Spatial variability in longitudinal elastic modulus of clear timber

Different factors such as age, location of timber within the tree, structural imperfections, load history such as wind and snow etc. can affect the material properties of timber taken from the same species, and grown in the same geographical location and local growth conditions. Consequently, there is a high variability in the mechanical properties [1-2]. This variability is both spatial and random, and is sometimes referred to as ‘random spatial variability’ [3]. Four groups of specimens of different lengths were prepared and their quasi-static behavior was experimentally investigated under tensile loading. In addition to the global displacement monitoring, the local deformations along the length of each specimen were measured. The effect of the mesostructure of the clear timber on the local elastic modulus was examined. The spatial variability of the elastic modulus was experimentally characterized. Also, Statistics concerning the elastic modulus for different lengths were derived and compared.

Quantification of spatial variability for transverse elastic modulus of spruce wood

Alireza Farajzadeh Moshtaghin, Steffen Franke, Thomas Keller, Anastasios Vassilopoulos

Different factors such as age, location of timber within the tree, structural imperfections, load history such as wind and snow etc. can affect the material properties of timber. Consequently, there is a high variability in the mechanical properties which is sometimes referred to as ‘random spatial variability’. In this work, the spatial variability of the transverse elastic modulus of clear spruce wood is quantified by conducting mechanical tests. Specimens of 120 mm nominal length with a small cross-sectional area were prepared and their quasi-static behavior was experimentally investigated under tensile loading. In addition to the global dis-placement monitoring, the local deformations along the length of each specimen were measured. Using these data, the spatial variability of the elastic modulus was experimentally characterized in both longitudinal and transverse directions. Variability coefficients were defined to quantify the variability in both directions. Also, the effect of the mesostructure of the clear timber on the local elastic modulus was examined. The results show a very significant spatial variability in the transverse elastic modulus, more 1000% within some specimens. The variability of the transverse elastic modulus is much higher in the transverse direction. The grain angle has the most important effect on the value of the local elastic modulus. The results of this work can be considered as part of establishing advanced stochastic models with ransom spatial variability for timber structures.

2016

Stochastic analysis of clear timber as a structural material

Alireza Farajzadeh Moshtaghin

Wood/timber has been widely used for house and bridge construction. It is a widely available natural material that necessitates low energy for the production, following simple processes. The environmentally friendliness, together with the low cost of raw material makes it an efficient building material. Moreover, timber possesses attractive mechanical properties such as high specific strength and stiffness. In contrast, timber constructions have, to a large extent, been based on experience and craftsmanship, which prevents taking full advantage of this material. There are several reasons for this. Timber has a complex mechanical behavior being a natural highly anisotropic fiber composite, with properties that are also affected by moisture content. For specific species, geographical location, local growth conditions and moisture content, the material properties depend, among others, on the age, the structural imperfections, the location of timber within the tree, and load history. Consequently, the mechanical properties of timber are, inherently, highly variable. Variability of timber properties includes statistical and spatial variabilities, referred to as random spatial variability (RSV). This entails adopting a probabilistic/stochastic approach to analysis of timer structures. The aim of this research is to understand and model the effect of the RSV on the clear timber mechanical properties, as well as the experimental characterization of RSV for clear timber, and also to develop a stochastic finite element framework for random response assessment of clear timber components. A size effect model was developed which takes into account the RSV in the strength field. The theory of random fields was used for this purpose. Using the spectral representation scheme, realizations of strength field in each specimen were generated. The stochastic response was obtained via the Monte Carlo method. The model results was compared to the existing experimental data in the literature. Also, an analytical expression was provided to facilitate the application of the model. Clear timber specimens of different lengths were fabricated for longitudinal tensile tests. Local deformations along the lengths of the specimens were recorded during the tests in order to characterize the RSV in longitudinal properties. A connection between the mesostructure of the clear wood and its local elastic modulus was observed. Statistics concerning the elastic modulus, strength and strain to failure and the effect of length change on these properties were extracted. The correlations between the strength, the elasticity and the density were obtained. Transverse properties were also investigated which are of particular importance in some applications such as mechanical and adhesively-bonded timber joints. Regularly positioned and randomly positioned specimens were cut from different timber boards. Statistics and size effects concerning the elastic modulus, strength and strain to failure as well as the correlation between the properties were studied. The spatial variability in the transverse elastic modulus, the tensile strength and the failure strain was also experimentally studied. Mesostructural patterns of clear timber were shown to have a direct effect on the local elastic modulus. Finally, a stochastic finite element framework was established by combining the spectral representation scheme for RSV modelling and the finite element software ABAQUS in a non-intrusive manner. This framework can be used for the stochastic structural response assessment of timber structural components made of clear timber. To show the applicability of the model in real applications, the failure of adhesively bonded double-lap timber joints were simulated under tensile loading. The effect of size on the strength was also taken into account. The results were in a fairly well agreement with the available experimental data in the literature.

EPFL2016

Autogenous Shrinkage and Hydration Kinetics of SH-UHPFRC under Moderate to Low Temperature Curing Conditions

Mohammadhadi Kazemi Kamyab

Strain Hardening Ultra High Performance Fiber Reinforced Concrete (SH-UHPFRC) were used successfully over the last 8 years in numerous cast in place rehabilitation applications as long lasting waterproofing layers (20 to 30 mm thickness) and, combined with rebar, to increase the structural load bearing capacity of existing bridge decks or building slabs (50 to 70 mm thickness). In composite applications on reinforced concrete substrates, SH-UHPFRC provide a deformation capability (strain hardening) larger than their free shrinkage which makes localized macro cracking at service state very unlikely. On the other hand some specific conditions of microclimatic state of the substrate (moisture and thermal conditions) and climatological (temperature and humidity) of the site such as casting at low temperatures (winter conditions) might increase the autogenous shrinkage and thus eigenstresses of the freshly cast SH-UHPFRC and hinder the development of its tensile strength or/and deformability. Combination of these specific circumstances could compromise the SH-UHPFRC protective functions due to the occurrence of localized macro cracks, making the objective of using SH-UHPFRC as a onetime intervention strategy in rehabilitation application obsolete. Advancement in hydration at early age leads to formation of partially emptied capillary spaces contributing to self-desiccation, decrease of the relative humidity and increase of the capillary depression. Since water is under depression, the solid porous material is under compression forcing the material to shrink. From the aforementioned, it can be deduced that the autogenous shrinkage is a force driven phenomenon: a force is applied on the ageing viscoelastic porous skeleton and the apparent structural response of the bulk cementitious material is the autogenous shrinkage strain. Based on the aforementioned two levels of investigation were considered in this thesis: I. Material level: ageing viscoelastic porous skeleton of hydrating cementitious material II. Structural level: autogenous shrinkage development under the action of its driving forces The objective of this thesis was to study the development of the autogenous shrinkage and its relation with the development of microstructure and mechanical properties in SH-UHPFRC cured at moderate and low temperature conditions (1 to 20°C). Focus was put on: (1) kinetics and magnitude of hydration of silica fume and cement, (2) activation energy of the processes, (3) stiffness (E modulus and Poisson ratio) development, and (4) states of water and pore development. Finally a cross link analysis of information obtained from material and structural level was carried out to better highlight the mechanisms and driving forces of autogenous shrinkage. CM22-TKK, a SH-UHPFRC developed at MCS for rehabilitation applications, on the basis of CEMTECmultiscale® fibrous mixes, was used. Silica fume is one of the major constituents of CM22-TKK (26% by mass of cement). Extent of the silica fume pozzolanic reaction significantly affects the pore size distribution of the UHPFRC matrix which then influences the development of the relative humidity, self-desiccation and finally autogenous deformation. Detailed experimental investigation performed showed that only maximum 8% by mass of cement out of 26% silica fume used in the recipe reacts in moderate and low temperature curing conditions. Finally, a model of silica-fume degree of reaction as a function of curing temperature (5 to 250 °C) was proposed on the basis of a detailed literature survey of existing works with low W/B mixes. The activation energy of the thermo-mechanical properties was evaluated for thermo (cumulative heat of hydration) and mechanical properties development (such as dynamic Elastic modulus, dynamic Poisson’s ratio and compressive strength). A single activation energy Ea of 27.4 KJ/mol could successfully model the activation of all properties. Since maturity was not a proper reference to compare the autogenous deformations at various temperatures, a more fundamental reference such as degree of hydration was used. Experimental investigation was carried out using different techniques such as isothermal calorimetry and 29Si solid NMR to evaluate the development of the degree of hydration of cement and silica fume in UHPFRC at moderate and low temperature curing conditions. The ultimate degree of hydration of cement in CM22-TKK for a closed system was 0.34. There was a close correspondence between the experimental results and the predictions of the volumetric phase distribution models of Waller (0.28) and Jensen (0.32). Finally, the De Schutter et al. 1996 model was used to describe the mechanical properties (Emodulus and Poisson ratio) as function of degree of hydration. Nondestructive and non-invasive 1H-NMR was used to evaluate volumetric phase distribution development at 20°C, especially the classification of the water types (capillary, gel and C-S-H interlayer water) which brought fully new and valuable information about the hydration kinetics and pore size development. The results were also compared with Jensen volumetric phase distribution model to check the advantages and limitation of both approaches. Finally experimental investigation was carried out to follow the development of autogenous shrinkage and eigenstresses (in case of restrained shrinkage) of CM22-TKK cured in isotherm conditions (1 to 20°C). Eigenstresses were obtained and used to highlight the effect of the viscous response of the material at the different temperatures investigated. The previously mentioned results on the kinetics of the silica fume reaction, cement hydration and evolution of states of water and development of stiffness were then put into perspective with the trends observed on the autogenous shrinkage and eigenstresses development.