CN109522571A - 一种基于Weibull方程的混凝土疲劳变形演化模型 - Google Patents
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Abstract
本发明公开了一种基于Weibull方程的混凝土疲劳变形演化模型。在不断发展的现代土木工程领域,混凝土材料的疲劳性能成为关注的重点之一。如何精确表征混凝土的疲性能演化和预测混凝土疲劳寿命成为工程建设领域中的重要问题。本发明所提供的模型可以用于表征压缩、拉伸和弯曲疲劳荷载作用下混凝土的变形演化规律。具有可适用的荷载形式多样、表达式简洁、易于使用、精度较高等优点。在使用过程中,可以极大地减少计算量,且只需测量疲劳荷载循环次数n以及第n个循环的某一个应力所对应的变形ε这两种疲劳参数,可以简化检测设备。所述的模型,可以为工程设计、建设、检测和维护全过程提供重要技术支撑。
Description
技术领域
本发明属于混凝土疲劳变形演化模型技术领域。
背景技术
自19世纪波特兰水泥问世以来,混凝土被广泛用于交通、建筑、水利、海洋等工程领域,是工程建设中用量最大的材料。20世纪初,随着钢筋混凝土桥梁的建设和发展,对混凝土材料疲劳性能的相关研究也逐步开展。21世纪以来,随着高速公路、高速铁路、超高层建筑、特高大坝、跨海大桥、海洋平台等大型基础设施的建设,混凝土结构面临着循环荷载、交变环境等更加复杂、严苛的服役条件。另一方面,混凝土结构设计理论的进一步发展和高强混凝土的推广应用使得混凝土在结构服役期间所承受的应力水平逐步提高,使得混凝土的疲劳破坏也更有可能发生。因此,在不断发展的现代土木工程领域,混凝土材料的疲劳性能成为关注的重点之一。如何精确表征混凝土的疲性能演化和预测混凝土疲劳寿命成为工程设计、建造、检测和维护过程中的重要问题。现有的混凝土材料疲劳性能表征和疲劳寿命预测主要基于材料疲劳损伤的演化过程。对于压缩、拉伸和弯曲疲劳荷载的作用,研究者们分别发展了一系列疲劳模型。这些模型主要通过材料弹性模量的衰减来建立疲劳损伤关系,并基于此建立复杂的疲劳性能表征和寿命预测模型。现有模型通常需要包括疲劳应变、疲劳应力、弹性模量和材料拟合参数等多种参数,模型形式较为复杂,且一般需要进行迭代计算,因而在工程建设中推广应用有一定的困难。因此,提出一种变量较少,参数易确定,精度较高,且不受荷载形式影响的混凝土疲劳演化模型十分迫切,可以为工程设计、建设、检测和维护全过程提供重要技术支撑。
发明内容
本发明的目的在于提供一种形式简单、易于使用、精度较高的疲劳变形演化模型。为此,本发明采用以下技术方案:
一种基于Weibull方程的混凝土疲劳变形演化模型,其特征是,混凝土在某一应力水平的疲劳荷载作用下的疲劳荷载循环次数n,以及第n个疲劳荷载循环的某一个应力所对应的变形ε使用下式表示:
n/Nf=1-exp(-((ε-ε0)/λ)k)
式中,Nf是疲劳寿命,ε0是位置参数,λ是比例参数,k是形状参数。
进一步地,所述的某一个应力大于等于0,且小于等于所述疲劳荷载的最大应力。
进一步地,所述的疲劳荷载可以是压缩疲劳荷载、拉伸疲劳荷载或者弯曲疲劳荷载。
如果已知i个疲劳荷载循环次数n以及第n个劳荷载循环的某一个应力所对应的变形ε,即(ε1,n1)、(ε2,n2)、(ε3,n3)、……、(εi,ni),所述的疲劳寿命Nf、位置参数ε0、比例参数λ和形状参数k可以使用上述i组数据通过拟合获得。此外,在疲劳寿命Nf已知的情况下,则其他参数也可通过同样方法获得。
进一步地,当所述的某一个应力为所述疲劳荷载的最大应力时,所述的变形ε为最大变形εs;混凝土在某一应力水平的疲劳荷载作用下的疲劳荷载循环次数n和第n个循环的最大变形εs可使用下式表示:
式中,Nf是疲劳寿命,εs0是位置参数,λs是比例参数,ks是形状参数。位置参数εs0的一种可选值是混凝土第一次达到所述疲劳荷载的最大应力时所对应的变形。
进一步地,当所述的某一个应力为0时,所述的变形ε为残余变形εp;混凝土在某一应力水平的疲劳荷载作用下的疲劳荷载循环次数n和第n个循环的残余变形εp可使用下式表示:
式中,Nf是疲劳寿命,εp0是位置参数,λp是比例参数,kp是形状参数。位置参数εp0的一种可选值是0,另一种可选值是混凝土在所述疲劳荷载的第一个循环后的残余变形。
进一步地,当形状参数ks和kp的其中一个为已知量时,另一个参数的值可以取为与所述已知量相等的值。
本发明提供了一种基于Weibull方程的混凝土疲劳变形演化模型。所述的模型可以用于表征压缩、拉伸和弯曲疲劳荷载作用下混凝土的变形演化规律。具有可适用的荷载形式多样、表达式简洁、易于使用、精度较高等优点。在使用过程中,可以极大地减少计算量,且只需测量疲劳荷载循环次数n以及第n个循环的某一个应力所对应的变形ε这两种疲劳参数,可以简化检测设备。所述的模型,可以为工程设计、建设、检测和维护全过程提供重要技术支撑。
附图说明
图1是本发明实施例1所述压缩疲劳荷载作用下混凝土最大变形和残余变形演化过程的实验结果与模型结果图。
图2是本发明实施例2所述拉伸疲劳荷载作用下混凝土最大变形和残余变形演化过程的实验结果与模型结果图。
图3是本发明实施例3所述弯曲疲劳荷载作用下混凝土最大变形和残余变形演化过程的实验结果与模型结果图。
具体实施方式
下面结合附图对本发明所提供技术方案的具体实施方式作进一步说明,本实施实例是对本发明的说明,而不是对本发明作出任何限定。
实施例1
本实施例采用文献“Holmen J O.Fatigue of concrete by constant andvariable amplitude loading[J].ACI Special Publication,1982,75:71-110.”中“Fig.11”的混凝土压缩疲劳试样D22的疲劳变形结果。所述的试样在压缩疲劳荷载作用下的最大变形εs、残余变形εp的演化规律如图1所示。需要说明的是,所述的疲劳试样的最大变形εs从所述文献中直接获得,残余变形εp从所述文献中疲劳变形结果计算得来。
根据图1所示的最大变形εs的试验值,通过拟合,可以获得位置参数εs0=0.09582,比例参数λs=0.11497,形状参数ks=3.16309。从而可以获得如下疲劳变形演化模型:
n/Nf=1-exp(-((εs-0.09582)/0.11497)3.16309),(r2=0.9971)
根据图1所示的残余变形εp的试验值,通过拟合,可以获得位置参数εp0=0.01483,比例参数λp=0.09422,形状参数kp=3.27520。从而可以获得如下疲劳变形演化模型:
n/Nf=1-exp(-((εp-0.01483)/0.09422)3.27520),(r2=0.9991)
所得的疲劳变形演化模型结果与试验值的相关系数较高,可以较为准确地表征压缩疲劳变形演化规律,对比如图1所示。
实施例2
本实施例采用文献“Chen X,Bu J,Fan X,et al.Effect of loading frequencyand stress level on low cycle fatigue behavior of plain concrete in directtension[J].Construction and Building Materials,2017,133:367-375.”中“Fig.8c”的混凝土拉伸疲劳试样S=0.85test data的疲劳变形结果。所述的试样在拉伸疲劳荷载作用下的最大变形εs、残余变形εp的演化规律如图2所示。需要说明的是,所述的疲劳试样的最大变形εs和残余变形εp均从所述文献中直接获得。
根据图2所示的最大变形εs的试验值,通过拟合,可以获得位置参数εs0=38.21874,比例参数λs=66.41625,形状参数ks=11.44255。从而可以获得如下疲劳变形演化模型:
n/Nf=1-exp(-((εs-38.21874)/66.41625)11.44255),(r2=0.9769)
根据图2所示的残余变形εp的试验值,通过拟合,可以获得位置参数εp0=-2.14727,比例参数λp=37.79211,形状参数kp=10.44414。从而可以获得如下疲劳变形演化模型:
n/Nf=1-exp(-((εp+2.14727)/37.79211)10.44414),(r2=0.9188)
所得的疲劳变形演化模型结果与试验值的相关系数较高,可以较为准确地表征拉伸疲劳变形演化规律,对比如图2所示。
实施例3
本实施例采用文献“Liu W,Xu S,Li H.Flexural fatigue damage model ofultra-high toughness cementitious composites on base of continuum damagemechanics[J].International Journal of Damage Mechanics,2014,23(7):949-963.”中“Fig.3a”的纤维混凝土弯曲疲劳试样S0.80的疲劳变形结果。所述的试样在弯曲疲劳荷载作用下的最大变形εs、残余变形εp的演化规律如图3所示。需要说明的是,所述的疲劳试样的最大变形εs从所述文献中直接获得,残余变形εp从所述文献中疲劳变形结果计算得来。
根据图3所示的最大变形εs的试验值,通过拟合,可以获得位置参数εs0=-2.27807,比例参数λs=4.85335,形状参数ks=9.28728。从而可以获得如下疲劳变形演化模型:
n/Nf=1-exp(-((εs+2.27807)/4.85335)9.28728),(r2=0.9983)
根据图3所示的残余变形εp的试验值,通过拟合,可以获得位置参数εp0=-1.30373,比例参数λp=2.98369,形状参数kp=7.78920。从而可以获得如下疲劳变形演化模型:
n/Nf=1-exp(-((εp+1.30373)/2.98369)7.78920),(r2=0.9965)
所得的疲劳变形演化模型结果与试验值的相关系数较高,可以较为准确地表征弯曲疲劳变形演化规律,对比如图3所示。
Claims (9)
1.一种基于Weibull方程的混凝土疲劳变形演化模型,其特征是,混凝土在某一应力水平的疲劳荷载作用下的疲劳荷载循环次数n,以及第n个疲劳荷载循环的某一个应力所对应的变形ε使用下式表示:
n/Nf=1-exp(-((ε-ε0)/λ)k)
式中,Nf是疲劳寿命,ε0是位置参数,λ是比例参数,k是形状参数。
2.根据权利要求1所述的一种基于Weibull方程的混凝土疲劳变形演化模型,其特征是,所述的某一个应力大于等于0,且小于等于所述疲劳荷载的最大应力。
3.根据权利要求1所述的一种基于Weibull方程的混凝土疲劳变形演化模型,其特征是,所述的疲劳荷载可以是压缩疲劳荷载、拉伸疲劳荷载或者弯曲疲劳荷载。
4.根据权利要求1所述的一种基于Weibull方程的混凝土疲劳变形演化模型,其特征是,疲劳寿命Nf、位置参数ε0、比例参数λ和形状参数k可以使用已测得的若干个所述的变形ε和与其对应的疲劳荷载循环次数n通过拟合获得。
5.根据权利要求1所述的一种基于Weibull方程的混凝土疲劳变形演化模型,其特征是,当所述的某一个应力为所述疲劳荷载的最大应力时,所述的变形ε为最大变形εs;混凝土在某一应力水平的疲劳荷载作用下的疲劳荷载循环次数n和第n个疲劳荷载循环的最大变形εs可使用下式表示:
式中,Nf是疲劳寿命,εs0是位置参数,λs是比例参数,ks是形状参数。
6.根据权利要求5所述的一种基于Weibull方程的混凝土疲劳变形演化模型,其特征是,位置参数εs0的一种可选值是混凝土第一次达到所述疲劳荷载的最大应力时所对应的变形。
7.根据权利要求1所述的一种基于Weibull方程的混凝土疲劳变形演化模型,其特征是,当所述的某一个应力为0时,所述的变形ε为残余变形εp;混凝土在某一应力水平的疲劳荷载作用下的疲劳荷载循环次数n和第n个疲劳荷载循环的残余变形εp可使用下式表示:
式中,Nf是疲劳寿命,εp0是位置参数,λp是比例参数,kp是形状参数。
8.根据权利要求7所述的一种基于Weibull方程的混凝土疲劳变形演化模型,其特征是,位置参数εp0的一种可选值是0,另一种可选值是混凝土在所述疲劳荷载的第一个循环后的残余变形。
9.根据权利要求1所述的一种基于Weibull方程的混凝土疲劳变形演化模型,其特征是,
当所述的某一个应力为所述疲劳荷载的最大应力时,所述的变形ε为最大变形εs;混凝土在某一应力水平的疲劳荷载作用下的疲劳荷载循环次数n和第n个疲劳荷载循环的最大变形εs可使用下式表示:
式中,Nf是疲劳寿命,εs0是位置参数,λs是比例参数,ks是形状参数;
当所述的某一个应力为0时,所述的变形ε为残余变形εp;混凝土在某一应力水平的疲劳荷载作用下的疲劳荷载循环次数n和第n个疲劳荷载循环的残余变形εp可使用下式表示:
式中,Nf是疲劳寿命,εp0是位置参数,λp是比例参数,kp是形状参数;
当形状参数ks和kp的其中一个为已知量时,另一个参数的值可以取为与所述已知量相等的值。
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