7.1.1 On use of different models
(1)Linear Elastic model(LE)
The Linear Elastic model is based on Hooke's law of isotropic elasticity.It involves two basic elastic parameters,i.e.Young's modulus E and Poisson's ratioν.Although the Linear Elastic model is not suitable to model soil,it may be used to model stiff volumes in the soil,like concrete walls,or intact rock formations.
(2)Mohr⁃Coulomb model(MC)
The linear elastic perfectly⁃plastic Mohr⁃Coulomb model involves five input parameters,i.e.E andνfor soil elasticity;ϕand c for soil plasticity andψas an angle of dilatancy.This Mohr⁃Coulomb model represents a‘first⁃order’approximation of soil or rock behaviour.It is recommended to use this model for a first analysis of the problem considered.For each layer,one estimates a constant average stiffness or a stiffness that increases linearly with depth.Due to this constant stiffness,computations tend to be relatively fast and one obtains a first estimate of deformations.
(3)Hardening Soil model(HS)
The Hardening Soil model is an advanced model for the simulation of soil behaviour.As for the Mohr⁃Coulomb model,limiting states of stress are described by means of the friction angle,ϕ;the cohesion,c;and the dilatancy angle,ψ.However,soil stiffness is described much more accurately by using three different input stiffnesses:the triaxial loading stiffness,E50,the triaxial unloading stiffness,Eur,and the oedometer loading stiffness,Eoed.As average values for various soil types,Eur≈3E50 and Eoed≈E50 are suggested as default settings,but both very soft and very stiff soils tend to give other ratios of Eoed/E50,which can be entered by the user.In contrast to the Mohr⁃Coulomb model,the Hardening Soil model also accounts for stress⁃dependency of stiffness moduli.This means that all stiffnesses increase with pressure.Hence,all three input stiffnesses relate to a reference stress,usually taken as 100 kPa(1 bar).Besides the model parameters mentioned above,initial soil conditions,such as pre⁃consolidation,play an essential role in most soil deformation problems.This can be taken into account in the initial stress generation.
(4)Hardening Soil model with small⁃strain stiffness(HSsmall)
The Hardening Soil model with small⁃strain stiffness(HSsmall)is a modification of the above Hardening Soil model that accounts for the increased stiffness of soils at small strains.At low strain levels,most soils exhibit a higher stiffness than at engineering strain levels,and this stiffness varies non⁃linearly with strain.This behaviour is described in the HSsmall model by using an additional strain⁃history parameter and two additional material parameters,i.e.Gref0 andγ0.7.Gref0 is the small⁃strain shear modulus andγ0.7 is the strain level at which the shear modulus has reduced to about 70% of the small⁃strain shear modulus.The advanced features of the HSsmall model are most apparent in working load conditions.Here,the model gives more reliable displacements than the HSmodel.When used in dynamic applications,the Hardening Soil model with small⁃strain stiffness also introduces hysteretic material damping.
(5)Soft Soil model(SS)
The Soft Soil model is a Cam⁃Clay type model especially meant for primary compression of near normally⁃consolidated clay⁃type soils.Although the modelling capabilities of this model are generally superseded by the Hardening Soil model,the Soft Soil model is better capable to model the compression behaviour of very soft soils.
(6)Soft Soil Creep model(SSC)
The Hardening Soil model is generally suitable for all soils,but it does not account for viscous effects,i.e.creep and stress relaxation.In fact,all soils exhibit some creep and primary compression and is thus followed by a certain amount of secondary compression.The latter is most dominant in soft soils,i.e.normally consolidated clays,silts and peat,and PLAXIS thus implemented a model under the name Soft Soil Creep model.The Soft Soil Creep model has been developed primarily for application to settlement problems of foundations,embankments,etc.For unloading problems,as normally encountered in tunnels and other excavation problems,the Soft Soil Creep model hardly supersedes the simple Mohr⁃Coulomb model.As for the Hardening Soil model,proper initial soil conditions are also essential when using the Soft Soil Creep model.This also includes data on the pre⁃consolidation stress,as the model accounts for the effect of over⁃consolidation.Note that the initial over⁃consolidation ratio also determines the initial creep rate.
(7)Modified Cam⁃Clay model(MCC)
The Modified Cam⁃Clay model is a well⁃known model from international soil modelling literature;see for example Muir Wood(1990).It is meant primarily for the modelling of near normally⁃consolidated clay⁃type soils.This model has been added to PLAXIS to allow for a comparison with other codes.
The Mohr⁃Coulomb model may be used for a relatively quick and simple first analysis of the problem considered.In many cases,even if good data on dominant soil layers is limited,it is recommended to use the Hardening Soil model or the HS small model in an additional analysis.No doubt,one seldomly has test results from both triaxial and oedometer tests,but good quality data from one type of test can be supplemented by data from correlations and/or in situ testing.Finally,a Soft Soil Creep analysis can be performed to estimate creep,i.e.secondary compression in very soft soils.