A Shear Response Surface for the Characterization of Unit-Mortar Interfaces
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15th International Brick and Block Masonry Conference Florianópolis – Brazil – 2012 A SHEAR RESPONSE SURFACE FOR THE CHARACTERIZATION OF UNIT-MORTAR INTERFACES Parisi, Fulvio1; Augenti, Nicola2 1 PhD, Post-Doc, University of Naples Federico II, Department of Structural Engineering, [email protected] 2 Professor, University of Naples Federico II, Department of Structural Engineering, [email protected] Shear behaviour of unit-mortar interfaces is typically characterized through the Mohr- Coulomb failure model and shear stress versus shear strain diagrams. In porous stone masonry types such as tuff masonry, dilatancy plays also a key role and shear strength of unit-mortar interfaces at zero confining normal stress is non-zero due to the slip surface’s roughness. To characterize nonlinear shear behaviour for tuff masonry assemblages, direct shear tests were carried out under different pre-compression levels. This paper summarises the experimental program discussing the main results. Empirical formulas are presented to define shear failure at both peak and residual stress levels. Shear deformation capacity, strength degradation, mode II fracture energy, and dilatancy coefficient were computed. Multiple regression analysis was applied to derive a shear response surface including both stress-strain diagrams and the frictional strength model. Constraints on the continuity of both the shear response surface and its first partial derivatives were imposed to nonlinear regression analysis, in order to represent shear softening behaviour in the inelastic range. The surface was defined in a dimensionless space to be used, in principle, for other stone masonry interfaces. This empirical model allows to simulate the shear behaviour over the whole range of allowable strains, and hence the stress-strain diagram at any confining stress level. The experimental results and the proposed empirical models could be employed in both micro-modelling numerical strategies and simplified nonlinear analysis methods based on the macro-element idealisation of masonry walls with openings. Keywords: Unit-mortar interface, direct shear tests, dilatancy, mode II fracture energy, shear softening, shear response surface INTRODUCTION Unit-mortar interfaces considerably affect the overall behaviour of masonry under any loading condition. Two basic failure modes can be identified for such interfaces: tensile failure (mode I) and shear failure (mode II). The former is the separation of the interface normal to the joints, the latter may consist of a shear failure of the mortar joint or sliding mechanism of the masonry units (i.e., bricks, blocks, stones, etc.). Since unit-mortar interfaces act as planes of weakness, mechanical properties of masonry significantly change with the loading direction. Therefore, the mechanical behaviour of masonry along those material discontinuities has been deeply investigated for a number of masonry classes (Atkinson et al. 1989; van der Pluijm 1993; Binda et al. 1994; Lourenço & Ramos 2004). Past studies have highlighted the potential for strain softening in both dry and mortar joints with rough surfaces. Furthermore, a significant dilatational behaviour of the masonry joint under shearing deformation has been 15th International Brick and Block Masonry Conference Florianópolis – Brazil – 2012 detected in most cases, that is, a transverse expansion resulting in a volume growth of mortar. This means a non-isochoric plasticity, as opposed to metals and plastics (van Zijl 2004), and hence a pressure build-up under the normal uplift if the volume increase of the masonry joint is prevented or resisted by confining boundary conditions. As a result, shear strength of the unit-mortar interface may significantly increase with the normal compressive stress even though shearing dilatancy is arrested at high pressure levels and at large shear strains. Shear strength of unit-mortar interfaces gives a major contribution to both shear and compressive strengths of masonry (Atkinson et al. 1982; McNary & Abrams 1985). Nevertheless, this issue has not yet been investigated in the case of tuff masonry, which until now has been widely used around the world even in earthquake-prone regions. This lack of knowledge inspired the authors to carry out a series of direct shear tests with the aim of (1) developing empirical models to be used in nonlinear analysis of masonry structures, and (2) assessing mechanical properties employed in both numerical and analytical models. Data processing was first addressed at evaluating shear modulus, shear strength at zero confining stress (i.e., cohesion), and friction coefficient in the range of small strains. Fracture energy and dilatancy angle were also estimated to be used in finite element (FE) analyses. Secondly, the Mohr-Coulomb failure criterion was characterized at both peak and residual shear stress levels and could be combined with a cap model in compression (Lourenço & Rots 1997) and a cut-off in tension (Binda et al. 1994). Several regression analysis techniques were employed (1) to define τ−γ constitutive laws at different pre-compression levels, and (2) to obtain a shear response surface τ(σ,γ) including shear stress-strain diagrams and the Mohr- Coulomb failure model. EXPERIMENTAL PROGRAM A series of monotonic direct shear tests on double-layer masonry specimens made of tuff stones and mortar joints were carried out. Those experimental tests were preferred over couplet and triplet tests, although the latter have been adopted as the European standard method (CEN 2002). In fact, triplet tests are more difficult to be controlled in the post-peak range of the stress-strain response because two joints are tested all together, while couplet tests are affected by parasite bending effects inducing a non-uniform distribution of stresses at the unit-mortar interface. The materials adopted for the specimens were: (1) yellow tuff stones from Naples, Italy, 300×150×100 mm in size, with uniaxial compressive strength fb = 4.13 MPa, Young’s modulus Eb = 1540 MPa, and shear modulus Gb = 544 MPa; and (2) premixed hydraulic mortar based on natural sand and a special binder with pozzolana-like reactive aggregates (water/sand ratio by weight 1:6.25, i.e., 4 L of water per 25 kg of sand). The mortar had low- medium mechanical characteristics and consistency to reproduce the actual conditions of tuff masonry in ancient buildings; indeed, it had an uniaxial compressive strength fm = 2.5 MPa, Young’s modulus Em = 1520 MPa, and shear modulus Gm = 659 MPa. Both strengths and elastic moduli were characterized through compressive tests according to European standards. As shown in Figure 1, each specimen consisted of a single-leaf, double-layer tuff masonry assemblage with a mortar bed joint. The gross dimensions of the specimen were 852×210×150 mm, while both head and bed joints had a thickness of 10 mm. The layers were shifted to each other in order to apply and measure the horizontal forces via simple contact 15th International Brick and Block Masonry Conference Florianópolis – Brazil – 2012 between devices and specimen. Two linear variable differential transformers (LVDTs) were placed on each side of the specimen to measure horizontal and vertical relative displacements induced by the shearing deformation and dilatancy. The vertical and horizontal LVDTs had a stroke of 20 and 50 mm, respectively. The latter were fixed to both masonry layers. 765 300 10 145 10 300 tuff stones LVDT #1 LVDT #2 71 100 45 10 72 210 210 100 bed 68 300 10 145 10 300 joint 150 263 261 241 765 765 Figure 1: Specimen geometry (dimensions in mm) and arrangement of LVDTs The experimental program consisted of three series of deformation-controlled tests performed at different pre-compression load levels. Each experimental test was carried out by subjecting the masonry specimen to increasing shear deformation along the mortar bed joint. The test set-up was slightly different from that used by Atkinson et al. (1989) for clay brick masonry, even if the ability to induce a rather uniform distribution of shear and normal stresses along the bed joint was preserved (Fig. 2). Both the applied and resisting lateral forces were applied at a distance from the bed joint which was defined on the basis of the size of the hydraulic jack and the height of the masonry layers. The masonry specimen was placed onto a L-shaped steel I-beam which was enabled to slip over the rigid base of an universal testing machine by means of two Teflon layers and two lateral unequal angles. A double-effect hydraulic jack with load capacity of 500 kN was positioned against the beam and a reaction frame. A further L-shaped I-beam was installed over the specimen and was forced against a load cell (with load capacity of 100 kN) anchored to another reaction frame. After two further Teflon layers were placed over the upper metallic beam, the hydraulic actuator of the universal testing machine (with load capacity of 3000 kN in compression) was pushed against the specimen. The loading plate of the universal machine was pinned to minimise bending effects. actuator reaction hydraulic jack LVDT #1 LVDT #2 load cell reaction frame frame two Teflon layers HEA160 M18 bolts Unequal angles two Teflon layers Figure 2: Experimental set-up for direct shear tests 15th International Brick and Block Masonry Conference Florianópolis – Brazil – 2012 Three sets of direct shear tests were carried out at different pre-compression loads corresponding to about 5%, 10% and 15% of the ultimate axial force resisted by the effective (horizontal) cross-section of the specimen. Namely, three direct shear tests were carried out under a pre-compression load of 25 kN corresponding to a vertical confining stress σ = 0.25 MPa (specimens C1 to C3). A second group of four tests were performed under a pre-compression load of 50 kN corresponding to σ = 0.50 MPa (specimens C4 to C7). A third set of two tests were conducted under a pre-compression load of 75 kN corresponding to σ = 0.75 MPa (specimens C8 and C9).