ALBERT

Notes: Summary The article outlines a seven-parametric yield function for geomaterials such as soils and rocks. Proceeding from a geometric representation in the principal stress space, the yield surface exhibits a closed shape, thus reflecting the sensitivity of the plastic response of this type of media to hydrostatic stresses. The yield function is able to describe the effects of primary yielding, as well as of isotropic and kinematic hardening. In addition the failure envelope contains an open cone when the number of material parameters is reduced from seven to five.

Notes: In this paper, a new homogenization technique for the determination of dynamic and kinematic quantities of representative elementary volumes (REVs) in granular assemblies is presented. Based on the definition of volume averages, expressions for macroscopic stress, couple stress, strain and curvature tensors are derived for an arbitrary REV. Discrete element model simulations of two different test set-ups including cohesionless and cohesive granular assemblies are used as a validation of the proposed homogenization technique. A non-symmetric macroscopic stress tensor, as well as couple stresses are obtained following the proposed procedure, even if a single particle is described as a standard continuum on the microscopic scale.

Notes: Summary The distribution of a crop rooting system can be defined by root length density (RD), root length (RL) per soil layer of depth Δz, sum of root length (SRL) in the soil profile (total root length) or rooting depth (z r . The combined influence of these root system parameters on water uptake is not well understood. In the present study, field data are evaluated and an attempt is made to relate a daily “maximum water uptake rate” (WUmax) per unit soil volume as measured in different soil layers of the profile to relevant parameters of the root system. We hypothesize that local uptake rate is at its maximum when neither soil nor root characteristics limit water flow to, and uptake by, roots. Leaf area index and the potential evapotranspiration rate (ET p ) are also important in determining WUmax, since these quantities influence transpiration and hence total crop water uptake rate. Field studies in Germany and in Western Australia showed that WUmax depends on RD. In general, there was a strong correlation between the maximum water uptake rate of a soil layer (LWUmax) normalized by ET p and RL normalized by SRL. The quantity LWUmax · ET p -1 was linearly related to (RL/SRL)1/2. The data show that the single root model will not predict the influence of RD on WUmax correctly under field conditions when water-extracting neighboring roots may cause non-steady-state conditions within the time span of sequential observations. Since the rooting depth z r was linearly related to (SRL)1/2, the relation: LWUmax · ET p -1 = f (RL1/2/z r ) holds. Furthermore it was found that the maximum “specific” uptake rate per cm root length URmax was inversely related to RD1/2 and to SRL1/2 or z r of the profile. Observed high specific uptake rates of shallow rooted crops might be explained not only by their lower RD-values but also by the additional effect of a low z r . The relations found in this paper are helpful for realistically describing the “sink term” of dynamic water uptake models. Growing plants extract water from the soil to meet transpiration needs. Rates of transpiration and of water uptake are set by evaporative demand and by plant and soil factors which influence capacity to meet that demand. These factors include crop canopy size and leaf characteristics, root system characteristics and hydraulic properties of the soil and the soil-root interface. Soil and root system properties vary with depth and all factors vary in time, so that parameters related to them require constant updating over a crop season. Dynamic simulation models describe water uptake by root systems under field conditions as a function of soil depth and time. Many of these simulation approaches are based on Gardner's (1960) single root model (Feddes 1981). These simulation procedures follow the assumption that water uptake is proportional to a difference in water potential between the bulk soil and the root surface or the plant interior, to the hydraulic conductivity of the soil-plant system and to the “effectiveness” of competing roots in water uptake. The effectiveness factor accounts more or less empirically for the influence of various root system parameters on water uptake such as percentage of “active” roots absorbing water, root surface permeability, root length density determining the distance between neighbouring roots, or total root length and depth of the root system. Such models however, will not always reflect correctly the influence of root system characteristics on water uptake since these assumptions have rarely been tested under field conditions. In many instances, there is better agreement between simulated and measured total water use of plants than between predicted and observed water depletion by roots within individual layers of the soil profile (Alaerts et al. 1985). Water uptake by an expanding root system as a function of depth and time has been studied under field conditions for several crops (listed in Herkelrath et al. 1977a; Feddes 1981; Hamblin 1985). They show that the dynamics of water uptake depend on root length density and the “availability” of soil water. However, the combined influence of root length density, total root length and rooting depth on the water uptake pattern has not been assessed. An evaluation of root system parameters with respect to soil water extraction should aid our understanding of how roots perform under field conditions and may assist our efforts to formulate the water uptake function of roots in dynamic simulation studies more realistically. The aim of the present investigation is to develop an approach that relates measured water uptake rates to relevant parameters of the root systems. This approach will be confined to situations where water uptake in a soil layer is not restricted by unfavorable soil conditions, such as in wet soil, by insufficient aeration and, in dry soil, by reduced water flow towards roots or by increased contact resistance (Herkelrath et al. 1977b). We will define a maximum water uptake rate WUmax that is neither soil-limited nor appreciably limited by the decreasing permeability of aging roots. This WUmax will be related to relevant root system parameters as they exist when WUmax is observed. Hence, water uptake by roots in a very wet, as well as in a dry soil, has been excluded from consideration.

Notes: Summary A simulation model of water uptake by a crop was developed to facilitate synthesis of field and laboratory observations with existing knowledge, and to analyze and predict affects of management practices, such as tillage, on water uptake from a drying soil. Radial water flow resistance in soil Rs was estimated by the single root flow model. Leaf stomata closure was represented by an observed minimal leaf water potential. Flow resistances, per unit root length Rr and in the plant Rp, were assumed to be constant and were evaluated together with an effective root length factor Frl, in the course of simulating a ten week period of observed soil water depletion by a crop of oats. Rr, Rp, and Frl were found to have similar values to those reported in the literature. Potential transpiration and evaporation and their ratio were estimated by the methods of Van Bavel (1966) and Denmead (1973). Evaporation reduction due to soil drying was estimated empirically. Cessation of soil water depletion (attainment of a permanent wilting soil water content) in the 0 – 20 cm soil layer, during the last ten-day period, was explained to be the net result of soil water extraction by the roots and backflow of water from the roots into the soil. Simulated onset of crop stress (closure of stomata) was found to be characterized by: (a) a steady decrease in average soil water potential, at a rate of about 500 cm-water per cm-soil water depletion; (b) a tenfold increase in the average soil resistance to radial flow, to about the same magnitude as average radial flow resistance in the roots; and (c) soil water diffusivities in the 0 – 50 cm layer being about 6 cm2/day. Sensitivity analyses showed that the ratio of actual to potential cumulative transpiration RCT depended primarily on potential evapotranspiration, rainfall, the unsaturated-to-saturated hydraulic conductivity exponent and plant cover. RCT was affected similarly by changes in Rr and in Rs. Under the conditions tested, zero tillage may increase RCT significantly only if it increases deep rooting beyond the 50 cm depth.

Notes: Summary In this paper, different formulations of finite isotropic hyperelastic material laws for compressible solids are considered. Material laws with an additive split of the hyperelastic strain energy function into isochoric parts and volumetric parts are often used in the numerical treatment of nearly incompressible solids. It will be shown that this formulation leads to unphysical results in the simple tension problem when we do not restrict ourselves to nearly incompressible materials.

Notes: Summary The present note contains some remarks on porous media theories. First, the necessary assumptions required to consider a porous medium as a continuous body are given. Then, some historical comments on the concept of volume fractions are offered.

Notes: Summary The paper concerns the relations between two principally different approaches to the formulation of momentum balance equations in porous media theories, namely, the dynamic approach similar to Biot's theory and the modern approach as a result of mixture theories extended by the concept of volume fractions. In particular, it is shown that both approaches necessarily lead to the same type of momentum balance equations and furthermore contain, in a certain sense, within the geometrically linear case, the well-known classical equations of Biot's theory.