砂土的剪胀性及本构模型的研究
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摘要
剪胀性和压硬性是岩土材料的基本特性,这是由岩土材料的颗粒性以及颗粒间摩擦性决定的。一个较成功的本构模型应当能够正确的反映剪胀性和压硬性这两个基本特性。对于压硬性的认识和利用已经比较成熟,而剪胀性由于其影响因素比较多,过程比较复杂,要恰当的描述剪胀性还要做许多工作。
本文首先对剪胀机理进行研究,提出了一种能描述砂土剪胀剪缩特性的简单的微观模型,同时在已有试验结果基础上定义了相变线,并提出了以相变状态为参考的状态参量和剪胀指标;接着,将剪胀指标引入到剑桥模型中,建立了基于剑桥模型的剪胀性砂土本构模型,另外结合热力学理论和边界面理论,并引入本文提出的剪胀指标和状态参量分别建立了基于热力学的剪胀性砂土本构模型和剪胀性砂土的边界面模型;最后,通过试验验证了本文建立的剪胀性砂土的边界面模型。
通过引入本文提出的以相变线为参考的状态参量和剪胀指标来描述剪胀性砂土的变形特性是本论文最显著的特点。本文的主要研究结果如下:
①利用本文提出的微观模型并与已有的变形机制相结合,解释了砂土的一系列变形特性:松砂只发生剪缩,而密砂则先剪缩后剪胀;对于剪胀性砂土,初始孔隙比越小(或者说越密实),峰值应力比越高,而相变应力比越低;同时也可以解释卸载体缩、相变状态以及临界状态,等等。与已有的以临界状态为参考的状态参数相比,本文提出的以相变状态为参考的状态参量和剪胀指标能够反映初始孔隙比对砂土变形过程中所处状态的影响,更适合描述剪胀性砂土的剪胀剪缩特性。
②以传统弹塑性理论为基础的剑桥模型简单实用,但不能恰当的描述剪胀性材料的变形特性。本文通过在剑桥模型的塑性势函数中引入以相变线为参考的剪胀指标,建立了一个基于剑桥模型的弹塑性本构模型,该模型能够较好的反应密实砂土先剪缩后剪胀的变形特性,并且对于松砂该模型能很自然的退化为剑桥模型。
③热力学理论能够从本质上解释传统弹塑性力学无法解释的一些岩土材料的变形特性,并使得传统弹塑性模型中的关联和非关联流动法则得到统一的描述。本文将热力学理论引入到本构模型中,同时针对密实砂土先剪缩后剪胀的变形特性,将本文所提出的剪胀指标引入到耗散空间的屈服函数中,建立了一个基于热力学的砂土本构模型,该模型的一个显著特点是能够很自然的运用非关联流动法则,而且能够描述密实砂土先剪缩后剪胀的变形特性,比较真实的反映砂土的变形特征。
④边界面理论引入到本构模型后,使得本构模型能够描述一些经典塑性理论无法描述的土的真实特性,例如循环荷载下砂土的变形特性,但在描述密砂由剪缩到剪胀的过程中遇到困难。本文把以相变线作为参考的状态参量以及剪胀指标引入到塑性模量和剪胀函数中,建立了一个基于边界面模型的剪胀性砂土本构模型,该模型能较好的描述密砂在循环荷载作用下的剪胀剪缩特性,并且能很自然的退化为比较简单的可以描述松砂变形特点的经典的边界面模型。
Stress-dilatancy and stress hardening are basic characters of soils, which are determined by the arrangement of grains and the friction among them, a good model should reflect the above two characters. Till now, the stress-hardening has been studied and applied successfully, but as for the stress-dilatancy, due to its complicated process and the many influencing factors, much research needs to be carried out to give a satisfactory description of stress-dilatancy.
In this dissertation, the mechanism of dilation in sands is researched, and on the basis of this research, we presented a microscope model which could describe sand's dilatant and compressive characteristics in a simple manner. With the help of some available experimental data, a phase transformation line is defined, and a state parameter together with a dilation index is introduced with the phase transformation line as a reference. Then, the dilation index was introduced into the Cam-Clay model and a stress-dilatancy model of sand was obtained. The thermomechanical framework and bounding surface theory could represent some behavior of some sand quite well, and combining with the proposed state parameter or the dilation index, those models could be more perfect, especially for describing compression and dilatancy. Finally, the proposed model based on the bounding surface theory was validated.
It's a distinct characteristic for the dissertation to introduce the state parameter and the dilation index, which took the transformation state as reference, into the models to describe the behavior of dilatant sand. The main conclusions are as follows:
①Combined with other mechanism, the presented micro-model could explain many characteristics of sands, such as bigger initial void ratio will result in a smaller peak value of stress ratio, loose sand compressed only while dense sand compressed first and then dilates, volume becomes small when unloading, and the state of transformation, the state of critical, the strength of sand can also take into account. Comparing with the previous state parameter which took the critical state as reference, the proposed state parameter and dilation index in the dissertation could represent the effect of the initial void on the state during deformation process, and is more suitable to describe the behavior of dilative sand.
②By introducing the proposed dilation index into the plastic potential function of the Cam-Clay model, a model for sand especially for dense sand was presented, which could describe the dense sand compressing first and then dilating. And as for loose sand, the presented model evolved into the Cam-Clay model.
③Combined with the thermo-mechanical framework, by introducing the proposed dilation index into the yield function of dissipative stress space, a model was brought forward; and it's the notable point of the model to apply the non-associated flow rule naturally and describe the true deformation of sand.
④By introducing the proposed sate parameter and dilation index into the plastic hardening modulus expression and the stress-dilatancy equation, a new dilatant constitutive model for sand was developed within the general framework of bounding surface, which could describe the characteristic of dense sand during cyclic loading. What's more, for loose sand, the model could evolve into the simple and classical bounding surface model naturally.
本文首先对剪胀机理进行研究,提出了一种能描述砂土剪胀剪缩特性的简单的微观模型,同时在已有试验结果基础上定义了相变线,并提出了以相变状态为参考的状态参量和剪胀指标;接着,将剪胀指标引入到剑桥模型中,建立了基于剑桥模型的剪胀性砂土本构模型,另外结合热力学理论和边界面理论,并引入本文提出的剪胀指标和状态参量分别建立了基于热力学的剪胀性砂土本构模型和剪胀性砂土的边界面模型;最后,通过试验验证了本文建立的剪胀性砂土的边界面模型。
通过引入本文提出的以相变线为参考的状态参量和剪胀指标来描述剪胀性砂土的变形特性是本论文最显著的特点。本文的主要研究结果如下:
①利用本文提出的微观模型并与已有的变形机制相结合,解释了砂土的一系列变形特性:松砂只发生剪缩,而密砂则先剪缩后剪胀;对于剪胀性砂土,初始孔隙比越小(或者说越密实),峰值应力比越高,而相变应力比越低;同时也可以解释卸载体缩、相变状态以及临界状态,等等。与已有的以临界状态为参考的状态参数相比,本文提出的以相变状态为参考的状态参量和剪胀指标能够反映初始孔隙比对砂土变形过程中所处状态的影响,更适合描述剪胀性砂土的剪胀剪缩特性。
②以传统弹塑性理论为基础的剑桥模型简单实用,但不能恰当的描述剪胀性材料的变形特性。本文通过在剑桥模型的塑性势函数中引入以相变线为参考的剪胀指标,建立了一个基于剑桥模型的弹塑性本构模型,该模型能够较好的反应密实砂土先剪缩后剪胀的变形特性,并且对于松砂该模型能很自然的退化为剑桥模型。
③热力学理论能够从本质上解释传统弹塑性力学无法解释的一些岩土材料的变形特性,并使得传统弹塑性模型中的关联和非关联流动法则得到统一的描述。本文将热力学理论引入到本构模型中,同时针对密实砂土先剪缩后剪胀的变形特性,将本文所提出的剪胀指标引入到耗散空间的屈服函数中,建立了一个基于热力学的砂土本构模型,该模型的一个显著特点是能够很自然的运用非关联流动法则,而且能够描述密实砂土先剪缩后剪胀的变形特性,比较真实的反映砂土的变形特征。
④边界面理论引入到本构模型后,使得本构模型能够描述一些经典塑性理论无法描述的土的真实特性,例如循环荷载下砂土的变形特性,但在描述密砂由剪缩到剪胀的过程中遇到困难。本文把以相变线作为参考的状态参量以及剪胀指标引入到塑性模量和剪胀函数中,建立了一个基于边界面模型的剪胀性砂土本构模型,该模型能较好的描述密砂在循环荷载作用下的剪胀剪缩特性,并且能很自然的退化为比较简单的可以描述松砂变形特点的经典的边界面模型。
Stress-dilatancy and stress hardening are basic characters of soils, which are determined by the arrangement of grains and the friction among them, a good model should reflect the above two characters. Till now, the stress-hardening has been studied and applied successfully, but as for the stress-dilatancy, due to its complicated process and the many influencing factors, much research needs to be carried out to give a satisfactory description of stress-dilatancy.
In this dissertation, the mechanism of dilation in sands is researched, and on the basis of this research, we presented a microscope model which could describe sand's dilatant and compressive characteristics in a simple manner. With the help of some available experimental data, a phase transformation line is defined, and a state parameter together with a dilation index is introduced with the phase transformation line as a reference. Then, the dilation index was introduced into the Cam-Clay model and a stress-dilatancy model of sand was obtained. The thermomechanical framework and bounding surface theory could represent some behavior of some sand quite well, and combining with the proposed state parameter or the dilation index, those models could be more perfect, especially for describing compression and dilatancy. Finally, the proposed model based on the bounding surface theory was validated.
It's a distinct characteristic for the dissertation to introduce the state parameter and the dilation index, which took the transformation state as reference, into the models to describe the behavior of dilatant sand. The main conclusions are as follows:
①Combined with other mechanism, the presented micro-model could explain many characteristics of sands, such as bigger initial void ratio will result in a smaller peak value of stress ratio, loose sand compressed only while dense sand compressed first and then dilates, volume becomes small when unloading, and the state of transformation, the state of critical, the strength of sand can also take into account. Comparing with the previous state parameter which took the critical state as reference, the proposed state parameter and dilation index in the dissertation could represent the effect of the initial void on the state during deformation process, and is more suitable to describe the behavior of dilative sand.
②By introducing the proposed dilation index into the plastic potential function of the Cam-Clay model, a model for sand especially for dense sand was presented, which could describe the dense sand compressing first and then dilating. And as for loose sand, the presented model evolved into the Cam-Clay model.
③Combined with the thermo-mechanical framework, by introducing the proposed dilation index into the yield function of dissipative stress space, a model was brought forward; and it's the notable point of the model to apply the non-associated flow rule naturally and describe the true deformation of sand.
④By introducing the proposed sate parameter and dilation index into the plastic hardening modulus expression and the stress-dilatancy equation, a new dilatant constitutive model for sand was developed within the general framework of bounding surface, which could describe the characteristic of dense sand during cyclic loading. What's more, for loose sand, the model could evolve into the simple and classical bounding surface model naturally.
引文
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