岩石蠕变实验及非定常参数粘弹模型
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摘要
地球介质的流变模型一般认为都是定常的,即模型参数不随时间的增长而变化,但实际上,地球介质在构造运动等因素的作用下,其力学参数随时间的变化十分明显,故引入非定常参数粘弹模型,本文将围绕这一点进行研究和探索。
分别选取了断层泥、大理岩、花岗岩和砂岩作为试样进行了一系列的蠕变实验,有恒定荷载、多级加载等实验方式,实验持续时间从几小时到几天、几十天,温度从常温到500℃。
在对实验数据的处理过程中发现岩石蠕变曲线的反演具有蠕变模型的不唯一性和蠕变参数随时间变化的不唯一性。对于同一组实验数据,可以用标准线性体、伯格斯体和对数模型等三种模型来反演,得到的理论曲线和实测曲线非常相似,相关系数很高,体现了岩石蠕变曲线的反演具有蠕变模型的不唯一性。但当实验数据被分成长短不同的时间段时,即实验在假定的时间段内结束,反演得出模型的力学参数都随时间而变化,并不是定值常数,体现了岩石蠕变曲线的反演具有蠕变参数随时间变化的不唯一性。
为了获得合理的蠕变模型,提出了辨别模型优劣的两个标准,即“吻合”和“预测”:首先由模型所计算出的理论数据要能很好的吻合过去的实验数据,即和实测数据有很高的相关系数和很小的均方差;其次模型要具有较好的预测未来蠕变变化趋势的能力。为此将实验数据分成长短不同的两个时间段来处理,用第一段的实验数据反演计算,并将时间外延到第二段的时间长度绘出理论曲线,再和第二段的实测曲线作比较,这样的目的既比较了模型和实测数据的“吻合”程度,又能在第二阶段的比较中,检验模型的“预测”能力,两者相结合就能找出合理的蠕变模型。对于第一个标准,已有大量的研究,但对第二个标准则讨论较少。
非定常参数粘弹模型即修正后的标准线性体能够同时满足“吻合”和“预测”2个判别标准。标准线性体模型用来表示地球介质的粘弹性较好,它在短时间内,表现出明显的弹性性质,而在较长时间内,表现出明显的流变特性。对实验所得的蠕变曲线进行分段处理,反演得出非定常参数模量比C或模量E_2和粘滞系数η或弛豫时间Υ随时间的变化规律,就可以确定修正函数的具体形式,引入非定常参数粘弹模型。对于具体的地球物理问题如冰后期地面回升的观测数据,非定常参数粘弹模型能很好地模拟该数据,并且能够简易地计算出软流层的粘滞系数。
这种修正的本质其实就是对牛顿流体假定(n=1)的修正,是时间尺度对岩石力学参数影响的一种补偿。
It is generally considered that the rheological model of the Earth's media is steady, that is,the parameters of the model do not increase with time changes.In nature, the mechanical parameters change clearly with time because of the Earth's tectonic movement and other factors.Therefore,the non-constant viscoelastic creep model is introduced and the paper will focus on this research and exploration.
A series of creep experiments have been carried out on fault gouges,marbles, granites and sandstones with step-loading and cyclic multi-level loading methods.The duration of experiments ranges from several hours to dozens of days,and the temperature is between normal temperature to 500℃.
In the process of experimental data,it is found that there is non-uniqueness in inversion of creep curve and parameters of rock.For the same set of experimental data,three models Standard Linear Model(SLM),Burgers and Logarithm can be used to inverse the dataset.The theoretical curves obtained by inversion are similar with the measured curves and they are highly correlated.This means that the creep curve has non-uniqueness in creep model.However,when the length of the experimental data was divided into different time segments,that is,the experiment ended at the assumption time and inverse the different segments.The mechanical model parameters of inversion obtained are not constant values and vary with time.So the creep curves have non-uniqueness in the model parameters too.
In order to obtain reasonable creep model,two pieces of criterion are put forward to identify excellent model,they are "match" and "prediction".First of all,the data generated by the model should be a good match to the experimental data in the past. That is,there is a high correlation coefficient and small standard deviation.The other is the model should have the ability to predict better the future of creep.For this reason the experimental data will be divided into several different lengths of time.The first segment of experimental data is used to inverse and draws the theoretical curves;the second segment of experimental data is for comparison.The purpose of this division is not only comparison the degree of "match" between models and measured data in the first segment,but also checking up the "prediction" ability in the comparison of the second segment.It will be able to find a reasonable creep model by combination.For the first criteria,there are many studies,but there is little discussion on the second one.
The non-constant viscoelastic creep model namely modified standard linear model can at the same time meet the two criterions:"match" and "prediction".It is better to use the standard linear model(SLM) simulating the earth medium crust.In a short period of time it shows elasticity,and it shows rheological properties in a long time.Inverse the different segments dataset and obtain the modulus ratio C or the modular E_2 and the viscosity coefficientηor the relaxation timeτwhich change as time regularly. Then we can determine the specific form of correct function and introduce a viscoelastic model of variable parameters.The modified standard linear model can better meet the criterions "match" and "prediction".In fact,the essence of this modification is to change Newtonian(n = 1 ) assumption by compensating for the effect of time scale on rock mechanical parameters.For large-scale geophysical measured data such as the postglacial rebounding of ground,the non-constant viscoelastic creep model can well simulate the data and calculate the viscosity coefficient.
分别选取了断层泥、大理岩、花岗岩和砂岩作为试样进行了一系列的蠕变实验,有恒定荷载、多级加载等实验方式,实验持续时间从几小时到几天、几十天,温度从常温到500℃。
在对实验数据的处理过程中发现岩石蠕变曲线的反演具有蠕变模型的不唯一性和蠕变参数随时间变化的不唯一性。对于同一组实验数据,可以用标准线性体、伯格斯体和对数模型等三种模型来反演,得到的理论曲线和实测曲线非常相似,相关系数很高,体现了岩石蠕变曲线的反演具有蠕变模型的不唯一性。但当实验数据被分成长短不同的时间段时,即实验在假定的时间段内结束,反演得出模型的力学参数都随时间而变化,并不是定值常数,体现了岩石蠕变曲线的反演具有蠕变参数随时间变化的不唯一性。
为了获得合理的蠕变模型,提出了辨别模型优劣的两个标准,即“吻合”和“预测”:首先由模型所计算出的理论数据要能很好的吻合过去的实验数据,即和实测数据有很高的相关系数和很小的均方差;其次模型要具有较好的预测未来蠕变变化趋势的能力。为此将实验数据分成长短不同的两个时间段来处理,用第一段的实验数据反演计算,并将时间外延到第二段的时间长度绘出理论曲线,再和第二段的实测曲线作比较,这样的目的既比较了模型和实测数据的“吻合”程度,又能在第二阶段的比较中,检验模型的“预测”能力,两者相结合就能找出合理的蠕变模型。对于第一个标准,已有大量的研究,但对第二个标准则讨论较少。
非定常参数粘弹模型即修正后的标准线性体能够同时满足“吻合”和“预测”2个判别标准。标准线性体模型用来表示地球介质的粘弹性较好,它在短时间内,表现出明显的弹性性质,而在较长时间内,表现出明显的流变特性。对实验所得的蠕变曲线进行分段处理,反演得出非定常参数模量比C或模量E_2和粘滞系数η或弛豫时间Υ随时间的变化规律,就可以确定修正函数的具体形式,引入非定常参数粘弹模型。对于具体的地球物理问题如冰后期地面回升的观测数据,非定常参数粘弹模型能很好地模拟该数据,并且能够简易地计算出软流层的粘滞系数。
这种修正的本质其实就是对牛顿流体假定(n=1)的修正,是时间尺度对岩石力学参数影响的一种补偿。
It is generally considered that the rheological model of the Earth's media is steady, that is,the parameters of the model do not increase with time changes.In nature, the mechanical parameters change clearly with time because of the Earth's tectonic movement and other factors.Therefore,the non-constant viscoelastic creep model is introduced and the paper will focus on this research and exploration.
A series of creep experiments have been carried out on fault gouges,marbles, granites and sandstones with step-loading and cyclic multi-level loading methods.The duration of experiments ranges from several hours to dozens of days,and the temperature is between normal temperature to 500℃.
In the process of experimental data,it is found that there is non-uniqueness in inversion of creep curve and parameters of rock.For the same set of experimental data,three models Standard Linear Model(SLM),Burgers and Logarithm can be used to inverse the dataset.The theoretical curves obtained by inversion are similar with the measured curves and they are highly correlated.This means that the creep curve has non-uniqueness in creep model.However,when the length of the experimental data was divided into different time segments,that is,the experiment ended at the assumption time and inverse the different segments.The mechanical model parameters of inversion obtained are not constant values and vary with time.So the creep curves have non-uniqueness in the model parameters too.
In order to obtain reasonable creep model,two pieces of criterion are put forward to identify excellent model,they are "match" and "prediction".First of all,the data generated by the model should be a good match to the experimental data in the past. That is,there is a high correlation coefficient and small standard deviation.The other is the model should have the ability to predict better the future of creep.For this reason the experimental data will be divided into several different lengths of time.The first segment of experimental data is used to inverse and draws the theoretical curves;the second segment of experimental data is for comparison.The purpose of this division is not only comparison the degree of "match" between models and measured data in the first segment,but also checking up the "prediction" ability in the comparison of the second segment.It will be able to find a reasonable creep model by combination.For the first criteria,there are many studies,but there is little discussion on the second one.
The non-constant viscoelastic creep model namely modified standard linear model can at the same time meet the two criterions:"match" and "prediction".It is better to use the standard linear model(SLM) simulating the earth medium crust.In a short period of time it shows elasticity,and it shows rheological properties in a long time.Inverse the different segments dataset and obtain the modulus ratio C or the modular E_2 and the viscosity coefficientηor the relaxation timeτwhich change as time regularly. Then we can determine the specific form of correct function and introduce a viscoelastic model of variable parameters.The modified standard linear model can better meet the criterions "match" and "prediction".In fact,the essence of this modification is to change Newtonian(n = 1 ) assumption by compensating for the effect of time scale on rock mechanical parameters.For large-scale geophysical measured data such as the postglacial rebounding of ground,the non-constant viscoelastic creep model can well simulate the data and calculate the viscosity coefficient.
引文
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