Shrinkage Curve Research Articles

Physics of the soil medium organization part 1: thermodynamic formulation of the pedostructure water retention and shrinkage curves

The equations used in soil physics to characterize the hydro-physical properties of the soil medium cannot be other than empirical since they do not take into account the multi-scale functional organization of the soil medium that is described in Pedology. To allow researching the correct formulation of the physical equations describing the soil medium organization and properties, a new paradigm of hydrostructural pedology is being developed. This paradigm is to establish the conceptual link between the classical Pedology and the soil-water physics (hydrostructural characterization and modeling of the soil medium). The paradigm requires the exclusive use of the concept of Structural Representative Elementary Volume (SREV) instead of the classical Representative Elementary Volume (REV) in any physical modeling of the hydrostructural behavior of the soil medium and of the links with the biotic or abiotic processes evolving within it. This article presents the development of the physical equations of the shrinkage curve and the soil water retention curve from the thermodynamic point of view according to the new paradigm. The new equations were tested and the theory validated using data of simultaneous measurement of both curves on a cylindrical soil sample (pedostructure). Implications of these results on the physical modeling in agro-environmental sciences are discussed.

Crystallization kinetics in a lithium alumosilicate glass using SnO2 and ZrO2 additives

The crystallization sequence, volume fractions and crystal sizes of nucleating agents, high-quartz (HQ-ss) and keatite (K-ss) solid solutions in a lithium alumosilicate glass with additions of SnO2 and ZrO2 were studied using high-temperature X-ray diffraction, differential thermal analysis and optical dilatometry. At low tin oxide fractions primary crystals were tetragonal zirconia solid solution, while at higher tin oxide fractions orthorhombic stannic srilankite solid solutions were detected. For continuously heated glasses we found that the substitution of zirconium by tin shifts in agreement with DTA and shrinkage curves the crystallization of HQ-ss and K-ss towards lower temperatures while only a minor effect on the glass transition temperature was evident. Isothermal annealing showed that the increase in the tin oxide fraction of the parent glass increases mainly the nucleation rate of HQ-ss (up to one order of magnitude) while the increase in the crystal growth rate is less pronounced. Dwelling of mixed ZrO2/SnO2-bearing glasses at the temperature of maximum nucleation results in fine-grained glass-ceramics (crystal size=50nm) of crystal number densities up to 1013mm−3.

A Framework for Unifying Soil Fabric, Suction, Void Ratio, and Water Content during the Dehydration Process

In the process of soil dehydration, the soil fabric, water content, and void ratio vary with soil suction. They all can be regarded as variables depending on soil suction and soil history. At a particular state, the soil fabric, which can be characterized by a pore size distribution, inherently determines the water content and the void ratio. In this study, the monotonic drying process of soil was analyzed under an integrated framework of soil fabric, suction, void ratio, and water content. Under this framework, the drying process of slurry samples and overconsolidated samples were distinguished and investigated separately, including their drying mechanisms and the variations of soil fabric, soil shrinkage curve, and soil water characteristic curve. From the theoretical analysis, in a monotonic drying process, the envelope of the cumulative pore volume curves was found to be the soil-water characteristic curve and the shrinkage curve was found to be located in a narrow range that can be determined using the cumulative pore volume curve. These findings were further verified by the laboratory test data on a clay with sand.

Pore rigidity in structured soils—only a theoretical boundary condition for hydraulic properties?

The quantification of water fluxes and the identification of site-specific hydraulic properties are widely required for various research, economic or environmental purposes. Pore rigidity, as one of the major boundary conditions, is always assumed to exist. Under in situ conditions the validity of this assumption is questionable and strongly depends on climate, land use, soil type and management. Changes of water content or water potential will change porosity for structured or homogeneous soils irrespective of geological origin and clay mineralogy. Shrinkage curves show volume loss with decreasing matric potential due to drying and this was more pronounced the less aggregated and the wetter the soils. Water retention curves as well as the hydraulic conductivity vs. matric potential curves differed all the more from the origin with increasing drying; the less rigid were the pores. The smaller the structural shrinkage range and the more pronounced the proportional shrinkage, the greater the difference between the measured and the corrected curves concerning the water retention and the hydraulic conductivity/matric potential. The shrinkage-induced volume change can result in up to 12% volume loss which is interpreted as water loss if pore rigidity is assumed. Underestimating the occurrence of shrinkage may result in incorrect data for modelling hydraulic functions. These incorrect hydraulic functions also introduce a high uncertainty in the forecast of changes in hydraulic site properties due to climatic change. Non-rigidity of soils should therefore be more intensely investigated in future research.

Suction effects on the residual shear strength of clays

The paper presents an experimental study on the residual shear strength of different clayey soils at varying total suctions. In a first part of the paper some insight into the behaviour of residual shear strength of a filled rock discontinuity is presented to bring into light the sensitivity to hydraulic states of a clayey gouge material subjected to shearing along large displacements. An adapted Bromhead ring shear apparatus, in which the sample is enclosed in a controlled relative humidity chamber, has been used to control total suction during shearing. Afterwards, results on different types of clayey materials are presented to discuss the importance of the plasticity of the clay on the residual friction angle changes. These changes show an important increase in the residual friction angle with imposed total suction that may reach 15° for medium plastic clay and without cohesion component. The reasons for this increase have been explained by the more granular character of the dry clay as a result of aggregate densification and desaturation during strong drying. The changes have been interpreted using a simple model inspired in both macroscopic and microstructural observations, which is based on the stiffness of the soil (or aggregates) and depends on the product of the total suction applied and the degree of saturation. A microstructural model, already developed to take into account microstructural aspects on water retention and following an equivalent behavioural response to the macroscopic shrinkage curve, has been used to estimate the degree of saturation at the microstructural level (inside aggregates). To highlight its applicability in geotechnical practice, the different parameters used in the water retention and residual shear strength models have been shown to depend on the plasticity index of the different clayey soils studied.

Influence of Li2Co3 and V2O5 combined additions on the sintering and dielectric properties of Ca0.5Sr0.5TiO3 ceramics prepared from powders synthesized by sol-gel method

In this work, we have studied the influence of lithium carbonate (Li2CO3) associated with the vanadium oxide (V2O5) on sintering and dielectrics properties of Ca0.5Sr0.5TiO3 ceramic materials obtained from nanopowder synthesized by sol-gel method. The nanopowder was obtained by controlled mixing of titanium butoxide dissolved in butanol-2 and acetic acid with a saturated aqueous solution of calcium acetate and strontium carbonate and subsequent drying of the formed gel at 80 ?C and calcination at 1100?C. The synthesized nanopowder was mixed with different amount of additives, and then uniaxally pressed and sintered in air atmosphere at temperature determined by dilatomertic measurements. The pure Ca0.5Sr0.5TiO3 sample obtained by this process required a sintering temperature around 1500?C. The addition of Li2CO3 combined with V2O5 improved sinterability and caused a shift of dilatimeric shrinkage curve to much lower temperatures. Thus, dense ceramics (98% of theoretical density) were obtained at sintering temperature ? 1300?C. The effect of adding Li2CO3-V2O5 on the structure of ceramics and the dielectric properties is discussed and show that type I dielectric properties (linear variation of the permittivity) are conserved, but with an increase of dielectric loss.

Shrinkage during holographic recording in photopolymer films determined by holographic interferometry

Shrinkage of photopolymer materials is an important factor for their use in holographic data storage and for fabrication of holographic optical elements. Dimensional change in the holographic element leads to a requirement for compensation in the reading angle and/or wavelength. Normally, shrinkage is studied at the end of the polymerization process and no information about the dynamics is obtained. The aim of this study was to use holographic interferometry to measure the shrinkage that occurs during holographic recording of transmission diffraction gratings in acrylamide photopolymer layers. Shrinkage in photopolymer layers can be measured over the whole recorded area by real-time capture of holographic interferograms at regular intervals during holographic recording using a complimentary metal-oxide-semiconductor camera. The optical path length change, and hence the shrinkage, are determined from the captured fringe patterns. Through analysis of the real-time shrinkage curves, it is possible to distinguish two processes that determine the value of shrinkage in the photopolymer layer. These processes are ascribed to monomer polymerization and crosslinking of polymer chains. The dependence of shrinkage of the layers on the conditions of recording such as recording intensity, single or double beam exposure, and the physical properties of the layers, such as thickness, were studied. Higher shrinkage was observed with recordings at lower intensities and in thinner layers. Increased shrinkage was also observed in the case of single beam polymerization in comparison to the case of double beam holographic exposure.

Development and optimisation of hydroxyapatite–ß-TCP functionally gradated biomaterial

Use of hydroxyapatite (HAP) for biomaterials is widely established, often in a combination with titanium alloy substrates in orthopaedic and other implants. Porous HAP-based coatings undergo sintering and heat treatment processes to achieve proper level of density yet avoiding undesirable reactions and phase changes. Thermal expansion mismatch between constituents may also lead to cracking of the coating due to excessive thermal stresses. Thus control of mechanical properties and stress state in the coating during the whole processing cycle represents some challenges when trying to combine conflicting objectives.In this work a method of optimisation of mechanical behaviour of an FGM biomaterial coating or scaffold composed of HAP and beta-tricalcium phosphate (ß-TCP) is considered. For coating on titanium-based substrates which have anatase (TiO2) top layer, thermodynamic equilibrium was analysed and the “safe” compositional path was found to ensure preservation of original ceramic phases during processing. Experimental studies of HAP–TCP sintering kinetics of different compositions were carried out with dilatometry to obtain true shrinkage curves and thermal expansion functions. These data were integrated with thermo-mechanical calculations of stresses and strains in HAP–ß-TCP FGM during processing, which were optimised with respect to minimal stresses, stresses derivatives and curvatures. The beneficial effect of compositional gradation on behaviour of these materials is shown.

A thermoanalysis of phase transformations and linear shrinkage kinetics of ceramics made from ultrafine plasmochemical ZrO2(Y)–Al2O3 powders

The methods of X-ray diffraction analysis, thermogravimetric analysis, differential scanning calorimetry, and dilatometry are used to study special features of the structural-phase state of the 80 mass% ZrO2(Y)–20 mass% Al2O3 plasmochemical powders (PCPs) and their effects on the sintering of composite ceramics. It is revealed that the ZrO2(Y)–Al2O3 powder composite represents a mechanical mixture containing crystalline tetragonal zirconium dioxide and aluminum oxide nanoparticles, the latter found in an amorphous state and partially included into the ZrO2(Y) lattice, thus forming metastable solid solutions of variable composition. Heating of the composite powder within the temperature range 740–1,000 °C reveals an exothermal effect associated with decomposition of metastable states of aluminum oxide. This is accompanied by the formation of the corundum-phase nuclei having subcritical dimensions. They achieve the critical sizes at higher temperatures T > 1200 °C, when α-Al2O3 is finally crystallized. The shrinkage response of the powder compacts during non-isothermal sintering is measured in a sensitive dilatometer. It is shown that the shrinkage curve consists of several stages that closely correlate with the concurrent structural-phase transformation in the composite ZrO2(Y)–Al2O3 powder mixture. The decisive contribution into shrinkage during non-isothermal sintering of composite comes from the high-temperature stages with the maximum shrinkage rate at the temperatures 1,250 and 1,550 °C. It is found out that the regime of sintering the ultrafine PCPs (T = 1,600 °C, t = 1 h) allows producing composite ceramic materials with a porosity of Q ≈ (5–7) %, microhardness Hv = 12.3 GPa, and crack resistance К1c = (10–11) MPa m0.5.

Shrinkage Properties of Repacked Soil at Different States of Uniaxial Compression

Compaction can severely impair soil structure, which may in turn affect shrinkage properties. The few studies that have so far investigated compaction effects on soil shrinkage behavior have produced seemingly inconsistent results, reporting an increase, decrease, or no change in shrinkage. The objective of this study was therefore to examine the changes in soil shrinkage under controlled laboratory conditions across a wide range of compression. We analyzed shrinkage curves of repacked aggregated soil recorded at increasing levels of uniaxial compression after conditioning to different initial water potentials. With increasing compression, the shrinkage curves changed from a sigmoidal shape typical for structured soil to the simple shape typical for unstructured soil such as a clay paste, indicating the loss of structural pores. The slopes of the shrinkage curves were less steep in the structural and basic shrinkage domains at moderate compression than in the uncompressed initial state, indicating a strengthening of interaggregate bonds and thus an increase in hydrostructural stability. The highly compressed soil, in contrast, showed distinctly steeper slopes, indicating decreased hydrostructural stability due to the breaking of interaggregate bonds. The compression effects on the shrinkage curves became more pronounced with increasing initial water potential during compression. This strong dependence on the degree of compression and initial water potential may be one reason for the variation of compaction effects on soil shrinkage properties reported in the literature. The results show that soil shrinkage is well suited for the assessment of soil structural stability and compaction effects on structured soil.

A microstructural insight into compacted clayey soils and their hydraulic properties

A review of the literature is initially presented to bring into light the important microstructural effects on the hydraulic properties of different compacted clayey soils. Experimental data coming from microstructural and macroscopic studies on different compacted clayey soils with dominant multi-modal pore size distribution are analysed to provide a comprehensive picture of different phenomenological features of hydraulic soil behaviour. The data come from clayey soils compacted on the dry side (i.e., with an intrinsic and permanent aggregated structure) or alternatively with dominant coarse fraction (i.e., sand–bentonite mixture with shielding skeleton and well-developed inter-grain porosity), which undergo important microstructural changes on wetting and drying. A microstructural model, already developed to take into account microstructural aspects on water retention curves, is used to plot in the Proctor plane the microstructure set up by compaction and its evolution along hydraulic paths. The model is also used to explain the evolution of hydraulic properties (water and air permeability, water retention) along wetting and drying paths on an artificially prepared mixture of sand and bentonite with dominant granular fraction. The bentonite strongly reacts to changes in water content and allows studying the transition from a granular soil with large pores between sand grains to a low-permeability material on wetting. The key point of this simple model is the introduction of the dependence of the microvoid volume (admitting saturated aggregates) on water content, following an equivalent behavioural response to the macroscopic shrinkage curve.

Shrinkage anisotropy characteristics from soil structure and initial sample/layer size

The objective of this work is a physical prediction of such soil shrinkage anisotropy characteristics as variation with drying of (i) different sample/layer sizes and (ii) the shrinkage geometry factor. With that, a new presentation of the shrinkage anisotropy concept is suggested through the sample/layer size ratios. The work objective is reached in two steps. First, the relations are derived between the indicated soil shrinkage anisotropy characteristics and three different shrinkage curves of a soil relating to: small samples (without cracking at shrinkage), sufficiently large samples (with internal cracking), and layers of similar thickness. Then, the results of a recent work with respect to the physical prediction of the three shrinkage curves are used. These results connect the shrinkage curves with the initial sample size/layer thickness as well as characteristics of soil texture and structure (both inter- and intra-aggregate) as physical parameters. The parameters determining the reference shrinkage curve (relating to the small samples) and initial sample size/layer thickness are needed for the prediction of the above soil shrinkage anisotropy characteristics. Using the available data on two soils and samples of two essentially different sizes, illustrative estimates of the relative sample sizes, new characteristic of the shrinkage anisotropy, and shrinkage geometry factor are given as the physically predicted values.

Integration of MnZn-ferrite tapes in LTCC multilayer

For co-firing of MnZn-ferrite tapes and LTCC dielectric tapes, the sintering shrinkage curves and the coefficient of thermal expansion of ferrite and dielectric tapes were matched. Highly densified embedded ferrite without any cracks could be manufactured by co-firing at 900 °C in nitrogen atmosphere. However, the permeability of MnZn-ferrite co-fired between dielectric tapes is significantly reduced (μ´=100) compared to that of the separately sintered ferrite (μ´=500). Changes in the phase stability and microstructure of MnZn-ferrite were investigated to explain the permeability reduction in the embedded ferrite. It is supposed that early densification of the dielectric tapes on the top and bottom of the ferrite layer prevent the gas exchange during sintering which is necessary for (Mn,Zn)Fe2O4 spinel formation. As a result, high amount of Fe2O3 secondary phase and a Mn-rich spinel phase with low permeability remain in the embedded ferrite layer.

Identifying Six Types of Soil Shrinkage Curves from a Large Set of Experimental Data

A typical soil shrinkage curve is S-shaped and composed of four phases termed structural, proportional, residual, and zero shrinkage. However, many studies have not found all four soil shrinkage phases despite investigating the full spectrum of soil moisture content. The objectives of this paper were to determine different soil shrinkage types based on the presence of shrinkage phases and to define relationships between the parameters of different shrinkage types and soil properties. A total of 270 sets of shrinkage data were collected from published (N = 245) and our unpublished work (N = 25), covering a wide range of soil types, sample sizes, and measurement methods. According to the presence of different shrinkage phases, six types of soil shrinkage curves were classified using the shrinkage model proposed by Peng and Horn (2005). Soil shrinkage types generally depended on soil structure, but not on the measurement method. The coefficient of linear extensibility (COLE) had a positive relation with saturated soil bulk density (r = 0.50, P < 0.001), clay content (r = 0.20, P < 0.05), and soil organic carbon (SOC) content (r = 0.46, P < 0.001). This paper is the first to propose six soil shrinkage types that will improve our understanding of the relationship between soil structure and soil water content.

Polder Effects on Sediment-to-Soil Conversion: Water Table, Residual Available Water Capacity, and Salt Stress Interdependence

The French Atlantic marshlands, reclaimed since the Middle Age, have been successively used for extensive grazing and more recently for cereal cultivation from 1970. The soils have acquired specific properties which have been induced by the successive reclaiming and drainage works and by the response of the clay dominant primary sediments, that is, structure, moisture, and salinity profiles. Based on the whole survey of the Marais Poitevin and Marais de Rochefort and in order to explain the mechanisms of marsh soil behavior, the work focuses on two typical spots: an undrained grassland since at least 1964 and a drained cereal cultivated field. The structure-hydromechanical profiles relationships have been established thanks to the clay matrix shrinkage curve. They are confronted to the hydraulic functioning including the fresh-to-salt water transfers and to the recording of tensiometer profiles. The CE1/5 profiles supply the water geochemical and geophysical data by their better accuracy. Associated to the available water capacity calculation they allow the representation of the parallel evolution of the residual available water capacity profiles and salinity profiles according to the plant growing and rooting from the mesophile systems of grassland to the hygrophile systems of drained fields.

Studies on sintering kinetics and correlation with the sinterability of 8Y zirconia ceramics based on the dilatometric shrinkage curves

Prediction of the dominant sintering mechanism and corresponding temperature regimes become important in arriving at the optimum sintering schedule of ceramics. The sintering kinetics of 8Y zirconia (8YSZ) submicron powders, with particle sizes ∼205 nm, has been evaluated through, (i) constant rates of heating and (ii) master sintering curve (MSC) technique. Slip cast green 8YSZ compacts, close to 50% of the theoretical density, have been subjected to dilatometry, for recording the shrinkage behavior, at constant heating rates of 5, 10 and 20 °C/min. The kinetics of the corresponding sintering process has been evaluated by estimating and comparing the apparent activation energies ( Q ) from the constant heating rate technique, and MSC approach. The observed apparent activation energy (∼350 kJ/mol) suggests grain-boundary diffusion to be the dominant mechanism in sintering of 8YSZ ceramics.

Sintering mechanisms of Yttria with different additives

Abstract The sintering behaviour of conventional yttria powder was investigated, with emphasis on the effect of sintering additives such as B2O3, YF3, Al2O3, ZrO2, and TiO2, etc. at sintering temperatures from 1000 °C to 1600 °C. Powder shrinkage behaviour was analysed using a dilatometer. The powder sintering mechanisms were identified at different temperatures using powder isothermal shrinkage curves. This analysis showed that the sintering additives B2O3 and YF3 could improve yttria sintering by changing the diffusion/sintering mechanisms at certain temperatures, while sintering additives TiO2, Al2O3 and ZrO2 appeared to retard the powder densification at temperatures around 1000 °C and are more suitable when used at temperatures in excess of 1300 °C. The powder with La2O3 added had the slowest densification rate throughout the test temperatures in this experiment and was also found to be more suitable when used at temperatures higher than 1550 °C.

Temporal changes in shrinkage behavior of two paddy soils under alternative flooding and drying cycles and its consequence on percolation

Paddy field is generally subjected to many cycles of alternative flooding and drying (AFD) during rice growing. The AFD cycles can create a large variation in soil structure that subsequently affects soil water and nutrient retention and migration. This study aimed to investigate the temporal change in soil shrinkage behaviour and to evaluate its consequences on water percolation in two paddy fields under AFD. One paddy field cultivated for 20years (YPF) and the other one for over 100years (OPF) were subjected to either AFD or continuous flooding (CF) as a control. During every AFD cycle, soil cores were sampled to determine soil shrinkage curve in the laboratory while cracks and water percolation were determined in the field. Our results showed that both paddy soils presented a temporal change in soil bulk density, soil shrinkage and cracks with cycles of AFD. The two paddy soils showed a high shrinkage capacity (COLE>0.06), in which the OPF was significantly greater than the YPF (P<0.001). The cracks area density, however, was lower in the OPF (3.66%) than in the YPF (5.13%). This discrepancy can be explained by more swelling clay content and higher soil organic matter in the OPF but greater AFD intensity in the YPF. As a result, the YPF showed higher water percolation as compared with the OPF. Our work demonstrates that the temporal changes in soil structure in paddy soils depend not only on intrinsic soil properties but also on external hydraulic stress.

Experimental Research on Concrete Shrinkage and Creep for Main Girder of Sutong Continuous Rigid-Frame Bridge

In order to obtain shrinkage and creep of HPC used in Sutong continuous rigid-frame bridge, shrinkage and creep of plain concrete and RC are investigated under natural environment over two years. Reinforcement ratio 0.76% is close to that of the middle span. Loading stress of creep test is about 15MPa, which is near the maximum stress of the bridge. Four loading ages, 7d, 14d, 21d and 28d, were used to simulate different loading ages in construction. The curves of creep and shrinkage were fitted from test values. The results show the test values of creep and shrinkage were less than the current Chinese bridge code JTG D62-2004, and the creep and shrinkage of RC is less than plain concrete. If the reinforcement ratio is low, reinforcement exerts less influence on creep and shrinkage, and the influence of reinforcement can be neglected in engineering application. Reinforcement can effectively reduce creep and shrinkage if the reinforcement ratio is high.

Modelling non-homogeneous stochastic reaction-diffusion systems: the case study of gemcitabine-treated non-small cell lung cancer growth

BackgroundReaction-diffusion based models have been widely used in the literature for modeling the growth of solid tumors. Many of the current models treat both diffusion/consumption of nutrients and cell proliferation. The majority of these models use classical transport/mass conservation equations for describing the distribution of molecular species in tumor spheroids, and the Fick's law for describing the flux of uncharged molecules (i.e oxygen, glucose). Commonly, the equations for the cell movement and proliferation are first order differential equations describing the rate of change of the velocity of the cells with respect to the spatial coordinates as a function of the nutrient's gradient. Several modifications of these equations have been developed in the last decade to explicitly indicate that the tumor includes cells, interstitial fluids and extracellular matrix: these variants provided a model of tumor as a multiphase material with these as the different phases. Most of the current reaction-diffusion tumor models are deterministic and do not model the diffusion as a local state-dependent process in a non-homogeneous medium at the micro- and meso-scale of the intra- and inter-cellular processes, respectively. Furthermore, a stochastic reaction-diffusion model in which diffusive transport of the molecular species of nutrients and chemotherapy drugs as well as the interactions of the tumor cells with these species is a novel approach. The application of this approach to he scase of non-small cell lung cancer treated with gemcitabine is also novel.MethodsWe present a stochastic reaction-diffusion model of non-small cell lung cancer growth in the specification formalism of the tool Redi, we recently developed for simulating reaction-diffusion systems. We also describe how a spatial gradient of nutrients and oncological drugs affects the tumor progression. Our model is based on a generalization of the Fick's first diffusion law that allows to model diffusive transport in non-homogeneous media. The diffusion coefficient is explicitly expressed as a function depending on the local conditions of the medium, such as the concentration of molecular species, the viscosity of the medium and the temperature. We incorporated this generalized law in a reaction-based stochastic simulation framework implementing an efficient version of Gillespie algorithm for modeling the dynamics of the interactions between tumor cell, nutrients and gemcitabine in a spatial domain expressing a nutrient and drug concentration gradient.ResultsUsing the mathematical framework of model we simulated the spatial growth of a 2D spheroidal tumor model in response to a treatment with gemcitabine and a dynamic gradient of oxygen and glucose. The parameters of the model have been taken from recet literature and also inferred from real tumor shrinkage curves measured in patients suffering from non-small cell lung cancer. The simulations qualitatively reproduce the time evolution of the morphologies of these tumors as well as the morphological patterns follow the growth curves observed in patients.Conclusionss This model is able to reproduce the observed increment/decrement of tumor size in response to the pharmacological treatment with gemcitabine. The formal specification of the model in Redi can be easily extended in an incremental way to include other relevant biophysical processes, such as local extracellular matrix remodelling, active cell migration and traction, and reshaping of host tissue vasculature, in order to be even more relevant to support the experimental investigation of cancer.