Teruo Nakai

Consequences of the tij-concept and a new modeling approach

Abstract The strength and the dilatancy of soils are largely influenced by the choice of the stress and strain increment variables. Cam-clay like models that use extended Mises strength criterion cannot consider the effect of intermediate principal stress properly and give unrealistic strength under generalized three-dimensional stresses except triaxial compression condition. Nakai and Mihara proposed a modified stress tensor ( t ij ) based on the Spatially Mobilized Plane (SMP) concept that uses Matsuoka–Nakai strength criterion to consider the influence of intermediate principal stress on the strength and the dilatancy of soils. Matsuoka–Nakai strength criterion is a convex surface on the π -plane in the ordinary stress space and satisfies Mohr–Coulomb criterion under axisymmetric conditions (triaxial compression and extension). Using the t ij -concept, isotropic and kinematic hardening clay and sand models have been proposed and experimentally verified. Recent investigations have revealed inconsistency of the t ij -concept with the critical state concept used in the original and modified Cam-clay models. In this paper the inconsistency of the t ij -concept with the critical state concept is pointed out first, then a modeling approach has been introduced, which virtually can adopt any strength criterion in a consistent way to incorporate the critical state concept. It is shown that the proposed stress and strain increment quantities are properly work conjugate. A compact stress–dilatancy relation is also introduced using the proposed stress and strain increment quantities, which gives a continuous and smooth plastic potential and has control over the stiffness of the model predictions.

Interaction Effect of Retaining Wall and Existing Foundations in Braced Excavation

Two-dimensional model tests are conducted to investigate the deformation mechanism of the ground and the earth pressure of retaining wall. Numerical simulations with finite element method using FEMtij-2D are also carried out for the same scale of the model tests. Subloading tij model is used in the analyses to model the ground material. Several patterns of the model tests are performed varying the length of the retaining wall and changing the distance between the foundation and wall. It is revealed in this research that maximum surface settlement does not always occur just behind the wall, but mostly at the position of the existing building. The rotation of the foundations depends on the distance between the foundation and wall. The numerical analyses can well simulate the observed earth pressures, surface settlements and deformation mechanism of the ground.

Simple modeling of stress-strain relation for unsaturated soil.

Though stress-strain characteristics of unsaturated soils are complicated and rather different from those of saturated soils, it should be described properly by a constitutive model for soils because soil usually stays under an unsaturated condition in actual field. In the current study, a simple elastoplastic model for saturated soil is extended to one applicable to unsaturated soils. The proposed model is formulated using the Bishop’s effective stress and the residual strength is, therefore, assumed to be constant. In the proposed model, the decrease (or increase) in the degree of saturation is linked with upward (or downward) movement of normally consolidated line in the compression plane of mean effective stress and void ratio, by which the typical volumetric and distortional behaviors of unsaturated soils are properly described. In addition, a simple method to extend classical water retention curves such as van Genuchten’s equation to be able to incorporate the influences of suction histories and density is proposed and applied to the proposed model. In the present paper, the outline of the proposed model is explained and applicability of the model is discussed through typical results of simulations.

3D Effects in Excavation Problems: Model Tests and Numerical Simulations

In order to investigate the fundamental mechanisms of the generation of earth pressure and the ground movement in excavation problems such as tunneling and open excavation, 2D and 3D model tests and the corresponding elastoplastic finite element analyses were carried out. It is experimentally shown that the earth pressure and the ground movement are very much influenced by 3D effects including excavation sequence. In tunneling problems, not only the arching effect in transverse direction to tunnel axis but also the arching in excavation direction should be considered for proper predictions. In retaining wall problems, the earth pressure on the wall in 3D condition is much smaller than that in 2D (plane strain) condition, and the surface settlement at the backfill in 3D condition occurs more locally than that in 2D condition. These differences between 3D and 2D are simulated quantitatively as well as qualitatively by the analyses using an elastoplastic constitutive model which can describe typical stress- strain behaviors in general 3D stress conditions.

A Unified Mechanical Quantity for Granular Materials in Three-Dimensional Stresses

Abstract A mechanical quantity is presented to describe uniquely the behavior of granular materials in three-dimensional stresses. The validity of this quantity is discussed on the basis of the results of triaxial compression and extension tests and true triaxial tests under constant mean principal stresses. A way to apply this quantity tij to ordinary elastoplastic theory is then mentioned.

Effect of Reinforcement on Bearing Capacity of Foundations

To increase bearing capacity of a foundation, geosynthetic is laid beneath the foundation. In previous research, the authors investigated the reinforcement mechanism by changing the length and the laying depth of the reinforcement (Nakai et al, 2009). In the present study, to get more bearing capacity, the reinforcing effect in the case that each edge of the reinforcement is fixed with the soil is investigated. For this purpose, 2D model tests and the corresponding non-linear finite element analysis are carried out. In these tests and simulation, the depth of the reinforcement is changed under constant length of reinforcement. Reinforcing effects, under concentric and eccentric load, are discussed. It is revealed that a significant increase of the bearing capacity is observed in the model tests when the reinforcement is set up in the ground with an appropriate depth under both concentric and eccentric loads. The results of numerical simulation - in which the stress-stain behavior of the soil and the frictional behavior between soil and reinforcement are properly taken into consideration - show good agreement with the observed results.

Elastoplastic modelling of soil anisotropy

Abstract An elastoplastic model for sand is extended to account for inherent anisotropy through the introduction of fabric anisotropy tensor. The validity of the proposed model is then confirmed by the results of isotropic compression test, triaxial tests and plane strain tests.

Numerical Investigation of Impact of Non-circular Tunneling in Sensitive Soft Clay Layers

Large section non-circular shield tunnel has been used for a new metro line where the underground space was not enough for the traditional parallel twin circular shield tunnel in the central area of Ningbo city in China. Ground of the construction site contains layers of very soft sensitive clay having a typical mechanical behavior of stress softening and others due to the destruction of the soil structure. In consequence, long-term consolidation settlement and inclination of the adjacent buildings could occur. In this paper, 2D soil-water coupling elastoplastic FE-analyses have been carried out to predict the impact of tunneling on the pile foundation of adjacent buildings, using FEMtij-2D program. As the constitutive model of soils, the Subloading tij model has been used which properly consider typical consolidation and shear behaviors of various kind of soils under general three-dimensional stress conditions.

Simple Modeling of Time-Dependent Behavior for Structured Soils

A simple model to describe time-dependent behavior of various soils in 1D stress conditions is presented in this paper. The model is formulated not using the usual viscoplastic theories such as over-stress type and non-stationary flow surface type but utilizing the subloading surface concept by Hashiguchi (1980), and paying attention to the experimental results that the normally consolidation line (NCL) on the e–ln σ plane shift depending on the strain rate. The present model can describe various time-dependent behaviors not only of normally consolidated soil but also of over consolidated and naturally deposited soils in the same manner without violating the objectivities. The 1D model can easily be extended to the 3D using the t ij concept (Nakai and Mihara 1984).

EFFECTIVENESS OF REINFORCEMENT IN EMBANKMENT GROUND SUBJECTED TO REPEATED SHEAR DEFORMATION

In this research, a comparative study is done on the effectiveness of reinforcement in embankment ground. The restraint effect of ground displacement by reinforcement of sheet pile and the sheet pile combined with the nailing method are investigated by model tests and corresponding finite element analyses. An elastoplastic model and subloading tij model are used in the analyses. Two loading conditions were applied namely, the simple vertical loading to the footing and cyclic loading associated with repeated shear deformation in the ground for both series of the model tests and the finite element analyses. Soil-water coupling analysis applying an inertial force to real ground embankment is also performed. It is revealed that when the bearing capacity of the ground increases, the lateral and vertical displacements are restrained. The reinforcement by the sheet pile combined with the nailing method is effective compared with that of the sheet pile alone.