Granular Matter (2010) 12:287–301 DOI 10.1007/s10035-010-0180-0 Shear banding and strain softening in plane strain extension: physical modelling L. Röchter · D. König · T. Schanz · T. Triantafyllidis Received: 3 May 2009 / Published online: 3 April 2010 © Springer-Verlag 2010 Abstract Localization of deformation in systems of shear bands or normal faults, respectively, as a consequence of extensional loading can be observed on a wide range of spa- tial scales in soil and rock formations. A series of plane strain model experiments was achieved in natural (1g) and increased (ng) gravity field (geotechnical centrifuge) with dry and moist sand as well as with dry and moist sand- clay mixtures. In these experiments, the geometry of the shear bands (inclination, width, spacing, sharpness) was de- tected by means of the digital image correlation (DIC) tech- nique. Comparison with existing analytical approaches for the determination of the spacing of shear bands is presented briefly. The stress-strain behaviour of the materials was deter- mined in a new biaxial test device, which allows for the per- formance of biaxial compression and extension tests. The evaluation focuses on the strain softening gradient, which is seen as a key parameter in the explanation of shear band spacing. Keywords Shear band patterns · Cohesive-frictional material · Physical modelling · Plane strain extension · Strain softening L. Röchter (B ) · D. König · T. Schanz Chair for Foundation Engineering, Soil and Rock Mechanics, Ruhr-Universität Bochum, Universitätsstr. 150, 44801 Bochum, Germany e-mail: lars.roechter@rub.de T. Triantafyllidis Institute of Soil Mechanics and Rock Mechanics, Universität Karlsruhe (TH), Engler-Bunte-Ring 14, 76131 Karlsruhe, Germany 1 Introduction 1.1 Shear band systems in situ, in physical and numerical modelling Localization of deformation in a system of shear bands or normal faults, respectively, as a consequence of exten- sional loading was reported on different spatial scales. On macro scale (10 2 –10 4 m), systems of parallel normal faults were documented in many extensional regions of the upper earth crust [5, 26, 32, 37, 53, 63, 64, 71]. Only McIntosh et al. [32] and Morellato et al. [37] presented quantitative data concerning the spacing of normal faults in situ. Numerous researchers addressed patterns of localization of deforma- tion in physical experiments on meso scale (10 -2 –10 -1 m). Different extensional mechanisms were applied in the field of experimental and numerical studies, such as stretching of a horizontal basement [5, 16, 18, 20, 30, 31, 42, 57], stretch- ing of an inclined basement [6, 58], imposing a disconti- nuity in the strain field [9, 12, 16, 38] or upward bending of the basement [6, 7]. But also in this field, only limited attention was paid to the quantitative determination of shear band spacing. In fact, only Le´ sniewska and Mróz [23, 24] and Wolf et al. [66–69] investigated this interesting topic. Wolf et al. investigated systematically the influence of speci- men’s height, granulometric properties, stress level and den- sity, using dry sand as model material. In this study, the process of localization of deformation was investigated in a broad range of material compositions, using dry and moist sand as well as dry and moist sand-clay mixtures as model material. The hitherto achieved large data base of about 60 model experiments allows for the analysis of shear band spacing depending on certain characteristics of the model material. 123