考虑颗粒破碎的粗粒土本构模型
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摘要
近年来随着大型机械碾压堆石技术的发展与应用，大粒径的粗粒土可以被碾压成相对紧密的状态。碾压粗粒土具有压缩性小、强度高以及良好的经济性及施工速度快等特点。因此被广泛应用于水利、交通等岩土工程建设中，特别是高土石坝建设中。
粗粒土是由粒径大小不等的颗粒彼此充填而呈粒状结构的散粒体，颗粒间常为点接触。试验表明，在压实和剪切等外力作用下，即使施加的能量和周围压力并不很大，也容易发生颗粒破碎。颗粒破碎改变了粗粒土的颗粒粒径、级配曲线及密实程度，影响其后继的应力应变行为，特别是对剪胀有较强的削弱作用。因此建立考虑颗粒破碎的粗粒土弹塑性本构模型，对准确把握粗粒土的工程性质，提高土石坝应力变形分析精度具有现实意义。
本文首先全面分析了前人关于土的颗粒破碎的度量方法，分析了各方法的优缺点和适用范围。研究中发现，粗粒土受力变形引起的颗粒破碎与自然风化引起的颗粒破碎有一定关系，可以采用自然风化模型的风化公比来描述粗粒土受力变形的颗粒破碎指数。通过对某工程粗粒土三轴试验中颗粒破碎试验数据的分析整理，提出了度量粗粒土颗粒破碎的计算公式。然后，分析了三轴应力条件下土颗粒的受力情况，根据罗维最小比能原理，推导出考虑颗粒破碎的粗粒土的屈服面。研究了粗粒土的流动法则，硬化规律和弹性规律，构建了考虑颗粒破碎的粗粒土本构关系模型。最后，采用改进的微粒群算法拟合三轴试验曲线，确定了模型参数。再用得到的模型参数计算了其它围压下的三轴试验曲线，与实际的试验曲线比较表明模型有较好的适应性。
In recent years, with the development and application of large machinery rolling rocktechnology, large size coarse granular soil can be rolled into a relative close state. Rolledcoarse granular soil has the characteristics of small compressibility, high strength, goodeconomic construction and construction fast. So it is widely used in water conservancy andtraffic earth engineering constructions especially in high embankment dam construction.
Coarse granular soil is made of soil granules of different size which fill each other. Testshows that the coarse granular soil is easy to break even though beared not extremely greatenergy and compression force. Particle breakage changed the particle size, size distributioncurve and dense of coarse granular soil, affect its subsequent stress-strain behavior, especiallyhas a strong role of weakening dilatancy. So developing elastoplastic constitutive modelincorporating particle breakage has practical significance of grasping the engineeringproperties of coarse granular soil and improving the analysis precision of stress-deformationfor embankment dam
This article first comprehensively analyzes parameters which are used to measureparticle breakage. This article also analyzes advantages, disadvantages and the scope ofapplication of each parameter. Research found that there is some relation between coarsegranular soil breakage caused by stress and deformation and particle breakage caused bynatural weathering, common ratio of natural weathering model can be used to describe brokenindex caused by stress and deformation of coarse granular soil. Through analyzing the testdata of particle breakage of triaxial test, the formula to calculate particle breakage parameteris developed. Then, through analysis of the force of soil particles under triaxial stress, a yieldsurface equation is derived which incorporates particle breakage according to Rowe'sminimum energy ratio principle. After studying plastic flow rule, harden law and elastic lawan elastoplastic constitutive model for coarse granular soil incorporating particle breakage isproposed. Finally the model parameters are determined by using the modified swarmoptimization fitting triaxial test curve. Using these parameters triaxial test stress-strain curveof other confming pressure is calculated. Comparing the results calculated by this model withtest data the valid of this model is verified.
粗粒土是由粒径大小不等的颗粒彼此充填而呈粒状结构的散粒体，颗粒间常为点接触。试验表明，在压实和剪切等外力作用下，即使施加的能量和周围压力并不很大，也容易发生颗粒破碎。颗粒破碎改变了粗粒土的颗粒粒径、级配曲线及密实程度，影响其后继的应力应变行为，特别是对剪胀有较强的削弱作用。因此建立考虑颗粒破碎的粗粒土弹塑性本构模型，对准确把握粗粒土的工程性质，提高土石坝应力变形分析精度具有现实意义。
本文首先全面分析了前人关于土的颗粒破碎的度量方法，分析了各方法的优缺点和适用范围。研究中发现，粗粒土受力变形引起的颗粒破碎与自然风化引起的颗粒破碎有一定关系，可以采用自然风化模型的风化公比来描述粗粒土受力变形的颗粒破碎指数。通过对某工程粗粒土三轴试验中颗粒破碎试验数据的分析整理，提出了度量粗粒土颗粒破碎的计算公式。然后，分析了三轴应力条件下土颗粒的受力情况，根据罗维最小比能原理，推导出考虑颗粒破碎的粗粒土的屈服面。研究了粗粒土的流动法则，硬化规律和弹性规律，构建了考虑颗粒破碎的粗粒土本构关系模型。最后，采用改进的微粒群算法拟合三轴试验曲线，确定了模型参数。再用得到的模型参数计算了其它围压下的三轴试验曲线，与实际的试验曲线比较表明模型有较好的适应性。
In recent years, with the development and application of large machinery rolling rocktechnology, large size coarse granular soil can be rolled into a relative close state. Rolledcoarse granular soil has the characteristics of small compressibility, high strength, goodeconomic construction and construction fast. So it is widely used in water conservancy andtraffic earth engineering constructions especially in high embankment dam construction.
Coarse granular soil is made of soil granules of different size which fill each other. Testshows that the coarse granular soil is easy to break even though beared not extremely greatenergy and compression force. Particle breakage changed the particle size, size distributioncurve and dense of coarse granular soil, affect its subsequent stress-strain behavior, especiallyhas a strong role of weakening dilatancy. So developing elastoplastic constitutive modelincorporating particle breakage has practical significance of grasping the engineeringproperties of coarse granular soil and improving the analysis precision of stress-deformationfor embankment dam
This article first comprehensively analyzes parameters which are used to measureparticle breakage. This article also analyzes advantages, disadvantages and the scope ofapplication of each parameter. Research found that there is some relation between coarsegranular soil breakage caused by stress and deformation and particle breakage caused bynatural weathering, common ratio of natural weathering model can be used to describe brokenindex caused by stress and deformation of coarse granular soil. Through analyzing the testdata of particle breakage of triaxial test, the formula to calculate particle breakage parameteris developed. Then, through analysis of the force of soil particles under triaxial stress, a yieldsurface equation is derived which incorporates particle breakage according to Rowe'sminimum energy ratio principle. After studying plastic flow rule, harden law and elastic lawan elastoplastic constitutive model for coarse granular soil incorporating particle breakage isproposed. Finally the model parameters are determined by using the modified swarmoptimization fitting triaxial test curve. Using these parameters triaxial test stress-strain curveof other confming pressure is calculated. Comparing the results calculated by this model withtest data the valid of this model is verified.
引文
[1]. Kjaernsli B, Sande A. Compressibility of some coarse grained materials[A]. Proc. European Conf. Soil Mech. And Found. Engrg. [C].Weisbaden: Germany, 1963.245-251.
[2]. Hall E B, Gordon B B. Triaxial testing with large-scale high pressure equipment. Laboratory Shear Testing of Soils. Spechial Tech. Pubication, 1963, 361: 315-328.
[3]. Vesic A, Clough G W. Behavior of granular materials under high stresses[J]. J. Soil Mech. and Found. Engrg. Div., ASCE, 1968,94(3): 661-688.
[4]. Mc Dowell G R, Boltom M D, Roberston D. The fractal crushing of granular materials[J].J. Mech. Soils, 1996,44(12):2079-2102.
[5]．蒙进，屈智炯．高压下冰碛土的颗粒破碎及应力应变关系[J]．成都科技大学学报，1989，43(1)：17-22．
[6]．马巍，吴紫汪，常小晓等．围压作用下冻结砂土微结构变化的电镜分析．[J]．冰川冻土，1995，17(2)：152-158
[7]．郭熙灵，胡辉等．堆石料颗粒破碎对剪胀性及抗剪强度的影响[J]．岩土工程学报，1997，19(3)：83-88．
[8]．刘崇权，汪稔．钙质砂在三轴剪切颗粒破碎评价及其能量公式[J]．工程地质学报，1999，7(4)：366-371．
[9]．温彦锋，蔡红，边京红．强风化岩防渗土料的压实及渗透特性[J]．水力发电学报，2002，69(2)：17-24．
[10]．汪稔，孙吉主．钙质砂不排水性状的损伤-滑移耦合作用分析[J]．水利学报，2002，(7)：75-78．
[11]．秦红玉，刘汉龙等．粗粒料强度和变形的大型三轴试验研究．[J]．岩土力学，2004，25(10)：1575-1580．
[12]．刘汉龙，秦红玉等．堆石粗粒料颗粒破碎试验研究．[J]．岩土力学，2005，26(4)：562-566．
[13]. Coop M R. The influence of particle breakage and state on the behaviour of sands[A]. Proc. International workshop on soil crushability[C]. Japan: Yamaguchi, 1999.
[14]. Joer H A, Bolton M D, Randoph M F. Compression and crushing behavio ur of calcareous soils[A]. Proc. International workshop on soil crushability[C].Japan: Yamaguchi, 1999.
[15]．屈智炯．土的塑性力学．成都：成都科技大学出版社，1987．
[16]．殷建华．土的三模量非线性模型及其推广．岩土力学，2000，21(1)：16-19．
[17]．陈正汉，周海清．非饱和土的非线性模型及其应用．岩土工程学报，1999，21(5)：603-608．
[18]. Duncan J M, Chang C Y Nonlinear analysis of stress-strain for soils[A], ASCE, 1970,96(5).
[19]. Duncan J M, Byrne P, Wong K S. Strength, stress-strain and bulk modulus parameters for finite element analysis of stresses and movements in soil masses[A]. Report No. UCB/CT/80-01.1980.
[20]. Janbu N. Soil compressibility as determined by Oedometer and triaxial tests[A]. European Conference on Soil Mechanics(CJ, 1963
[21]．沈珠江．考虑剪胀性的土和石料的非线性应力应变模式．水利水运科学研究，1985，4：12-17．
[22]. Norris, V.A., Numerical modeling of soil response to cyclic loading "stress-reversal surfaces". International symposium numerical models in geomechanics. Zurich:1982, 38-49.
[23]．孙吉主，周健．土的边界面本构模型研究进展．岩土力学，1997，18(2)：91-95．
[24]. Iwan, W.D., On a class of models for the yielding behavior of continuous and composite systems. Transactions on ASME J. Appl. Mech., 1976, 1(2):195-216.
[25]. Prager, W., A new method of analyzing stresses and strains in work-hardening plastic solids. J. Appl. Mech., 1956, 78:493-496.
[26]. Morz, M., Norris, V.A. and Zienkiewicz, O.C., Application of an anisotropic hardening model in the analysis of elasto-plastic deformation of soil. Geotechnique, 1979, 29(1):1-34.
[27]. Pender, M.J., A model for the behavior of over-consolidated soil. Geotechnique, 1978, 28(1):1-25.
[28]. Dafalias, Y.F., Popov, E.P., A model of non-linearly hardening materials for complex loadings. Acta Mechanica, 1975, 21(3):173-192.
[29]. Norris, V.A., Numerical modeling of soil response to cyclic loading "stress-reversal surfaces". International symposium numerical models in geomechanics. Zurich:1982, 38-49.
[30]．郭庆国．粗粒土的工程特性及应用[M]．郑州：黄河水利出版社，1998．
[31]．张克昌．含泥砂砾石的强度特性[J]．岩土工程学报，1985，7(6)：51-59．
[32]．郭庆国．关于粗料土抗剪强度特性的试验研究[[J]．水利学报，1987，(5)：59-65．
[33]. Leps T M. Review of shearing strength of rockfill[J]. Journal of the Soil Mechanics and Foundation Division, ASCE, 1983,96(SM4):667-678.
[34]. Duncan J M, Byrne 1'et al. Strength, stress-strain and bulk modulus parameters for finite element analysis of stress sand movements in soil masses[R]. In:Report No. UCB/GT/80-01, University of California, Berkerley, 1980.
[35]. Marsal R J. Large scale testing of rockfill materials[J].Jourmal of the Soil Mechanics and Foundations Division. 1967, 93(SM2): 27-43.
[36]．Marsal R J．土石坝工程[M]．(第四章)．江苏：水利出版社，1979．
[37]. Lee K L, Seed H B. Drained strength characteristics of sand, Proc[C]. ASCE, JSMFD. 1967, 93 (SM6)
[38]. Lee K L, Farhoomand I. Compressibility and crushing ofgranular soils in anisotropic triaxial compression[J]. Can. Geotech., 1967, (14): 68-86.
[39]. Norihiko Miura and Sukeo O-hara, Particle crushing of a decomposed granite soil under shear stresses[J]. Soils and Foundations. JSSMFE. 1979,19(3)
[40]. Poul V lade, Jerry A, Yamamuro, Paul A Bopp. Signification of particle crushing in granular materials[J]. Journal of Geotechniall Engineering, ASCE, 1996,122(4).
[41]. Bobby O, Hardin F. Crushing of soil particles[J]. Journal of Geotechnical Engineering, ASCE, 1985, 111(10).
[42]. Bishop A W. The strength of soils as engineering materials[J]. Geotechnique, 1966, 16: 91-128.
[43]. Yukio Nakata. Microscopic particle crushing of sand subjected to high pressure one-dimensional compression[J]. Soils and foundations 2001, Vol. 41, No. 1, 69-82
[44]. Takeaki Fukumoto. A grading equation for decomposed granite soil. [J]. Soils and foundations 1990, Vol. 30, No.1, 27-34
[45]．陈惠发，萨里普A F．土木工程材料的本构方程[M]．中华科技大学出版社，2001．
[46]. Tzou-Shin Ueng and Tse-Jen Chen. Energy aspects of particle breakage in drained shear of sands. Geotechnique, 2000, vol. 50, No1, 65-72
[47]．姚仰平，罗汀。岩土硬化的应力路径相关性及硬化参数的构造方法。中国岩土力学与工程学会第七次学术大会论文集。中国，西安。2002．9，106-119
[48]．钱家欢，殷宗泽．土工原理与计算(第二版)[M]．北京：中国水利水电出版社，1996，54-60
[49]．曾建潮，崔志华。微粒群算法的统一模型及分析。计算机研究与发展。2006，43(1)：96—100。
[2]. Hall E B, Gordon B B. Triaxial testing with large-scale high pressure equipment. Laboratory Shear Testing of Soils. Spechial Tech. Pubication, 1963, 361: 315-328.
[3]. Vesic A, Clough G W. Behavior of granular materials under high stresses[J]. J. Soil Mech. and Found. Engrg. Div., ASCE, 1968,94(3): 661-688.
[4]. Mc Dowell G R, Boltom M D, Roberston D. The fractal crushing of granular materials[J].J. Mech. Soils, 1996,44(12):2079-2102.
[5]．蒙进，屈智炯．高压下冰碛土的颗粒破碎及应力应变关系[J]．成都科技大学学报，1989，43(1)：17-22．
[6]．马巍，吴紫汪，常小晓等．围压作用下冻结砂土微结构变化的电镜分析．[J]．冰川冻土，1995，17(2)：152-158
[7]．郭熙灵，胡辉等．堆石料颗粒破碎对剪胀性及抗剪强度的影响[J]．岩土工程学报，1997，19(3)：83-88．
[8]．刘崇权，汪稔．钙质砂在三轴剪切颗粒破碎评价及其能量公式[J]．工程地质学报，1999，7(4)：366-371．
[9]．温彦锋，蔡红，边京红．强风化岩防渗土料的压实及渗透特性[J]．水力发电学报，2002，69(2)：17-24．
[10]．汪稔，孙吉主．钙质砂不排水性状的损伤-滑移耦合作用分析[J]．水利学报，2002，(7)：75-78．
[11]．秦红玉，刘汉龙等．粗粒料强度和变形的大型三轴试验研究．[J]．岩土力学，2004，25(10)：1575-1580．
[12]．刘汉龙，秦红玉等．堆石粗粒料颗粒破碎试验研究．[J]．岩土力学，2005，26(4)：562-566．
[13]. Coop M R. The influence of particle breakage and state on the behaviour of sands[A]. Proc. International workshop on soil crushability[C]. Japan: Yamaguchi, 1999.
[14]. Joer H A, Bolton M D, Randoph M F. Compression and crushing behavio ur of calcareous soils[A]. Proc. International workshop on soil crushability[C].Japan: Yamaguchi, 1999.
[15]．屈智炯．土的塑性力学．成都：成都科技大学出版社，1987．
[16]．殷建华．土的三模量非线性模型及其推广．岩土力学，2000，21(1)：16-19．
[17]．陈正汉，周海清．非饱和土的非线性模型及其应用．岩土工程学报，1999，21(5)：603-608．
[18]. Duncan J M, Chang C Y Nonlinear analysis of stress-strain for soils[A], ASCE, 1970,96(5).
[19]. Duncan J M, Byrne P, Wong K S. Strength, stress-strain and bulk modulus parameters for finite element analysis of stresses and movements in soil masses[A]. Report No. UCB/CT/80-01.1980.
[20]. Janbu N. Soil compressibility as determined by Oedometer and triaxial tests[A]. European Conference on Soil Mechanics(CJ, 1963
[21]．沈珠江．考虑剪胀性的土和石料的非线性应力应变模式．水利水运科学研究，1985，4：12-17．
[22]. Norris, V.A., Numerical modeling of soil response to cyclic loading "stress-reversal surfaces". International symposium numerical models in geomechanics. Zurich:1982, 38-49.
[23]．孙吉主，周健．土的边界面本构模型研究进展．岩土力学，1997，18(2)：91-95．
[24]. Iwan, W.D., On a class of models for the yielding behavior of continuous and composite systems. Transactions on ASME J. Appl. Mech., 1976, 1(2):195-216.
[25]. Prager, W., A new method of analyzing stresses and strains in work-hardening plastic solids. J. Appl. Mech., 1956, 78:493-496.
[26]. Morz, M., Norris, V.A. and Zienkiewicz, O.C., Application of an anisotropic hardening model in the analysis of elasto-plastic deformation of soil. Geotechnique, 1979, 29(1):1-34.
[27]. Pender, M.J., A model for the behavior of over-consolidated soil. Geotechnique, 1978, 28(1):1-25.
[28]. Dafalias, Y.F., Popov, E.P., A model of non-linearly hardening materials for complex loadings. Acta Mechanica, 1975, 21(3):173-192.
[29]. Norris, V.A., Numerical modeling of soil response to cyclic loading "stress-reversal surfaces". International symposium numerical models in geomechanics. Zurich:1982, 38-49.
[30]．郭庆国．粗粒土的工程特性及应用[M]．郑州：黄河水利出版社，1998．
[31]．张克昌．含泥砂砾石的强度特性[J]．岩土工程学报，1985，7(6)：51-59．
[32]．郭庆国．关于粗料土抗剪强度特性的试验研究[[J]．水利学报，1987，(5)：59-65．
[33]. Leps T M. Review of shearing strength of rockfill[J]. Journal of the Soil Mechanics and Foundation Division, ASCE, 1983,96(SM4):667-678.
[34]. Duncan J M, Byrne 1'et al. Strength, stress-strain and bulk modulus parameters for finite element analysis of stress sand movements in soil masses[R]. In:Report No. UCB/GT/80-01, University of California, Berkerley, 1980.
[35]. Marsal R J. Large scale testing of rockfill materials[J].Jourmal of the Soil Mechanics and Foundations Division. 1967, 93(SM2): 27-43.
[36]．Marsal R J．土石坝工程[M]．(第四章)．江苏：水利出版社，1979．
[37]. Lee K L, Seed H B. Drained strength characteristics of sand, Proc[C]. ASCE, JSMFD. 1967, 93 (SM6)
[38]. Lee K L, Farhoomand I. Compressibility and crushing ofgranular soils in anisotropic triaxial compression[J]. Can. Geotech., 1967, (14): 68-86.
[39]. Norihiko Miura and Sukeo O-hara, Particle crushing of a decomposed granite soil under shear stresses[J]. Soils and Foundations. JSSMFE. 1979,19(3)
[40]. Poul V lade, Jerry A, Yamamuro, Paul A Bopp. Signification of particle crushing in granular materials[J]. Journal of Geotechniall Engineering, ASCE, 1996,122(4).
[41]. Bobby O, Hardin F. Crushing of soil particles[J]. Journal of Geotechnical Engineering, ASCE, 1985, 111(10).
[42]. Bishop A W. The strength of soils as engineering materials[J]. Geotechnique, 1966, 16: 91-128.
[43]. Yukio Nakata. Microscopic particle crushing of sand subjected to high pressure one-dimensional compression[J]. Soils and foundations 2001, Vol. 41, No. 1, 69-82
[44]. Takeaki Fukumoto. A grading equation for decomposed granite soil. [J]. Soils and foundations 1990, Vol. 30, No.1, 27-34
[45]．陈惠发，萨里普A F．土木工程材料的本构方程[M]．中华科技大学出版社，2001．
[46]. Tzou-Shin Ueng and Tse-Jen Chen. Energy aspects of particle breakage in drained shear of sands. Geotechnique, 2000, vol. 50, No1, 65-72
[47]．姚仰平，罗汀。岩土硬化的应力路径相关性及硬化参数的构造方法。中国岩土力学与工程学会第七次学术大会论文集。中国，西安。2002．9，106-119
[48]．钱家欢，殷宗泽．土工原理与计算(第二版)[M]．北京：中国水利水电出版社，1996，54-60
[49]．曾建潮，崔志华。微粒群算法的统一模型及分析。计算机研究与发展。2006，43(1)：96—100。