AbstractThis study proposes a new method to introduce the cementation effect into existing elastoplastic constitutive models for soils. The mechanical properties of cement-treated soil are evaluated via element tests and compared with those of naturally deposited clay. The similarities and differences between cement-treated soils and naturally deposited clays are studied, focusing on two states, the undisturbed and remolded states. The effective stress for cement-treated soils incorporating an internal state variable representing the cementation effect is newly defined to describe the mechanical properties of cement-treated soils. Moreover, by applying this extended effective stress to the super-subloading yield surface (SYS) Cam-clay model, which is an elastoplastic model for soils based on the skeleton structure concept, the scope of this constitutive model is extended to include cement-treated soils. The cementation effect introduced by the proposed method allows reproducing the mechanical behavior of the cement-treated soil. Finally, a brittle behavior not described at the element level can be obtained, leading to a soil–water coupled finite deformation analysis incorporating the proposed constitutive model.IntroductionA large amount of soil is deposited near the river mouths which is dredged in the ports and the harbors of Japan to secure shipping routes. Most of this soil is conveyed to an offshore sediment disposal site and reclaimed. The landfills remain unusable since it takes a long time for the dredged sediment to settle and for the convergence of the self-weight consolidation. The pneumatic flow mixing method (Coastal Development Institute of Technology 2008; Kitazume and Sato 2003) has been developed to construct sea-based facilities such as international airports by utilizing the dredged soil. This method pumps dredged soil, which has high water content, under high pressure along with mixing cement, in a tube. By depositing the end of the tube on the seabed, the suppression of the increase in the water content ratio is greater when compared to dumping sediment on the sea surface. Since the cement solidification of the pumped sediment occurs before the self-weight consolidation can progress, the landfill site can be utilized earlier. However, it is necessary to set the soil strength based on the intended use of the reclaimed ground in order to conserve the amount of cement because a large amount of cement is required. The numerical analysis methods, such as the finite-element method, are required to accurately predict the deformation and the failure of the artificial ground constructed by cement solidification methods. This study extends elastoplastic constitutive models for naturally deposited soils to describe the mechanical behavior of cement-treated soils. To this end, oedometer and undrained triaxial tests of cement-treated soil are presented. From an experimental perspective, this study discusses the material properties of cement-treated soil and compares them with those of naturally deposited clays. Further, the viewpoints of undisturbed and remolded states, which are familiar to naturally deposited clays, are employed for cement-treated soil. In addition, this study discusses similarities and differences in the mechanical properties between cement-treated soils and naturally deposited clays. The conclusion is that undisturbed cement-treated soil, i.e., the as-made cement-treated soil, has a large pore structure and can take a state in the impossible region (Atkinson and Bransby 1978) of the remolded soil. Besides, as the plastic deformation progresses, the cement-treated soil approaches its fully remolded state. These characteristics are similar to those of a well-known mechanical property occurring in naturally deposited clays (e.g., Schmertmann 1953; Asaoka et al. 2000; Noda et al. 2005b). While the effective stress path in the undrained shear process is similar to that of naturally deposited clays, the cement-treated soil differs significantly in that the plastic compression occurs above the critical state line (CSL) of the remolded soil. This behavior is unique to cement-treated soils, which is revealed through a comparison with naturally deposited clays. Another mechanical feature of cement-treated soils, which is easy to understand for our senses, is their high initial stiffness even under low confining pressure.As the properties of cement-treated soils are similar to those of naturally deposited soils, the super-subloading yield surface Cam-clay model, namely, the super-subloading yield surface (SYS) Cam-clay model proposed by Asaoka et al. (2002), which can describe the mechanical behavior of naturally deposited soils, is considered in this study. The SYS Cam-clay model is an elastoplastic constitutive model based on the skeleton structure concept. The skeleton structure concept was first suggested by Mikasa (1964), who believed that the mechanical properties of soils are determined by the kind and state. He called factors other than density and water content as the skeleton structure among factors that determine the latter. Furthermore, Asaoka et al. (2002) considered the structure, overconsolidation, and anisotropy as independent factors in the formation of the skeleton structure for the development of an elastoplastic constitutive equation for naturally deposited soil. The SYS Cam-clay model is based on a modified Cam-clay model (Roscoe and Burland 1968; Muir Wood 1990) that introduces a superloading surface to realize the structure concept (Asaoka et al. 2000), a subloading surface (Hashiguchi 1978, 1989; Asaoka et al. 1997) to realize the overconsolidation concept, and rotational hardening (Hashiguchi and Chen 1998) to represent the induced anisotropy. This model describes the process of the transition from highly structured and overconsolidated states to the fully remolded and normally consolidated states by evolving three independent factors in association with each other through plastic deformation. Several research papers (e.g., Noda et al. 2005a, b, 2007; Takaine et al. 2010; Tashiro et al. 2011, 2015; Nguyen et al. 2015) have reported that the SYS Cam-clay model is highly capable of simulating the mechanical behavior of naturally deposited clays.To represent differences between cement-treated soils and naturally deposited clays, the SYS Cam-clay model was extended in this study. The key points of the extension are: (1) the translation of each loading surface in the negative direction on the mean effective stress axis, (2) degradation of the translation associated with the plastic deformation, and (3) description of a core elastoplastic constitutive model (an existing model without cementation effect) by the extended effective stress. Key point (1) is a commonly used method for modeling cement-treated soils (e.g., Gens and Nova 1993; Matsuoka and Sun 1995; Kasama et al. 2000, Lee et al. 2004; Horpibulsuk et al. 2010). In this study, the amount of translation of each loading surface is treated as an internal state variable representing the cementation effect. Key point (2) is based on the experimental fact that undisturbed cement-treated soil asymptotically approaches its remolded state due to plastic deformation. This requirement is reflected in the evolution rule for the internal state variable representing the cementation effect. Similar efforts have been made by Lee et al. (2004), Hashiguchi and Mase (2007), Suebsuk et al. (2011), and Rahimi et al. (2016). Key point (3) is to define a new effective stress for the deformation of cement-treated soils using the presented internal state variables and to describe the core elastoplastic constitutive model using this extended effective stress. This serves as a countermeasure to the possibility that the mean effective stress may be negative due to the translation of the loading surface. The application of extended effective stress also provides a high initial stiffness under low confining pressure. The extended constitutive model returns to the core constitutive model in the limit of the degradation of cementation, which is achieved by applying the extended effective stress. Moreover, the application of the extended effective stress integrates the entire proposed method through a very simple procedure. It must be noted that key point (3) is the most significant feature of the proposed method, which has not been presented in previous studies.The remainder of this paper is organized as follows: Section “Experimental Consideration: Similarities and Differences between Cement-Treated Soils and Naturally deposited Clays” describes the experiments and discusses the similarities and differences between cement-treated soils and naturally deposited clays. Section “Elastoplastic Constitutive Model for Soils Considering Cementation Effects” presents the method for expressing the cementation effect with the extended effective stress and introduces this method into the SYS Cam-clay model. In the section “Simulation of Element Tests with the Extended SYS Cam-Clay Model,” the results of element tests of cement-treated soil are reproduced using the proposed model. In the section “Simulation of Triaxial Tests as Initial Value and Boundary Value Problem,” a soil–water coupled finite deformation analysis of an undrained triaxial compression test is performed. This simulation shows that the brittle behavior, which is excluded from the modeling can be explained by the shear band formation. Section “Conclusions” concludes this paper. Even though a constitutive model is developed and validated from a standpoint that the triaxial test is considered as an element test in the sections “Experimental Consideration: Similarities and Differences between Cement-Treated Soils and Naturally Deposited Clays, Elastoplastic Constitutive Model for Soils Considering Cementation Effects, and Simulation of Element Tests with the Extended SYS Cam-Clay Model,” the triaxial test is considered as an initial and boundary value problem in the section “Simulation of Triaxial Tests as Initial Value and Boundary Value Problem.” This paper addresses the extraction of the mechanical properties of the cement-treated soils from the triaxial test results but does not aim to perfectly reproduce the result of the so-called element test by a single constitutive model. This paper aims to develop a constitutive model for cement-treated soil phenomenologically based on these two stand-points.Experimental Consideration: Similarities and Differences between Cement-Treated Soils and Naturally Deposited ClaysOedometer tests and undrained triaxial tests were performed to understand the mechanical properties of cement-treated soils. In the following, the mechanical behavior of a cement-treated soil is characterized by comparison with that of a naturally deposited clay.Physical Properties of the Base Material and Blending Condition for Cement-Treated SoilClayey soil (60% clay and 40% silt) dredged from the Yuraku-cho Formation in the Tokyo harbor was used as a base material for the cement-treated soil. The dredged material in the Yuraku-cho formation has a liquid limit wL=91.2% and a plastic limit wP=39.0%. Assuming that the dredged soil is treated following the pneumatic flow mixing method, the target flow value was set to 90–100 mm, and the target strength of the unconfined compression tests after 28 days of curing was set to 100–200 kPa. These values are determined based on a manual of the technology on the pneumatic flow mixing method (Coastal Development Institute of Technology 2008). Table 1 shows the blending conditions satisfying the presented target values. The water content of the dredged material indicates the value before blending with cement. In the table, S, W, and C indicate the masses of soil particles, water, and cement in 1 m3 of the mixed sample in saturation, respectively.Table 1. Blending conditionTable 1. Blending conditionWater content of dredged soil, w0 (%)Additive amount of cement, C (kg/m3)Ratio of water to cement, W/CRatio of soil to cement, S/C1705016.19.47The samples mixed as presented were cured in water for at least 56 days after filling the molds. The specimens were cured under no confining pressure. An oedometer test specimen of 6 cm in diameter and 2 cm in height and a triaxial test specimen of 5 cm in diameter and 10 cm in height were prepared by trimming. The specimens prepared in this manner are referred to as undisturbed cement-treated soil. In contrast, the samples prepared in the presented manner and then fully disturbed into a paste are referred to as remolded cement-treated soil. For the oedometer test of the remolded cement-treated soil, a paste-like sample was filled into the consolidation ring and then loaded. The triaxial specimens of the remolded cement-treated soil were prepared by preconsolidation at 98.1 kPa for one week and then by trimming it into a cylindrical shape.Oedometer TestsFig. 1 shows the oedometer test results for undisturbed and remolded cement-treated soil. The specific volume v is plotted over the vertical effective stress σv′. As shown in Fig. 1, the state of the undisturbed sample can exist above that of the remolded sample. The experimental results indicate that the undisturbed sample is in a bulky state when compared to the remolded sample, i.e., the undisturbed sample has a larger void ratio than the remolded sample at the same vertical pressure. The undisturbed sample gradually approaches the remolded sample as the plastic deformation progresses beyond the consolidation yield stress. Fig. 2 shows the oedometer tests for the naturally deposited clays in undisturbed and remolded states sampled from Urayasu, Japan, by Nakai et al. (2014). As shown in the figures, the presented features are common to naturally deposited soils with highly developed structures.Fig. 1 includes the test results of the remolded base material (dredged soil) with the same water content as the liquid limit at the initial state for comparison. The compression line of the untreated soil is located far below the remolded cement-treated soil, implying that adding cement caused a change in the properties of the base material that did not disappear even if the treated soil is fully remolded. The undisturbed cement-treated soil is asymptotically closer to not the remolded base material, but to the remolded cement-treated soil with plastic deformation. Therefore, the reference condition of the cement-treated soil should be considered for its remolded state and not for the base material. The reference condition of a soil in the skeleton structure concept is a basic state to which the soil is asymptotically close because of plastic deformation. The compression behavior of the remolded cement-treated soils is considered different from that of the base materials themselves; however, its compression line is almost linear on the single logarithmic chart, as it is for the remolded sample of the naturally deposited clays.Undrained Triaxial TestsThe undrained shear behavior of the remolded cement-treated soil is shown in Fig. 3. p′ and q in Fig. 3 are defined as follows: p′=−(1/3)T′, q=(3/2)‖S‖, S=T′+p′I, where T′ denotes the effective stress tensor defined as positive in tension, ‖‖ denotes the norm of a tensor (‖A‖=A·A=AijAij,A∀), and the operator “ ·” denotes the inner product of the tensor. εa is the conventional axial strain. The effective stress path for the confining pressure value of 98.1 kPa resembles that of the typical remolded and lightly overconsolidated clays because the preconsolidation pressure is also 98.1 kPa. The effective stress path for the confining pressure value of 294.3 kPa resembles that of the undrained shear of the typical remolded and normal consolidation clays. The CSL in the mean effective stress p′− deviator stress q plane can be represented as a straight line through the origin. Moreover, the soil shows the same characteristics as soils without cement, where M denotes the slope of the CSL and is referred to as critical state constant. When combined with the results of the oedometer test in Fig. 1, the remolded cement-treated soils show the same mechanical properties as the remolded clays without cement even though they cannot return to the base material.Fig. 4 shows the results of undrained triaxial compression tests of undisturbed cement-treated soil. The CSL obtained from the undrained shear test of the remolded cement-treated soil is also shown in the figure. For comparison, the undrained shear behavior of the undisturbed sample of naturally deposited clay sampled at the depth of 32–41 m at Urayasu is shown in Fig. 5 (Nakai et al. 2014). There are similarities in the shear behavior of the cement-treated soil and the naturally deposited clay. In particular, the softening behavior of naturally deposited clays with plastic compression (a decrease in the mean effective stress under the undrained condition) due to structural degradation, which is the typical behavior of highly structured clay, and is observed in cement-treated soils. This indicates that the skeleton structure concept (Asaoka et al. 2000, 2002) is valid for cement-treated soils. The undisturbed cement-treated soil eventually approached the CSL of the remolded cement-treated soil. Note that the reference condition of the cement-treated soil is considered for its remolded state.Furthermore, Fig. 4 shows an unusual behavior of the cement-treated soil not seen in naturally deposited clays, which is the point where plastic compression (a decrease in the mean effective stress under the undrained condition) occurs above the CSL. The decrease in mean effective stress occurs only below the CSL in Fig. 5, while it also occurs above in Fig. 4. The tension cutoff line (q=3p′) is shown in Fig. 4. This line represents the state where the lateral effective stress is zero. When the soil under test can actually reach above this line, the triaxial test cannot cope with this type of stress state. A characteristic of the cement-treated soil is that the stress ratio is high enough to reach this line when the confining pressure is low; therefore, the test results near this line should be carefully monitored.Elastoplastic Constitutive Model for Soils Considering Cementation EffectsThis section presents a new method to introduce the cementation effect into elastoplastic constitutive models that can represent the mechanical behavior of naturally deposited soils based on the presented experimental facts. The proposed method was applied to the SYS Cam-clay model, which describes the function of the skeleton structure of the soil, to construct a constitutive model that can reproduce the mechanical behavior of cement-treated soil.Proposal for Modeling the Cementation Effect Using the Extended Effective StressOutline of the Proposed MethodThe key points of the proposed method are divided into the following three parts.The upper chart of Fig. 6 shows the three loading surfaces of the SYS Cam-clay model: normal yield surface, superloading surface (Asaoka et al. 1998, 2000, 2002), and subloading surface (Hashiguchi 1989; Asaoka et al. 1997). The first key point of the proposed method is the translation of each loading surface in the negative direction on the mean effective stress axis, as shown in the lower chart of Fig. 6. This method makes the core constitutive model withstand some tensile stress like cement-treated soils. The equation, η⌣2=Ma2 shown in Fig. 6 indicates the threshold line between the plastic compression and the plastic expansion of this model, and Area A, shown in the lower chart, indicates the plastic compression region that is newly added by the translation. The existence of this region enables plastic compression behavior above the CSL, which is observed in the undrained shear test of the cement-treated soil.The second key point of the proposed method is to solve the translation of each loading surface when plastic deformation occurs. The experiment shows that the undisturbed cement-treated soils asymptotically approached the remolded state with plastic deformation, and the remolded cement-treated soils showed the same mechanical properties as the remolded sample of naturally deposited soils. This experimental fact requires that by undergoing plastic deformation, the model considering the cementation effect should return to the Cam-clay model that describes the mechanical behavior of the fully remolded and normally consolidated clays. To achieve this requirement, the translation of each loading surface is solved with plastic deformation. The amount of translation is treated as an internal state variable Ψ(≥0), and the degradation process of the cementation effect is described by its evolution rule. Ψ is referred to as cementation in this study.The third key point of the proposed method is to newly define the effective stress for the deformation of the cement-treated soil, which is the stress obtained by isotropically subtracting the translation amount Ψ from the effective stress tensor T′ according to the general definition, and to set the SYS Cam-clay model as the core constitutive model. This defined stress is called extended effective stress because it can be regarded as an extension of the effective stress principle. The translation of each loading surface creates the possibility that the mean effective stress p′ becomes negative, which represents Area B shown in the lower chart of Fig. 6. As the Cam-clay model is based on the v−lnp′ relationship, it is necessary to prevent p′ from becoming negative. Describing the core constitutive models using the extended effective stress can help solve this problem. Moreover, as the isotropic component of the extended effective stress is larger than the normal mean effective stress by Ψ, the confining pressure increases by this amount in the extended model. Thus, the initial shear stiffness of the proposed model becomes greater than that of the core constitutive model. As Ψ decreases monotonically with plastic deformation and the extended effective stress becomes identical to the normal effective stress at Ψ=0, the model with the cementation effect can perfectly return to the core constitutive model at the ultimate state. Thus, the experimental fact that the cement-treated soil has the same mechanical properties as the naturally deposited soil samples can be expressed.Specific Procedures for Introduction of Cementation EffectBecause of introducing the extended effective stress, the specific procedures for introducing the cementation effect into the core constitutive model can be summarized as follows:Scheme 1. Converts the normal effective stress into the extended effective stress using the internal state variable Ψ.Scheme 2. Describes the core elastoplastic constitutive model using the extended effective stress and obtains the constitutive relation between the rate of the extended effective stress tensor and the stretching tensor.Scheme 3. Obtains the constitutive relation between the rate of the normal effective stress and the stretching by the inverse transformation from the extended effective stress into the normal effective stress in the rate-type formula.The evolution rule for the internal state variable Ψ describing the degradation process of cementation is incorporated into the model in the last inverse transformation scheme. One of the advantages of the proposed method is that the cementation effect can be introduced without forcing changes in the core constitutive model. In other words, the existing constitutive models can be directly used in Scheme 2.In this study, although the SYS Cam-clay model is used as the core constitutive model for the formulation of the above procedure, the proposed method can be adopted to another existing constitutive model. That is to say, the proposed method possesses high adaptability. However, it is also important to understand that the potential of the core constitutive model determines the performance of the extended model.Transformation from Normal Effective Stress to Extended Effective Stress Considering the Cementation EffectDefinition of Extended Effective StressThe extended effective stress tensor T′⌣ considering the cementation effect is defined as (1) where Ψ(≥0) = objective internal state variable, providing the magnitude of the translation of each loading surface from the origin. Note that Ψ has the same dimension as the stress. Eq. (1) serves as the conversion formula from T′ to T′⌣ using Ψ.Description of Core Constitutive Models Using the Extended Effective StressIn this section, the SYS Cam-clay model, which is the core constitutive model, is described using the extended effective stress tensor T′⌣.Additive Decomposition of StretchingThe stretching tensor D (defined as positive in tension) is additively decomposed into elastic De and plastic components Dp(2) Yield FunctionThe yield function is expressed in terms of the extended effective stress T′⌣ as (3) F(T′⌣,β,R*,R,εvp)=f(p⌣′,η⌣*)+MDlnR*−MDlnR−εvp=0(4) f(p⌣′,η⌣*)=MDlnp⌣′p˜c0′+MDlnM2+η⌣*2M2In these equations, D = dilatancy coefficient, defined as D=(λ˜−κ˜)/Mv0, where v0 denotes the initial specific volume. The conventional volumetric strain εvp, which is defined as positive in compression, can be calculated as εvp=(v0−v)/v0=−∫0tJtrDpdτ. Here, J denotes the volume change ratio, and it is defined as J=v/v0=detF, where F denotes the deformation gradient tensor of soil skeleton. p˜c0′ denotes the initial size of the normal yield surface and is given such that Eqs. (3) and (4) are satisfied at the initial state. λ˜, κ˜, and M are material constants, called compression index, swelling index, and critical state constant, respectively. p⌣′ and η⌣* are invariants of T′⌣ and are defined as p⌣′=−(1/3)T′⌣, η⌣*=3/2‖η⌣*‖, η⌣*=η⌣−β, η⌣=s⌣/p⌣′, and, s⌣=T⌣′+p⌣′I Among these invariants, η⌣* is invariant to represent the rotation of a yield surface. β denotes a back stress ratio tensor (or rotational hardening variable tensor), and its magnitude is expressed as ζ=3/2‖β‖. R*(0

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