摘要
随着可再生能源和地源热泵技术的不断发展,浅层地热能的开发逐渐成为学者们重点研究的课题之一,但其理论研究远远落后于工程应用,尤其是土体在应力场和温度场复杂耦合作用下的力学机理研究尚不成熟。对于砂土、黏土、粉土等单一土体,学者们从温控试验和本构理论两方面展开研究,取得了一系列成果,对土体的热力学特性有一定认识。为了更全面深入地认识土体的热力学特性,使热本构模型在能源工程中更贴合实际地进行推广和应用,首先概述土体热力学性质的试验研究现状,随后,重点综述基于不同理论框架建立的土体热力学本构关系研究进展和现状,阐述热力学本构关系在实际工程中的应用,最后,针对目前存在的问题,提出进一步研究的建议,讨论并展望土体热力学本构关系的研究发展趋势。
近年来,清洁能源的高效率开发逐渐成为能源开发进程中的重中之
对于土体热力学性质的研究,通常包括试验研究、理论研究和数值研究三方面。通过开展考虑温度影响的室内试验,即温控试验,探索温度场和应力场耦合作用下土体的应力变形特性,并将其与常规应力场中土体的应力特性进行比较分析,得出土体的热力学特性,探索温度对土体变形、强度、剪胀方程、屈服方程、临界状态等方面的影
基于近年来对土体热力学本构关系的研究,结合笔者的部分研究成果,综述土体的温控试验、基于不同理论框架建立的热力学本构关系以及本构关系在数值分析中的应用等方面的主要进展,分析目前土体热力学本构关系仍需进一步突破的方向,为浅层地热能、能源桩等温度相关实际工程提供重要的理论依据。
土体热力学本构关系的提出需以土体的应力-应变关系为研究对象,在大量温控试验的基础上,得出土体的屈服特性、剪胀特性、固结特性等随应力和温度的演变规律,在弹塑性理论框架下,基于一定的基本假设,建立能够合理描述土体的基本特性、亚基本特性和关联基本特
为明确温度对土体本构关系的影响,确定本构模型相关参数,进而建立可靠的土体热力学本构模型,不少学者在常规杠杆式固结仪、四联直剪仪、静三轴仪、动三轴仪、空心扭剪仪和真三轴等室内试验仪器的基础上,设置螺旋型加热管、热电偶、水浴箱、不锈钢金属压力罩和隔热罩等设备,赋予常规试验仪器加热和温度监测功能,从而能够进行一
通过一维温控固结试验,Abuel-Naga
通过温控直剪试验,李春红
通过温控静三轴试验,郭桢
考虑到实际能源工程中经常遇到车辆荷载、地震荷载等循环荷载的作用,不少研究者通过开展饱和与非饱和状态下的温控动三轴试验,发现非饱和土体的累积塑性变形与温度和基质吸力有关,且基质吸力一定时,累积塑性变形随着温度的增加而增加,当温度一定时,累积塑性变形随着基质吸力的增加而减
本构关系又称为土体的力学本构方程,或土体的应力-应变模型,是描述土体力学特性的数学表达式。通过开展温控试验,学者们对土体在不同工况下的热力学性质有所认识,结合温控试验结果,提出力学或热屈服面方程、剪胀方程、临界状态方程等,随后,基于不同的弹塑性理论框架,建立考虑温度效应的土体本构关系。
作为非线性弹性模型的典型代表,邓肯-张模型包括-和-两种模型,其模型参数均可由常规三轴试验结果确定。
郭桢
英国剑桥大学的Roscoe
Hueckel
在修正剑桥模型的基础上,在临界土力学理论框架下,Abuel-Naga
(1) |
(2) |
式中:为各向同性先期固结应力;为应力比,即;为塑性势函数;和分别为塑性体积变形增量和塑性剪切变形增量;和为材料参数。通过温控试验数据,建立温度与材料参数和的关系式,从而提出一种适用于饱和黏土的热弹塑性本构模型。该模型中的材料参数随着温度的增加而线性增加,当为0时,该屈服面退化为修正剑桥模型的屈服面,该模型退化为不考虑温度影响的修正剑桥模型,如

图1 SBS等体积截面的几何形状随参数的变化规
Fig. 1 Change in geometry of constant-volume section of SBS with fabric parameter [
Cui

(a) 力学屈服曲线随参数的变化规律

(b) 热屈服曲线随参数的变化规律
图2 力学固结和热固结屈服函
Fig. 2 Yield functions of loading and thermal consolidatio
在Cui
Graham
前述热力学本构模型常用于模拟土体在大应变情况下的应力变形特性,但这些模型通常假定屈服面形状与温度无关,仅尺寸随温度变化,导致预测土体剪切特性时产生不可忽略的误差。因此,Zhou
在该模型基础上,在边界面内部区域考虑塑性应变,Zhou
此外,Zhou
在剑桥模型的基础上,结合广义Mises、SMP、Lade等强度准则,姚仰平
通过已有的温控试验数据,姚仰平
(3) |
其中:
(4) |
(5) |
式中:和分别为当前温度和初始温度作用下的临界状态应力比;、和均为材料参数。最后,基于SMP准则,将模型进行三维化,提出适用于超固结土体的考虑温度影响的本构模型。该模型可描述饱和超固结土体的热变形特性,以及温度不变时,正常固结土和超固结土体在复杂应力路径下的应力变形特性。在该模型的基础上,姚仰平
在热UH模
热力学是从宏观角度研究物质的热运动性质及其规律的学科,主要从能量转化的角度研究物质的热性质,揭示能量从一种形式转换为另一种形式时所遵循的宏观规律。
Zhang
Bai
Kurz
在温控循环试验数据的基础上,Ma
Zhang

图3 实际应力与温度变化引起的等效应力导致的体积应变相
Fig. 3 Similarity of volumetric strain caused by real stress and equivalent stress due to change of temperatur
在实际能源结构工程中,土体长期经历应力和温度的影响,时间对土体力学特性的影响显得格外重要。因此,非常有必要研究温度和时间作用下软岩等土体的蠕变破坏特性。Zhang
通过温控试验总结土体的热力学性质,结合相关理论建立土体的本构模型,其最终目的是将本构模型通过二次开发引入有限元软件中,并通过数值分析方法开展工程应用。
祁良
费康
1)现有的温控试验大多局限于黏土、粉土、砂土等单一土体,是一种理想状态下的土体,缺乏对粉砂、黏土-膨润土等混合土体热力学行为的研究。实际工程中的土体并不是纯砂土、纯粉土或纯黏土等单一土体,而是一种具有不同细粒含量的砂土、粉土或黏土的混合土体,且粉土或黏土占整个土体的比例不同时,土体呈现的热力学特性也有所不同。在今后的温控试验研究中,建议针对不同混合体或实际工程中的土体开展热力学试验,如此,室内的热力学试验结果更接近于实际工程中的监测值,更具有参考价值。
2)目前已有的温控试验主要集中于重塑土,该试样具有分层沉积特性,可考虑初始各向异性,但对于原状土的温控试验研究较少,即考虑土体的次生各向异性的研究较少。在今后的温控试验研究方面,建议多针对原状土,多考虑土体的结构性进行。
3)已有的温控静三轴、动三轴或空心扭剪试验均考虑土体在温度作用下的力学性质,仅考虑由温度引起的土体本身体积或强度变化,未考虑与温度有关的结构物以及结构物与周围土体接触面的热力学性质。而能源结构物与土体接触面往往是整个结构的薄弱环节。在今后的试验研究方面,建议多开展能源结构物和土体的模型试验以及现场的热响应试验,这样既能考虑温度变化对能源结构物和土体本身的力学性质的影响,又能考虑两者之间接触面的影响,从而更全面地考虑能源结构物和土体之间的相互作用。其试验结果更贴合实际工程,可以更好地应用于实际能源工程的设计与施工中。
4)以温控静三轴试验为例,已有的热力学试验过程常常为:土体先在常温下进行力学固结,随后,压力不变,进行加热或温度循环等热固结过程,然后,温度不变,在排水或不排水条件下进行剪切过程。在该过程中,温度和力学是分开加载的,不是真正意义上的热力耦合作用,而在实际能源工程中,土体中的应力场和温度场是同时存在的。为了减少室内试验和实际工程的误差,开展热破坏、应力-温度耦合加载、非比例加载、多重温控循环等复杂载荷作用下土体热力学行为试验研究尤为重要,同时为相关工程应用提供坚实的理论支持。
5)已有的土体热力学性质,主要是通过温控试验研究土体在温度变化下的变形和强度等宏观响应,是土体整体上的力学特征,但对于土体内部,特别是温度变化下试样不同部位孔隙水和土体颗粒之间的力学变化特性的研究相对较少。在之后的热力学特性研究方面,可利用CT、PFC等手段,研究在温度变化过程中土体内部发生的热力学特性,即从微观维度探索土体的热力学机理。
1)已有的热力学模型主要在剑桥或修正剑桥模型基础上建立先期固结应力、二次压缩系数、超固结比等参数与温度之间的关系,再结合临界状态理论,提出考虑时间效应、应力历史、各向异性等适用于饱和与非饱和粉土(黏土)的热力学模型。虽然考虑的作用形式较多,但土体种类较为单一,主要集中于黏土,对砂土或实际工程中较为常见的砂土-黏土混合物的热力学模型的研究相对较少。在今后的热力学模型方面,建议针对含有一定量粉土或黏土的粉砂类混合土体的力学模型进行研究,提出饱和粉砂在应力场及温度场耦合作用下的状态相关力学模型具有重要的理论意义。
2)已有的热力学模型建模过程大多较为复杂,参数不易确定,只适用于某些特定加载条件下土体的应力-应变响应。此外,大多数模型是基于一维固结或三轴压缩应力状态建立的,关于三维空间中土体强度和变形特性的研究较少。在今后的热力学模型研究中,建立易于确定参数的、考虑三维空间的热力学模型,从而更好地预测土体复杂的热力学特性是非常必要的。
3)目前对土体热力学本构关系的研究仍处于探索阶段。在温控试验的基础上,不少研究者已经建立了一些土体热力学本构关系,但如何在现有的理论基础上,面对复杂载荷条件下(如应力场和温度场耦合加载,非比例加载和升温、多重温控循环、循环荷载等)土体的力学响应,发展出更为合理准确的本构关系,还有待进一步深入研究。
已有的数值应用,通过不同的数值积分算法,将热力学模型应用于ABAQUS、COMSOL、MATLAB等软件中,建立考虑温度效应的有限元模型,并对能源结构进行数值模拟。由于对数值积分算法的认识还不够统一,热力学模型在实际工程中的应用远远滞后于本构理论的发展。对于不同的有限元软件,采用的数值积分算法各不相同。此外,已有的数值应用常模拟温控三轴试验过程和结果,数值模拟过于简单,没有能源结构物的参与,与实际工程差异较大。
在今后的数值应用中,针对不同框架下建立的热力学模型,建立可靠且通用的数字积分算法,并将该算法开发到有限元中,利用有限元对缩尺的模型试验或足尺的现场热响应试验进行模拟,将模拟值与监测值进行对比分析,从而验证该数值方法的可靠性,使模拟值更具有普适性,更好地应用于实际能源工程的设计与施工中。
浅层地热能是一种典型的可持续能源,其开发技术具有形式多样、高效节能、绿色低碳等特点。中国浅层地热资源丰富、类型齐全、分布广泛,能够形成或催生多领域、更广泛的利用方式,具有广阔的工程应用前景。地热资源开发过程中涉及应力场和温度场的耦合作用,土体、结构物以及两者之间接触面的力学行为的外在表现与内在机理均非常复杂。
微观维度上的热力学特性研究尚不多见,宏观维度上的热力学试验研究多为力学荷载和温度荷载分开加载,是“假”热-力耦合作用,而对于力学荷载和温度荷载同时加载的“真”热-力耦合作用的试验研究较少。因此,可在“假”热-力耦合温控试验基础上,通过分析力学固结和热固结两个阶段土体所发生的应力变形特性,分析该特性产生的力学机理,从而分析更为复杂的“真”热-力耦合温控试验中土体的热力学特性及其机理。室内温控试验研究还可以从常规的应力路径(力学固结-热固结-剪切)过渡到主应力旋转等复杂载荷下土体的热力学响应。室内温控试验主要研究土体的热力学特性,未考虑结构物的影响,其结果仅适用于能源结构工程的地基变形,即仅考虑能源结构物周围土体的热应力变形,而无法考虑能源结构物本身及其与周围土体接触面的热力学特性。因此,通过缩尺模型槽试验(如能量桩模型试验)和足尺现场热响应试验可以监测能源结构物、周围土体及其接触面的应力变形特性,结果更接近于实际能源工程。此外,将微观尺度上的温控试验数值模拟,宏观尺度上的室内常规温控试验,模型槽试验与现场热响应试验结合起来,通过开展不同尺度的热力学试验,全方位考虑尺寸效应对土体及结构物热力学性质的影响,从而基于相关理论,提出考虑土体热力学微观机理与宏观性质的本构关系,从而加深对土体热塑性变形机理的认识,这也是今后土体热力学性质研究的重中之重。
对于土体热力学本构模型的研究,其目的是进行工程应用,因此,加强土体热力学本构关系的二次开发,充分利用有限元计算分析软件开展相关工程数值模拟研究,建立考虑温度效应的土体数值分析方法非常必要。
总之,尽管目前已经取得了一定的研究成果,这些成果也在浅层地热能开发过程中发挥着非常重要的理论指导作用,但关于土体热力学本构关系的研究还处于起步阶段,在热力学试验、本构理论和数值应用方面仍存在诸多问题,亟须克服。这也需要更多的岩土工作者加倍努力,积极创新,不畏困难,从不同角度开展研究,从而建立土体热力学性质的研究体系,进一步认清土体的热力学机理,将其更好地应用于能源工程中。
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