Fabric Evolution and Its Effect on Strain Localization in Sand

Transcription

1 Fabric Evolution and Its Effect on Strain Localization in Sand Ziwei Gao and Jidong Zao Abstract Fabric anisotropy affects importantly te overall beaviour of sand including its strengt and deformation caracteristics. Wile bot experimental and numerical evidence indicates tat soil fabric evolves steadily wit te applied stress/strain, ow evolving fabric influences te initiation and development of sear band in sand remains an intriguing question to be fully addressed. In tis paper, we present a numerical study on strain localization in sand, igligting te special role played by soil fabric and its evolution. In particular, a critical state sand plasticity model accounting for te effect of fabric and its evolution is used in te finite element analysis of plane strain compression tests. It is found tat te initiation of sear band is controlled by te initial fabric, wile te development of sear band is governed by two competing pysical mecanisms, namely, te structural constraint and te evolution of fabric. Te evolution of fabric generally makes te sand response more coaxial wit te applied load, wile te structural constraint induced by te sample ends leads to more inomogeneous deformation witin te sand sample wen te initial fabric is non-coaxial wit te applied stress. In te case of smoot boundary condition, structural constraint dominates over te fabric evolution and leads to te formation of a single sear band. Wen te boundary condition is roug, te structural constraint may play a comparable role wit fabric evolution, wic leads to symmetric cross-sape sear bands. If te fabric is proibited from evolving in te latter case, a cross-sape sear band pattern is found wit te one initiated first by te structural constraint dominant over te second one. Z. Gao ( ) Scool of Engineering, University of Glasgow, Rankine Building, Oakfield Avenue, Glasgow G12 8LT, UK Ziwei.Gao@glasgow.ac.uk J. Zao Department of Civil and Environmental Engineering, Hong Kong University of Science and Tecnology, Clearwater Bay, Kowloon, Hong Kong Springer International Publising Switzerland 2015 K.-T. Cau and J. Zao (eds.), Bifurcation and Degradation of Geomaterials in te New Millennium, Springer Series in Geomecanics and Geoengineering, DOI / _4 21

2 22 Z. Gao and J. Zao 1 Introduction Strain localization is frequently observed in sand and is considered an important precursor of te failure of soil and relevant geostructures. Numerous investigations ave been carried out on strain localization in sand but relatively less attention as been paid to te correlation of strain localization wit te presence of an evolving fabric (e.g., Borja et al. 2013). Fabric anisotropy as been widely regarded to affect te key beaviour of sand including dilatancy, liquefaction and critical state. Based on plain strain compression tests, Tatsuoka et al. (1990) found tat te sear band development in sand was dependent on te initial bedding plane orientation, or te fabric, of te sample. Meanwile, micromecanical studies indicate tat fabric evolves steadily wit deformation and te evolving fabric exibits unique caracteristics wen a sand sample reaces liquefaction, critical state and oter states (Guo and Zao 2013; Zao and Guo 2013a, b). As an important type of instabilities, strain localization as been commonly observed in sand. Te correlation between fabric and fabric evolution is an interesting topic but remains less explored. Inerent fabric anisotropy as recently been considered in a ypoplastic model by Tejcman et al. (2007) in te simulation of sear band development in sand but te interplay between fabric evolution and te development of sear band as not been properly considered. In tis study, we employ an anisotropic sand model developed recently by te autors (Gao et al. 2014) and finite element metod to investigate strain localization in sand under plane strain compression werein te special role of fabric and its evolution is igligted. 2 Finite Element Analysis of Strain Localization in Plane Stain Compression Te constitutive model used in tis study was developed by Gao et al. (2014). It as been implemented in te finite element package ABAQUS troug te user-material interface. Te test data presented by Tatsuoka et al. (1990) will be employed to bencmark te model simulations. Te model parameters ave been calibrated based on te plane strain test results on Toyoura sand. Te initial degree of anisotropy F 0 is set to be Te model simulations for single element tests can be found in Gao et al. (2014) and Gao and Zao (2013). In te finite element analysis, te sample setup is te same as tat in Tatsuoka et al. (1990) (Fig. 1). Uniform 4-noded plane strain elements of 2.5 mm 2.5 mm in size are used and constant confining pressure is applied in te orizontal direction of te sample. Vertical displacement is applied to te top end of te sample by increment to ensure quasi-static loading. Bot smoot (te top and bottom ends are free to move orizontally) and roug (te orizontal displacements of te top and bottom ends are restricted) boundary conditions wit and witout fabric evolution are considered and te initial void ratio distribution is assumed to be uniform trougout te entire sample.

3 Fabric Evolution and Its Effect on Strain 23 =10.5cm Bedding plane y z w=4cm x α Fig. 1 Sample setup, element size, orientation of bedding plane and te reference coordinate system (a) (b) Type-b sear band Fig. 2 Predicted strain localization for te cases wit smoot boundary condition and a evolving fabric; b constant fabric at vertical strain ε = / = 12 % Figure 2 sows te predicted sear band pattern in smoot boundary condition cases wit initial void ratio e 0 = 0.7, confining pressure σ c = 400 kpa and bedding plane orientation α = 45. It can be seen tat te simulated sear band and bedding plane lie on te same side (left side in te upper part of te sample for te present study) of te major principal stress direction (Fig. 2a) and Tatsuoka et al. (1990) terms similar sear band pattern tey observed in laboratory tests as Type-b sear band. Indeed, Type-b sear band is te most commonly observed pattern in laboratory tests wit smoot boundary (Tatsuoka et al. 1990). Wen te fabric is assumed constant (te fabric is proibited from evolving wit deformation), te

4 24 Z. Gao and J. Zao (a) Type-a sear band (b) Type-b sear band Fig. 3 Predicted strain localization for te cases wit roug boundary condition and a evolving fabric; b constant fabric at vertical strain ε = / = 15.5 % strain concentration in te sear band (Fig. 2b) will be more intense tan te fabric evolution case (Fig. 2a). In addition, it is observed tat te predicted vertical strain level corresponding to sear band initiation is independent of initial bedding plane orientation if te fabric is assumed constant, wic appears to be inconsistent wit te observations in Tatsuoka et al. (1990). Tis indicates tat fabric evolution sould be properly accounted for in te strain localization analysis. Figure 3 sows te predicted sear band pattern in roug boundary condition cases (e 0 = 0.7, σ c = 400 kpa and α = 45 ). Two symmetric and asymmetric sear bands are observed for te cases wit and witout fabric evolution, respectively. Te sear strain level in Type-a sear bands [according to te definition by Tatsuoka et al. (1990)] is iger tan tat in te Type-b sear bands in bot cases. 3 Mecanisms Governing te Sear Band Patterns Our study sows tat te development of a sear band is essentially governed by two competing mecanisms te fabric evolution wic reduces te non-coaxial strain increment wen te fabric and applied stress are initially non-coaxial and alleviates te strain localization and te structural constraint imposed by te boundary conditions wic promotes te sear band development. Te structural constraint can be better described by te reaction forces at te top and bottom sample ends as sown in Fig. 4. In te smoot boundary condition cases, te initial bedding plane constitutes a natural weakened plane along wic te sample can develop sear strain concentration and te vertical reaction forces on te two ends drive te upper and lower

5 Fabric Evolution and Its Effect on Strain 25 (a) (b) (c) (d) R Positive orizontal reaction force b a Bedding plane α R Total reaction force R wen R < 0 f Total reaction force R wen R = 0 f Total reaction force R wen R > 0 f Fig. 4 Definition of a te positive direction of te orizontal reaction force R, c d tree cases of te total reaction force imposed on te sample by te boundary Fig. 5 Evolution of te orizontal reaction force at te top end of te sand sample wit α = 45 and roug boundary condition (e 0 = 0.7, σ 3 = 400 kpa): a considering fabric evolution; b considering constant fabric parts of te sample to te rigt and left respectively. Tis causes te occurrence of a single Type-b sear band. Since te strain localization initiates at relatively low strain level, te effect of fabric evolution is not large enoug to prevent te sear band development in tis case. In te roug boundary condition cases, negative R develops to prevent te orizontal displacement of te top and bottom ends due to te non-coaxial strain increment at te initial loading stage (Fig. 5), wic leads to a Type-a sear band initially. As te sample is weakened along direction-a due to stain localization (Fig. 5a), te magnitude of R decreases and becomes positive subsequently. Tis causes te initiation of Type-b sear band. Meanwile, te evolution of fabric can eventually lead to rater symmetric geometry of te two bands as well as sample sape (Fig. 4a). If te fabric is fixed witout evolution, te final sample sape and sear bands are asymmetric as R will become negative again later on (Fig. 5b).

6 26 Z. Gao and J. Zao 4 Conclusions Te effect of fabric evolution on strain localization in plane strain compression as been studied numerically. It is found tat te evolution of fabric generally tends to make te sand response more coaxial wit te applied stress and alleviate te strain localization, wile te structural constraint induced by te sample ends leads to more inomogeneous deformation witin te sand sample wen te initial fabric is non-coaxial wit te applied stress. In smoot boundary condition cases, structural constraint dominates over te fabric evolution and leads to te formation of a single sear band. Wen te boundary condition is roug, te structural constraint may play a comparable role wit fabric evolution, wic leads to symmetric cross-sape sear bands. If te soil fabric is not allowed to evolve, asymmetric cross-sape sear bands develop. Acknowledgements Te study was financially supported by RGC/GRF and DAG08/09.EG04. References Borja RI, Song XY, Recenmacer AL, Abedi S, Wu W (2013) Sear band in sand wit spatially varying density. J Mec Pys Solids 61: Gao ZW, Zao JD (2013) Strain localization and fabric evolution in sand. Int J Solid Struct 50: Gao ZW, Zao JD, Li XS, Dafalias YF (2014) A critical state sand plasticity model accounting for fabric evolution. Int J Numer Anal Met Geomec 38: Guo N, Zao JD (2013) Te signature of sear induced anisotropy in granular media. Comput Geotec 47:1 15 Tatsuoka F, Nakamura S, Huang CC, Tani K (1990) Strengt anisotropy and sear band direction in plane strain tests of sand. Soils Found 30(1):35 54 Tejcman J, Bauer E, Wu W (2007) Effect of fabric anisotropy on sear localization in sand during plane strain compression. Acta Mec 189:23 51 Zao JD, Guo N (2013a) Unique critical state caracteristics in granular media considering fabric anisotropy. Géotecnique 63(8): Zao JD, Guo N (2013b) A new definition on critical state of granular media accounting for fabric anisotropy. In: Powders and grains 2013: AIP conference proceedings, vol 1542, pp doi: /