Rheological Behavior of Ultra-Soft Soil Case Sstudy

Rheological Behavior of Ultra-Soft Soil—Case Study: Urmia Lake Causeway Embankment Subsidence

Ebrahim Ebrahimnezhad Sadigh MSc in Geotechnical Engineering, University of Tabriz, Tabriz, Iran [email protected]

Dr. Tohid Akhlaghi Associated Professor, Department of Geotechnical Engineering, University of Tabriz, Tabriz, Iran. [email protected]

ABSTRACT Rheology is a branch of continuum mechanics that studies material flows in non-Newtonian fluids, soft solids and wax like solids that traditional concepts of the elasticity and plasticity could not describe their behavior completely. Soil rheology is a branch of soil mechanics that studies origin and time dependent changes of stress and strain terms in soil. Application of rheology concepts for description of ultra-soft soils behavior after failure is a new idea that is introduced in this paper. General rheological equation of soil was analyzed by Bingham model for Urmia lake causeway rock fill subsidence and its results were compared with field measurements. The numerical results are consistent with the measured values and using rheological models is proposed as a suitable solution to solve complex geotechnical engineering problems in ultra-soft soils. KEYWORDS: Soil rheology, Ultra-soft soils, Subsidence, Urmia lake causeway

INTRODUCTION Incomplete consolidation is generally associated with the existence of excess pore pressures in the soil, such that the in-situ effective stressσσ' = −u is less than the calculated effective overburden pressure γ 'z [1]. Sangrey (1977) identifies that rapid rate of sedimentation, gas in marine sediments, leakage from an artesian water or gas pressure source and wave-induced repeated loading are possible mechanisms which may result in the existence of excess pore pressure and "unconsolidated" sediments [2]. During rapid rate of sedimentation, the total stress increases as does the excess pore pressure, but dissipation of this excess pore pressure may be relatively slow. Sangrey et al. (1979) have reported a study in which rapid sedimentation in a sediment which was less than 10% consolidated, i.e. the effective stresses were less than 10% of the effective overburden pressures [3].

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This means that ultra-soft sediments mainly squeeze under loads without considerable consolidation and their behavior is same as a Bingham non-Newtonian fluid with high viscosity and yield stress [4]. Subsidence rate in such a continuum environment is a time dependent function with slowing rate and in some cases rate is fixed for a long time and slowly reduced. For example, we can refer to Urmia lake causeway project with 14 kilometers length that the resistance of the upper layers of soil is Φ ≈ 0̊ and C ≈ 1-20 kPa. Subsidence of the embankment on the lakebed has been measured over 25 meters. Since modeling in geotechnical softwares such as Plaxis, Geo-Office, Flac and etc is based on small displacement and the results are attributable before failure and the modeling of the embankment construction by "displacement filling" with common geotechnical softwares isn't possible. Large shear displacements with ultra-soft sediments failure during embankment construction are mainly subsidence or squeezing without consolidation of sediments (Figure 9). Thus, utilizing the rheological models with the Navier-Stokes and continuity equations can be a good idea to describe the behavior of soil squeezing in embankment construction by "displacement filling" method.

Rheology The term “rheology” has been related to flowing media, since the main root of the word - rheo in Greek- means “to flow" [5]. Starting with Amenemhet’s need for a viscosity correction to improve the accuracy of his water clock in ~1600 BCE, rheology has primarily been concerned with solving practical problems. At the same time, the complexity of the issues involved both of physical and mathematical nature has attracted some of the finest scientific minds [6]. Rheology as an independent branch of natural sciences emerged more than 80 years ago [5]. The name “rheology” was proposed to describe “the study of the flow and deformation of all forms of matter” by E.C. Bingham and M. Reiner on 29 April 1929; Heraclitus quote “everything flows" was taken to be the motto of the subject [7]. Its origin was related to observation of “strange” or abnormal behavior of many well-known materials and difficulty in answering some very “simple” questions. For example: Clay looks quite like a solid but everybody knows that it can be shaped; it also takes the form of a vessel like any liquid does; if clay is a solid, why does it behave like a liquid? Rheology is a science concerned with mechanical properties of various solid-like, liquid-like, and intermediate technological and natural materials [5]. As per strict definition, rheology is concerned with the description of flow behavior of all types of matter. A useful engineering definition of rheology is the description of materials using "constitutive equations" between the stress history and the strain history [8]. Rheology is a branch of Continuum mechanics that deals with the deformation and flow of matter, especially the non-Newtonian flow of liquids and the 'soft solids' or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force [5].

Soil Rheology Soil rheology is a branch of soil mechanics investigating the origin of, and the time-dependent changes in the stressed and strained state of soil. Although the rheology of clay soils has sprouted into

Vol. 22 [2017], Bund. 10 4213 a self-contained branch of knowledge quite recently, the rheological properties of these soils have been given very careful consideration for a long time [4]. Referring to the data on long-term tests of clay, Terzaghi (1925, 1943) has pointed out that soils explicitly exhibit the properties of elastic after-effect (denoted as creep) [9]. Flow is also a term frequently used to describe the secular deformation of rock mass, glacier movements, etc. It is also popular in soil mechanics, being used there as a synonym of the term "creep". However, if we use creep to denote, as settled above, the time-dependent deformation of all kinds, then, strictly speaking, flow is a special case of creep, referring to that stage when deformation is developing at a constant rate. In the theory of creep, plastic flow is understood to be a viscous flow induced by a load exceeding a certain limit (the so-called Bingham limit of plasticity); quite frequently it is referred to as viscoplastic flow [4]. The importance of taking into account the property of flow in soils was stressed by Puzyrevsky (1934) [10]. Gersevanov (1937) wrote that soil is likely to develop Bingham's flow which is a state in which a body, subjected to a certain stress, begins to unceasingly change its shape, passing into a viscous condition like a viscous fluid [11]. Rheological models for soft soils can roughly be categorized as one of the following types (Yuan Jing 2001): (1) elementary rheological models, (2) yield surface model, (3) endochronic plasticity model, (4) empirical model [12]. although soil rheology was used for describing time dependent phenomena such as creep, relaxation and the deterioration of strength due to a long-term load application, but using of rheology concepts to describe ultra-soft soils flow after the failure is new ideas that is presented in this paper.

Rheology of Ultra Soft Soils or Mud Cohesive sediments or mud are common in marine, estuarine and coastal environments [13-14- 15-16-17 and 18]. The term mud commonly describes a complex mixture of fine-grained mineral sediment (clay and silt), small amounts of sand, water and organic material of diverse nature [19]. During formation of mud deposits, several mud states may appear. Such as dilute suspension, fluid mud and semi to fully consolidated mud beds. Appearance and composition of cohesive sediments are highly variable [20]. In general, rheological studies have been performed on artificial cohesive sediment suspensions (as reviewed by Coussot 1997), although some rheological characterization of natural mud has been done as well (e.g. O’Brien and Julian 1988; Aijaz and Jenkins1994; van Kessel and Blom 1998; Faas and Wartel 2006). During formation of fluid mud, the rheological properties are changing from Newtonian to non-Newtonian, i.e. non-linear response to the shear rate [21-22-23]. Currently, the vast majority of study was limited to the macro level, microscopic level and micro level were hardly ever investigated, and nanoscopic level study have not been actually carried out. Some studies have performed at microscopic level in recent years and the concept of “fluid rheology” and “rheological phase material” proposed [24]. The transition from a loosely packed layer of fluid mud to a compacted mud occurs due to further self-weight consolidation. Porewater is driven out of the flocs and the space between the flocs caused by the submerged weight of subsequently depositing particles which lead to an increase of density and a decrease in void ratio and permeability through time [25].

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There is good relevance between the model parameters and rheological phase material and it indicates that the proposed model may provide a new way for preliminarily establishing the relationship between macro behavior and microscopic physical mechanism of fluid rheological properties of soft soil [26].

Soil Constructional Equations as a Viscoplastic Material At an early stage, attempts were made to apply the Newtonian mechanism of ideally viscous flow to soils. For example, Hvorslev (1937, 1939) treated soils on these lines. In the 1940s, Haefeli and Schaerer (1946), pointed out that in the general case the flow rate-stress relation is non-linear in soils. Approximately at the same time, Casagrande and Wilson (1950) succeeded in establishing the fact of clay failure due to a long-term creep from uniaxial compression. The acquired results from almost all the early rheological studies was that, unlike an ideal viscous liquid flowing in response to any load, soils set out to flow only when stress exceeds a certain limit. This implies that the Bingham theory of viscoplastic flow for soils is better than the theory of Newtonian viscous flow. The applicability of Bingham’s law for soils was also demonstrated by Geuze and Tan (1954) in their papers on the torsional tests of hollow cylinders presented at the 2nd International Congress on Rheology as well as in a number of later publications. Experimental proofs of the applicability of the law governing the viscoplastic Bingham flow to soils were performed in the works of Sotnikov (1960), Kisiel (1967), Sorokina (1965), and others. A modification of Bingham's law which takes into account the non-linear relation between the rate of flow and stress was suggested by Vyalov (1959). The physical mechanisms that cause plastic deformation can vary widely. Soils, particularly clays, display a significant amount of inelasticity under load. The causes of plasticity in soils can be quite complex and are strongly dependent on the microstructure, chemical composition and water content. As far as soils are concerned, the available experimental data on viscosity have spread varying between 106and 1017 P. In other cases, viscosity is a time-dependent variable which may significantly change, by a factor. Thus, if at the beginning of a process the viscosity is between109 and1010 P, its final value can be1013 to10I4 P [4]. The model of viscoplastic Bingham body consists of an elastic element H, a viscous element N and a Saint-Venant element SV (Figure1).

N SV

Figure 1: Bingham viscoplastic body

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H The pattern of deformation of a Bingham body may be defined by the conditionττ= + τy . Hence, it follows that:

for ττ<=: τG γ (1) y for τ≥ τ: τ −= τ ηγ (2) y y pl where G is the elastic modulus of the Hookean element; η is the coefficient of viscosity of the

Newtonian element; τ y is the ultimate shear strength of the Saint-Venant element [4]. Properly invariant three-dimensional constitutive equations for the Bingham fluid were introduced by Oldroyd (1947) and Prager (1961). Oldroyd’s formulation assumes that the material is a linearly elastic solid at stresses below the yield criterion, where the yield surface is defined by a von Mises criterion. The full constitutive equation is then as follows:

 τ 1 τµ=+∆≥y τ2 py, IIτ (3) 1 2 II∆ 2 1 2 τγ=G, IIτ < τy (4) 2

Here, II ∆ ≡ A: Ais the second invariant of the tensor A, ∆ ≡ v+ vT is the rate of deformation tensor, andγ is the strain tensor [27]. ∇ ∇ Continuity equation or mass conservation in an incompressible flow of rheological environment is as follow:

∂u ∂v ∂w + + =0 (5) ∂x ∂y ∂z

Momentum equations that govern fluid flow, are Navier-Stokes equations and is generally expressed as follows:

∂∂uu∂∂p  ∂u∂u 2 ∂ u  ρii+uj =− +Β +µδ i +j − k  ∂t ∂ x ∂ xi ∂ x  ∂∂ xx3 ij ∂ x  (6) j i j  ji k 

In this equationui is Component of the velocity vector in i direction, Βi volumetric force in i  direction and µ is viscosity. By accepting a slight error for an incompressible flow∇=/V 0, the above equation is as follows:

Vol. 22 [2017], Bund. 10 4216  DV ρµ=−∇pV +Β+ ∇2 (7) Dt

METHODOLOGY Whereas impossibility of soft muddy sediments characterization by in-situ or laboratory tests and also adequate information about Urmia lake causeway embankment subsidence, in this study we used combination of analytical models and field studies especially geotechnical observational methods. The Urmia Lake is located in a high depression in Azerbaijan Province of Iran, with an average elevation of 1275 masl. It is formed tectonically and located in part of a tectonic mush zone between Arabia and Eurasia plates and micro plates of Iran and Turkey that have compressed in between the above plates (Figure2). At its full size, it is the second saltiest lake on the world with a surface area of approximately 5,200 km2, 140 km length, 15-55 km width and max. 16 m depth. The salinity is obviously linked to the water level of the lake and varies between 300 to 350 gr/L. The lake is fed by 13 permanent rivers and many small springs, as well as rainfall directly into the lake. The rivers enter more than 5.5 million tons’ clayey sediments into the lake yearly. This means that the sedimentation is taking place at a rate of approximately 0.8 meters per 1000 years. Based on the age determination by carbon 14 method, the age of the upper 5 meters of the sediments is between 7,000 to 9,000 years old. The age of the sediments below 35 m from the lake bed is nearly 117,000 years and is formed of clastic and authigenic sediments. The mineralogical XRD-analysis indicated that the soil is dominated by Quartz (25–30%) but have also significance contents of other minerals. Typical clay minerals are Montmorillonite (12–17%) and Muscovite (Illite) (5–7%) [28]. The Urmia Lake Bridge is the largest and longest bridge in Iran. It crosses the lake and connects East and West Azerbaijan provinces (Figure 3). It reduced the driving distance between Tabriz and Urmia cities to 135 km. The causeway was constructed from 1979 by using “displacement filling” concept and by dumping and pushing the rockfill out with bulldozers from each landside (Figure 4). Used rock materials in the body of the causeway were prepared from the Andesite and Volcanic quarries. The ranges of rock weight in the core layer are 0.5kg up to 1000kg (Figure 5).

Figure 2: Location of Urmia Lake Figure 3: Satellite Image of Causeway

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Figure 4: Dumping and Pushing Rockfill Figure 5: Quarry Material

Due to the soft nature of the upper semi consolidated clayey layers, failures occurred more or less continuously as it was attempted to raise the embankment above the original seabed level. Consequently, the fill punched down into the seabed and soft clay/mud was squeezed up to the sides and the front of the fill. Thus, had to refill areas which had undergone failures for several times. Along each side of the embankment, clay was locally squeezed up to about +1275.5 masl. Figure 6 gives a schematic picture of the probable failure mechanisms and associated displacements that occurred during the filling process. As illustrated, there must have been a mass balance between the volume of embankment that penetrated into the original lakebed and the volume of clay that was squeezed up above the original lakebed level. Figure7 presents the construction time history of embankment. The rate of construction generally decreased with increasing distance from land. Probably it's because of increase in penetration depth of the rockfill into the soft seabed clays. The last phase of construction, from 10.3 to 11 km, was particularly slow. The reason is increasing of water flow through the remaining opening in the lake that caused severe erosion and removal of filling material. Slow progress led to stop rock filling and a suspended bridge between two parts of the embankment was made. Figure 8 shows the embankment subsidence and lake sediment layers along the causeway based on the investigation boreholes were drilled in 2003.

Figure 6: Illustration of Displacements Figure 7: Causeway Construction and Failures Caused by Construction Progress

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Field Measurements In addition of measuring subsidence of embankment during construction and operation by leveling along the causeway to control the ongoing leveling, three deep benchmarks were installed along the embankment at different sections in 120 m below the crest. Also piezometer strings were installed at the centerline at 9.0 and 10.7 km for measuring pore pressure. Each string contains 4 vibrating wire type piezometers at depths of 10, 20, 30 and 50 meters below the embankment. The pore pressure of piezometers with Lake water level are shown in Figure9 and the benchmark measurements are presented in Figure11.

Figure 8: Lake Sediment Layers Figure 9: Pore Water Pressure in 4, 9 and Description 10.7 km

Figure 10: Thickness of Rockfill Figure 11: Post construction Subsidence of

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Causeway in Different Sections

Numerical modeling The finite-difference method (FDM) was widely prevalent by the 1960s when transistor technology first came into bloom. More powerful techniques like the finite-element method (FEM) which was initiated in 1956 (Turner et al. (1956)), the boundary element method (BEM) (Cruse and Rizzo (1968)) and the spectral methods (SM) (e.g., Gottlieb and Orzag (1977)) were developed as computer technology improved. All these methods essentially reduce the PDEs of the rheological field problems to a set of simultaneous, non-linear, equations for the nodal variables. A major problem in numerical simulations was the so-called High Weissenberg Number Problem (the existence of a critical Weissenberg number above which the algorithms failed). Some significant early works in this area are Beris et al. (1987), Yoo and Joseph (1985), Walters and Tanner (1992), and Crochet and Walters (1993). An analogous finite volume method was applied to three dimensions’ flows by Xue et al. (1995) [8]. The finite volume method derives directly from the integral form of the conservation laws for fluid motion and therefore, naturally possesses the conservation properties. Computational Fluid Dynamics (CFD) is a method of simulating a flow process in which standard flow equations such as the Navier-Stokes and continuity equation are discredited and solved for each computational cell [29]. Lake Causeway embankment subsidence is simulated by using the Flow 3D software for maximum cross-section of the embankment with combination of 5 rectangular blocks. Side blocks are hole type and the main body is central block (Figure 12).

Figure 12: Lake causeway embankment Figure 13: Geometry of embankment cross- model and its cross-section geometry section

Embankment modeled with general moving object (GMO). Lakebed and minimum lake water level changes are considered respectively 1269 and 1270 to 1274 masl (Figure 13). Simulations of the lake bed sediments have been using Bingham rheological model and due to the limitations of the software and the lack of bed rheological testing results, the following items are assumed in the numerical model. 1. Lake bed sediments is simulated with a single non-Newtonian fluid (Bingham rheological model). 2. Since the sludge has not penetrated into the pores of embankment so the body is assumed to be nonporous.

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3. Due to the insignificance internal deformation of embankment in comparison with subsidence amount, embankment is assumed as a rigid body. 4. Whereas simultaneous simulation of rheological environment and water fluid isn't possible in 3D FLOW, the buoyant unit weight of rockfill is considered under the water level. 5. In order to consider the dimension effects in model, the embankment length to width ratio is selected equal 7. 6. Since the effective density of embankment (the moving object) is less than lakebed density, so numerical analysis has been done by implicitly method. 7. Due to the 3D FLOW software limitations in solving rheological environment problems with 5 high viscosity, the viscosity of lakebed sediments is limited to10 Pa.s and dimensionless quantity, time normalized (T / Ti) is used instead of time quantity. 8. According to the technical literature and software limitations, bed and embankment rheological parameters were selected in table 1.

Table 1: Embankment and lake bed rheological parameters Rheological properties of materials Symbol Unit Value

γseabed Sea bed density kN/m3 17 Bingham yield stress of Sea bed τ0 kPa 20 Shear module of Sea bed G kPa 103 Viscosity of Sea bed μ Pa.s 105 γω Sea water density kN/m3 11.2 γsat Saturated density of embankment kN/m3 22 γnat Natural density of embankment kN/m3 19.8 ' Effective density of embankment g avg kN/m3 12.7 - 14

RESULTS AND DISCUSSION To investigate the lakebed rheological parameters and water level changes effects on the amount of subsidence, sensitivity analysis carried out for water level changes from 1274 to 1270 masl and the following results were obtained. Figure 14 shows the embankment subsidence three-dimensional model and its adjacent sediments uplift during the time for Lake water level 1270. Embankment subsidence for water level 1270 masl is equal26.3 meters and bed uplift in sides is estimated 5.9 meters. Lake water level reduction from 1274 to 1270 causes an incensement in the subsidence equal 0.9 meter.

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Free surface Free surface

a b

(1) (2) Free surface Free surface

c d

(3) (4) Figure 14: Embankment subsidence three-dimensional model and its adjacent sediments uplift during the time for lake water level 1270 masl.

Figure 15 shows elevation profiles of squeeze at different times .T is the time required to complete subsidence and (Ti / T) is dimensionless normalized time. The starting point of each curve in vertical axis represents the amount of subsidence at the relevant time. Figure 16 shows squeeze velocity surface in three-dimensional coordinates (t, s, v).

-5

-10

-15

-20 Time -25 Subsidence, m 0.10 T 0.15 T -30 0.20 T 0.50 T -35 0.70 T

-40 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Velocity

Figure 15: Elevation profiles of squeeze at different times

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Figure 16: Squeeze velocity surface in three-dimensional coordinates (t, s, v).

CONCLUSIONS (1) In many cases, actual behavior of ultra-soft soils and muddy sediments is different significantly with general concepts and common behavior patterns of soil mechanics. The main cause of soil mechanical models incompatibility to predict the behavior of ultra-soft soils is occurrence of high shear strain under load because of low shear strength. Such sediments aren't consolidated under the loads but they are squeezed and often they behave such as a non-Newtonian fluid with high viscosity. (2) Large shear displacements with lake bed failure during embankment construction mainly are subsidence and squeeze without consolidation occurrence in sediment. Therefore using the flow standard equations such as Navier-Stokes and continuity equations with considering rheological properties can be a suitable idea to modeling embankment construction by "displacement filling" in marine ultra-soft sediments. (3) The embankment subsidence by Bingham non-Newtonian fluid model is estimated 25.4 meters for water level 1274 masl. (4) Due to the sharp decrease of minimum water level from 1274 to 1270 masl in the last 10 years, the amount of subsidence and bed uplift around the embankment are estimated respectively equal 26.3 and 5.9 meters. In the other words, every meter decrease in minimum water level, can cause an increase about 0.2 meter in subsidence. (5) Based on Drilling boreholes on the causeway in 2003, the embankment subsidence was about 25 meters. According to the settlement monitoring from 2006 to 2010, the average rate of subsidence was obtained 0.2 mm/day. Due to the passing 13 years from drilling date, the subsidence till now is estimated about over 25.8 m that suggests model good conformity with the measured values. (6) In subsidence for the buoyancy balance state can be defined an obvious surface in the three- dimensional coordinates of time, subsidence and velocity (t, s, v).

ACKNOWLEDGEMENTS The authors are grateful to Dr. A. Jalali and Mr. R. Shahinpar for their supports in various ways during the writing of this paper.

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Editor’s note. This paper may be referred to, in other articles, as: Ebrahim Ebrahimnezhad Sadigh and Dr. Tohid Akhlaghi: “Rheological Behavior of Ultra-Soft Soil—Case Study: Urmia Lake Causeway Embankment Subsidence” Electronic Journal of Geotechnical Engineering, 2017 (22.10), pp 4211-4224. Available at ejge.com.