土本构关系及数值建模
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摘要
土是三相介质,其本构关系受许多因素的影响。由于土的本构模型是土工计算的基础,因而其本构关系及其建模方法的研究自二十世纪六十年代以来一直都受到诸多学者的重视。
本文首先总结了影响土本构关系的各种因素,并对多种土本构模型进行了评述,指出利用神经网络对土的本构关系进行数值建模是一种比较好的方法。
第二,对用于土本构关系数值建模的BP网络和RBF网络作了介绍。
第三,对土本构关系的数值建模方法进行了研究,这是本文的重点工作。本文对砂土和淤泥质粘土做了室内三轴试验。其中砂土是室内配制,淤泥质粘土为原状土样。结果显示无论是配制试样还是原状试样,试验数据往往很分散。当试验数据比较有限而且比较分散时,常规方法训练出的网络要么精度较低,要么出现过拟合现象,从而影响模型的准确性。本文着重对此进行了研究。方法之一是通过插值补充训练样本,这在一定程度上可以提高精度,减少过拟合现象。但这种方法并不是总很有效,而且这种方法要求试验的应力范围必须覆盖实际工程可能的应力范围;方法之二是归一化方法。研究发现土的应力-应变关系具有归一化特征,选择合适的归一化指标对三轴试验数据进行归一化处理,以归一化数据作为训练样本对RBF网络进行训练,得到了比较理想的土的神经网络本构模型(包括非线性弹性及弹塑性模型)。这种方法能够避免网络的过拟合现象,减小噪声信号的干扰,有效降低数据的有限性和分散性造成的影响,自动实现概率寻优,而且能反映土的剪胀性和应力路径对本构关系的影响。
神经网络用于拟合一般是将样本分为两部分,一部分用于训练网络,另一部分与网络的预测值进行比较,以验证网络的泛化性能。但这种方法用于土本构关系的建模并不十分理想,这是因为土工试验数据比较有限而且往往很分散。为此本文提出另一种判定网络训练效果的方法:(1)利用训练好的网络进行仿真,将应力-应变关系进行可视化,可视化图上应该没有过拟合现象;(2)将所有试验路径上的仿真值与试验值进行比较,大部分应该比较符合。满足了上述两点,即可保证在试验覆盖的应力范围内网络的可靠性。根据这个判定方法,本文提出的利用土应力-应变关系的归一化特征所建立的数值模型是成功的。
第四,对神经网络有限元进行分析;推导了基于广义塑性力学的土弹塑性矩阵;将砂土在增p路径和等p路径情况下获得的神经网络本构模型分别纳入有限元程序,分别对增p路径和等p路径加载的三轴试样进行了计算,结果良好,并且显示土体有限元计算应当采用能反映应力路径影响的本构模型。
Soils are aggregates of mineral particles, and together with air and/or water in the void spaces they form three-phase systems. The constitutive relations of soils are influenced by many factors, and they are the basis of computer simulation of soil body, so many scholars have paid attention to investigation of constitutive relations of soils since 1960s.
Many factors which influence constitutive relations of soils are summerized in this paper at first.And many constitutive models of soils are commentated.Then point out that it is a proper method to model constitutive relations by means of neural networks.
Secondly, the neural networks of BP and RBF which can be applied for modeling constitutive relations of soil are introduced.
Thirdly,the numerical modeling methods of constitutive relations of soil are researched,which is the major work of this paper.The triaxial tests of sand and mucky soil have been done.The sand used in triaxial test is graded one and the mucky soil is undisturbed .The test result shows that the test data are very discrete whenever the soil sample is made up or undisturbed.When the test data are discrete and the quantity of data is not enough,the neural network trained by conventional method will have lower accuracy or bring about over-fitting.These are primarily studied in this paper.One of the ways which is used to improve the precision of networks is to add new training samples by interpolation,which can take effect to a certain extend but is not always effective, moreover the stress range of the training samples should cover the possible stress range of actual engineering when the neural network models are applied in engineering;The second way is the method of normalization.Research shows that the stress-strain relationship of soil have the charactoristic of normalization. The triaxial test data are normalized by choosing proper normalization parameter. The neural networks of RBF are trained by regarding the normalized data as samples and then the ideal constitutive model of soil described by neural networks are obtained(include nonlinear elastic model and elastoplastic model). This way can reduce the interference of noise signal, avoid over-fitting of networks, lower the infuence caused by insufficiency and scatter of test data and can achieve probabilistic optimization automatically,furthermore,can reflect dilatancy and influence of stress path.
The data samples are usually divided into two parts when neural networks are applied in fitting constitutive relations of soils.One part is used in training network,the other is used to compare with predictive value of network to test the generalization capability of network.But this method to be used in modeling constitutive relation is not very ideal because the test data of soil are usually insufficient and discrete.So another way to judge training success is given in this paper:1) There should be no overfitting by observing the visualization curved surfaces obtained from simulating;2) The simulation value on every test stress path should close to the test value.The reliability of network in the range of test stress will be guaranteed if the above-mentioned two points are satisfied.According to the way of judgement,the numerical models obtained by using normalization charactoristic of stress-strain relation of soil are successful.
Fourthly, the FEM with constitutive model described by neural networks is analyzed;The elastroplastic matrix of soil based on generalized theory of plasticity is deduced; The neural network model of sand is brought into FEM program , then the calculation to the test sample is done and the results fit the experimental data well. Moreover the results show that the constitutive model adopted in FEM should reflect influence of stress path when soil body is computed.
本文首先总结了影响土本构关系的各种因素,并对多种土本构模型进行了评述,指出利用神经网络对土的本构关系进行数值建模是一种比较好的方法。
第二,对用于土本构关系数值建模的BP网络和RBF网络作了介绍。
第三,对土本构关系的数值建模方法进行了研究,这是本文的重点工作。本文对砂土和淤泥质粘土做了室内三轴试验。其中砂土是室内配制,淤泥质粘土为原状土样。结果显示无论是配制试样还是原状试样,试验数据往往很分散。当试验数据比较有限而且比较分散时,常规方法训练出的网络要么精度较低,要么出现过拟合现象,从而影响模型的准确性。本文着重对此进行了研究。方法之一是通过插值补充训练样本,这在一定程度上可以提高精度,减少过拟合现象。但这种方法并不是总很有效,而且这种方法要求试验的应力范围必须覆盖实际工程可能的应力范围;方法之二是归一化方法。研究发现土的应力-应变关系具有归一化特征,选择合适的归一化指标对三轴试验数据进行归一化处理,以归一化数据作为训练样本对RBF网络进行训练,得到了比较理想的土的神经网络本构模型(包括非线性弹性及弹塑性模型)。这种方法能够避免网络的过拟合现象,减小噪声信号的干扰,有效降低数据的有限性和分散性造成的影响,自动实现概率寻优,而且能反映土的剪胀性和应力路径对本构关系的影响。
神经网络用于拟合一般是将样本分为两部分,一部分用于训练网络,另一部分与网络的预测值进行比较,以验证网络的泛化性能。但这种方法用于土本构关系的建模并不十分理想,这是因为土工试验数据比较有限而且往往很分散。为此本文提出另一种判定网络训练效果的方法:(1)利用训练好的网络进行仿真,将应力-应变关系进行可视化,可视化图上应该没有过拟合现象;(2)将所有试验路径上的仿真值与试验值进行比较,大部分应该比较符合。满足了上述两点,即可保证在试验覆盖的应力范围内网络的可靠性。根据这个判定方法,本文提出的利用土应力-应变关系的归一化特征所建立的数值模型是成功的。
第四,对神经网络有限元进行分析;推导了基于广义塑性力学的土弹塑性矩阵;将砂土在增p路径和等p路径情况下获得的神经网络本构模型分别纳入有限元程序,分别对增p路径和等p路径加载的三轴试样进行了计算,结果良好,并且显示土体有限元计算应当采用能反映应力路径影响的本构模型。
Soils are aggregates of mineral particles, and together with air and/or water in the void spaces they form three-phase systems. The constitutive relations of soils are influenced by many factors, and they are the basis of computer simulation of soil body, so many scholars have paid attention to investigation of constitutive relations of soils since 1960s.
Many factors which influence constitutive relations of soils are summerized in this paper at first.And many constitutive models of soils are commentated.Then point out that it is a proper method to model constitutive relations by means of neural networks.
Secondly, the neural networks of BP and RBF which can be applied for modeling constitutive relations of soil are introduced.
Thirdly,the numerical modeling methods of constitutive relations of soil are researched,which is the major work of this paper.The triaxial tests of sand and mucky soil have been done.The sand used in triaxial test is graded one and the mucky soil is undisturbed .The test result shows that the test data are very discrete whenever the soil sample is made up or undisturbed.When the test data are discrete and the quantity of data is not enough,the neural network trained by conventional method will have lower accuracy or bring about over-fitting.These are primarily studied in this paper.One of the ways which is used to improve the precision of networks is to add new training samples by interpolation,which can take effect to a certain extend but is not always effective, moreover the stress range of the training samples should cover the possible stress range of actual engineering when the neural network models are applied in engineering;The second way is the method of normalization.Research shows that the stress-strain relationship of soil have the charactoristic of normalization. The triaxial test data are normalized by choosing proper normalization parameter. The neural networks of RBF are trained by regarding the normalized data as samples and then the ideal constitutive model of soil described by neural networks are obtained(include nonlinear elastic model and elastoplastic model). This way can reduce the interference of noise signal, avoid over-fitting of networks, lower the infuence caused by insufficiency and scatter of test data and can achieve probabilistic optimization automatically,furthermore,can reflect dilatancy and influence of stress path.
The data samples are usually divided into two parts when neural networks are applied in fitting constitutive relations of soils.One part is used in training network,the other is used to compare with predictive value of network to test the generalization capability of network.But this method to be used in modeling constitutive relation is not very ideal because the test data of soil are usually insufficient and discrete.So another way to judge training success is given in this paper:1) There should be no overfitting by observing the visualization curved surfaces obtained from simulating;2) The simulation value on every test stress path should close to the test value.The reliability of network in the range of test stress will be guaranteed if the above-mentioned two points are satisfied.According to the way of judgement,the numerical models obtained by using normalization charactoristic of stress-strain relation of soil are successful.
Fourthly, the FEM with constitutive model described by neural networks is analyzed;The elastroplastic matrix of soil based on generalized theory of plasticity is deduced; The neural network model of sand is brought into FEM program , then the calculation to the test sample is done and the results fit the experimental data well. Moreover the results show that the constitutive model adopted in FEM should reflect influence of stress path when soil body is computed.
引文
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