Appl. Rheol. 2019; 29 (1):202–221 Review Article Juliana Keiko Tsugawa, Roberto Cesar de Oliveira Romano, Rafael Giuliano Pileggi, and Maria Eugenia Gimenez Boscov* Review: Rheology concepts applied to geotechnical engineering https://doi.org/10.1515/arh-2019-0018 Received Apr 22, 2019; accepted Dec 23, 2019 1 Introduction Abstract: The effect of time on soil properties, notice- The term Rheology, from the Greek “rheos”- flow and “lo- able in many earthworks, is recognized by geotechni- gos” - study, was presented in 1929 by Professor Eugene cians. For example, secondary compression and aging pre- Cook Bingham and defined as “the study of deformation consolidation are considered in geotechnical design, and and flux of matter” [1]. Rheology, as a Science, originated strain rate is standardized in geotechnical laboratory and from the observation of real materials, which considerably field tests. Elastic-plastic models, from rigid-perfect plas- differ from ideal solids (elastic) and ideal liquids (viscous) tic to Modified Cam Clay, which do not consider the effects as proposed, respectively, by the Hooke and Newton mod- of time, solve most geotechnical problems. However, so- els [2]. lutions for prolonged settlements, landslides, debris flow Rheology is an important topic of scientific studies, and mudflow could profit from a deeper understanding of industrial applications and engineering materials, includ- rheological models. In fact, rheological concepts, despite ing metals and alloys, plastics, ceramics, composites, con- not always clearly stated, have been used to address some crete, paints, inks, paper, cosmetics, food, pharmaceu- of these problems, and may also be important for using ticals, agrochemicals, liquid detergents, glass, oils, lu- new materials in geotechnical practice (tailings, sludge, bricants, greases, emulsions (liquid/liquid), suspensions soil-polymer mixtures and other materials with water con- (solid/liquid) [1–3], biochemical materials such as wastew- tent higher than the liquid limit). This paper introduces ba- ater sludge, sewage sludge and water treatment sludge [4– sic concepts of rheology for geotechnicians, specially high- 7], soils [8–14], among others. lighting viscoelasticity under simple shear stress, which Rheology concepts are important to develop techno- explains with reasonable accuracy well known phenom- logical processes (e.g., cold punching and shaping), to ena dependent on time in soils. The objective is to bring understand the flow of different materials, such asmud geotechnicians to rheology and show another important stream, coal, minerals and pulps [2], to characterize ma- tool to access geotechnical problems. On the other hand, terials properties, and to produce new models describing a brief explanation of geotechnical tests is presented for the behavior of real materials [15]. rheologists not acquainted with geotechnical engineering. Soil rheology can be used to evaluate the time- Geotechnical tests procedures are discussed in the light dependent changes in the stress-strain state of soils, of rheology concepts, terminology is clarified, examples mainly when soil behavior fails to fit the traditional elas- of application of rheology in geotechnics are presented, ticity and plasticity models [15]. On the Third International and determination of soil rheological parameters by tradi- Conference on Soil Mechanics and Foundation Engineer- tional geotechnical tests as well as by tests on concrete is ing in 1953, Zurich, soil rheology was recognized as an in- commented. Keywords: soil rheology, viscoelasticity, geotechnical en- gineering, time-dependent phenomena, creep Juliana Keiko Tsugawa: Department of Structural and Geotechni- cal Engineering, School of Engineering, University of São Paulo, Sao PACS: 46.35.+z; 81.40.Lm; 83.10.-y; 83.80.Fg; 83.60.Pq Paulo, Brazil; 05508-970; Email: [email protected] Roberto Cesar de Oliveira Romano: Department of Civil Engineer- ing, School of Engineering, University of São Paulo, Sao Paulo, *Corresponding Author: Maria Eugenia Gimenez Boscov: De- Brazil; 05508-970; Email: [email protected] partment of Structural and Geotechnical Engineering, School of Rafael Giuliano Pileggi: Department of Civil Engineering, School Engineering, University of São Paulo, Sao Paulo, Brazil; 05508-970; of Engineering, University of São Paulo, Sao Paulo, Brazil; 05508- Email: [email protected] 970; Email: [email protected] Open Access. © 2019 J. Keiko Tsugawa et al., published by De Gruyter. This work is licensed under the Creative Commons Attri- bution 4.0 License Review: Rheology concepts applied to geotechnical engineering Ë 203 dependent branch of soil mechanics [16], and henceforth tion 2). When 훾 is very small, tan 훾 is approximately equal research applied to soft soils, landslides, debris flows and to 훾. F mudflow has been developed [17–25]. Moreover, geotech- τ = A (1) nical engineers are nowadays concerned with waste reuse, which introduces new materials to the scope of soil me- δu 훾 = (2) chanics, such as sewage, wastewater and water treatment l sludge, mining tailings (pulps), oil drilling fluid, and poly- meric suspensions for excavation stabilization, and brings 2.1 Hooke elasticity law forward a new interest in soil rheology. This paper contributes with an overview of the con- In 1678, Robert Hooke proposed the True Theory of Elas- cepts of rheology to make literature more easily under- ticity which established that “the power of any spring is in standable and available to geotechnicians. Viscoelastic- the same proportion with the tension thereof ” [1]. In other ity is especially highlighted, which explains with reason- words, the force is proportional to the displacement. This able accuracy well known phenomena dependent on time idea, applied to an elastic solid body, is expressed by the in soils: secondary compression, aging pre-consolidation statement that stress is proportional to strain. pressure, flow, creep and thixotropy. Terminology is clar- The curve shear stress versus shear strain (Figure 2a) ified and some examples of the application of rheologi- is a straight line and the slope is equal to the shear mod- cal models in geotechnics are presented: prediction of in- ulus, G (G’ in rheology, Appendix A), as follows in Equa- stability propagation, demonstration of geotechnical tests tion 3. For Hookean materials, G is independent of the ap- procedures in the light of rheology concepts, and determi- plied stress and of the strain, i.e. is constant and an intrin- nation of rheological parameters by traditional geotechni- sic property of the material. cal tests and by tests on the rheology of concrete. τ = G훾 [τ in Pa, G in Pa, 훾 dimensionless] (3) For ideal elastic solids, deformation is immediate and 2 Fundamental concepts independent of time. The sum of solicitations applied to a real body may be divided into normal stresses that generate volumetric 2.2 Newton viscosity law strain, and shear stresses that generate distortion (shape changes). In geotechnical engineering, symbols for nor- In Principia published in 1687,Isaac Newton defined the re- mal stress, volumetric strain, shear stress and shear strain sistance of a fluid (viscosity) as “the resistance which arises are, respectively, σ, ϵ, τ and 훾. Despite the symbol for shear from the lack of slipperiness originating in a fluid, other stress in rheology generally being σ (Appendix A), in this things being equal, is proportional to the velocity by which paper, we will use τ for shear stress. the parts of the fluid are being separated from each other” [1]. This lack of slipperiness is called viscosity µ,(η in rhe- ology, Appendix A), the result of “internal friction” which measures the “resistance to flow” [1]. By definition, fluids deform (flow) continuously when submitted to shear stress. For fluids, however, the applied stress cannot be correlated with a unique value of defor- mation, since shear strain continues to occur along time. Therefore, the stress is correlated with the shear rate, 훾˙ , Figure 1: Body deformation by simple shear. Modified from [3]. which is the change of shear strain with time (Equation 4). d훾 d (︂ δu )︂ v 훾 ˙ = dt = dt l = l (4) Shear stress (τ) is defined as tangential force (F) per unit of area (A) as shown in Figure 1 and Equation 1. Shear where, 훾 is the shear strain, t is the time, δu is the tangen- strain (훾) is defined as the angle of the displacement re- tial displacement, v is the velocity and l is the distance be- lated to a reference layer i.e., the tangential displacement tween two parallel plates (Figure 1). (δu) per distance (l) between two parallel plates (Equa- For ideal liquids, as proposed by Newton, the applied stress (τ) is proportional to the shear rate (훾˙ ), as shown in 204 Ë J. Keiko Tsugawa et al. τ τ τ τy γ γ γ (a) (b) (c) τ τ τ τy τy τy γ γ γ (d) (e) (f) Figure 2: Typical stress-strain relation for solid bodies: (a) linear elastic (Hookean solid); (b) non-linear elastic; (c) rigid-perfectly plastic; (d) elastic-perfectly plastic (elastoplastic); (e) rigid linear hardening; (f) linear elastoplastic hardening. Modified from [15, 16] Figure 3a, and the proportionality constant is the viscosity Studying metal extrusion, in 1864 Tresca issued “On (µ), as follows in Equation (5). For Newtonian fluids, µ is the flow of a solid body subjected to high pressure”, stating independent of the shear stress and of the shear rate, i.e. that metal flows under a certain shear stress (the“shear- is constant and an intrinsic property of the material. ing flow stress”), and determined values of this parame- ter for many metals. Continuing Tresca’s studies, Saint- τ µ훾 τ µ 훾 −1 = ˙ [ in Pa in Pa s, ˙ in s ] (5) Venant published a pioneer paper on elastic-plastic anal- ysis in 1871 [27]. For ideal Newtonian fluids, deformation is continuous Plasticity is a property of a body to change its shape along time. irreversibly without failure when subjected to an external force; a minimum stress, called yield stress, τy (σy in rheol- 2.3 Historical notes of elasticity, plasticity ogy, Appendix A), must be reached for the plastic deforma- and viscosity tion to occur, and when the stress is removed, at least part of the deformation is not restored.