n/N.sub.f=1exp(((.sub.p0.01483)/0.09422).sup.3.27520), (r.sup.2=0.9991)

[0019] The fatigue deformation evolution model results obtained are highly correlated to the experimental values, which can accurately characterize the evolution law of compression fatigue deformation, as shown in FIG. 1.

Example 2

[0020] This example uses the fatigue deformation results of concrete tensile fatigue specimen S=0.85 test data in FIG. 8c of the document Chen X, Bu J, Fan X, et al. Effect of loading frequency and stress level on low cycle fatigue behavior of plain concrete in direct tension. Construction and Building Materials, 2017, 133: 367-375. The evolution law of the maximum deformation .sub.s and residual deformation .sub.p under the tensile fatigue load are shown in FIG. 2. It should be noted that, both the maximum deformation .sub.s and the residual deformation .sub.p of the fatigue specimen are obtained directly from the document.

[0021] According to the experimental values of maximum deformation .sub.s shown in FIG. 2, the position parameter .sub.s0=38.21874, scale parameter .sub.s=66.41625, shape parameter k.sub.s=11.44255 can be obtained by fitting, so as to obtain the following fatigue deformation evolution model.

n/N.sub.f=1exp(((.sub.s38.21874)/66.41625).sup.11.44255), (r.sup.2=0.9769)

[0022] According to the experimental values of residual deformation .sub.p shown in FIG. 2, the position parameter .sub.p0=2.14727, scale parameter .sub.p=37.79211, shape parameter k.sub.p=10.44414 can be obtained by fitting, so as to obtain the following fatigue deformation evolution model.

n/N.sub.f=1exp(((.sub.p+2.14727)/37.79211).sup.10.44414), (r.sup.2=0.9188)

[0023] The fatigue deformation evolution model results obtained are highly correlated to the experimental values, which can accurately characterize the evolution law of tensile fatigue deformation, as shown in FIG. 2.

Example 3

[0024] This example uses the fatigue deformation result of fiber concrete flexural fatigue specimens S0.80 in FIG. 3a of the document Liu W, Xu S, Li H. Flexural fatigue damage model of ultra-high toughness cementitious composites on base of continuum damage mechanics. International Journal of Damage Mechanics, 2014, 23(7): 949-963. The evolution law of the maximum deformation .sub.s and residual deformation .sub.p under the flexural fatigue load are shown in FIG. 3. It should be noted that, the maximum deformation .sub.s of the fatigue specimen is obtained directly from the document, and the residual deformation .sub.p is calculated from the fatigue deformation results in the document.

[0025] According to the experimental values of maximum deformation .sub.s shown in FIG. 3, the position parameter .sub.s0=2.27807, scale parameter .sub.s=4.85335, shape parameter k.sub.s=9.28728 can be obtained by fitting, so as to obtain the following fatigue deformation evolution model.

n/N.sub.f=1exp(((.sub.s+2.27807)/4.85335).sup.9.28728), (r.sup.2=0.9983)

[0026] According to the experimental values of residual deformation .sub.p shown in FIG. 3, the position parameter .sub.p0=1.30373, scale parameter .sub.p=2.98369, shape parameter k.sub.p=7.78920 can be obtained by fitting, so as to obtain the following fatigue deformation evolution model.

n/N.sub.f=1exp(((.sub.p+1.30373)/2.98369).sup.7.78920), (r.sup.2=0.9965)

[0027] The fatigue deformation evolution model results obtained are highly correlated to the experimental values, which can accurately characterize the evolution law of flexural fatigue deformation, as shown in FIG. 3.