7.5.3 Parameters of the Soft Soil Model
The parameters of the Soft Soil model include compression and swelling indicies,which are typical for soft soils,as well as the Mohr⁃Coulomb model failure parameters.In total,the Soft Soil model requires the following parameters to be determined:
Basic parameters:
(1)Modified swelling index and modified compression index
These parameters can be obtained from an isotropic compression test including isotropic unloading.When plotting the logarithm of the mean stress as a function of the volumetric strain for clay⁃type materials,we can approximate it by two straight lines.The slope of the primary loading line gives the modified compression index and the slope of the unloading(or swelling)line gives the modified swelling index.Note that there is a difference between the modified indicesκ∗and λ∗and the original Cam⁃clay parametersκandλ.The latter parameters are defined in terms of the void ratio e instead of the volumetric strainεv.
Apart from the isotropic compression test,the parametersκ∗andλ∗can be obtained from a one⁃dimensional compression test.Here a relationship exists with the internationally recognized parameters for one⁃dimensional compression and swelling,Cc and Cs.These relationships are summarized in Table 7.1.
Table 7.1(a) Relationship to Cam⁃clay parameters
Table 7.1(b) Relationship to internationally normalized parameters
Remarks on Table 7.1:
①In relations 1 and 2,the void ratio,e is assumed to be constant.In fact,e will change during a compression test,but this will give a relatively small difference in void ratio.For e,one can use the average void ratio that occurs during the test or just the initial value.
②In relation 4 there is no exact relation betweenκ∗and the one⁃dimensional swelling index Cs,because the ratio of horizontal and vertical stresses changes during one⁃dimensional unloading.For this approximation,it is assumed that the average stress state during unloading is an isotropic stress state,i.e.the horizontal and vertical stresses are equal.
③In practice,swelling is often assumed to be equivalent to recompression behavior,which may not be right.Henceκ∗should be based on Cs rather than the recompression index Cr.
④The factor 2.3 in relation 3 is obtained from the ratio between the logarithm of base 10 and the natural logarithm.
⑤The ratioranges,in general,between 2.5 and 7.
(2)Cohesion
The cohesion has the dimension of stresses.A small effective cohesion may be used,including a cohesion of zero.Entering a cohesion will result in an elastic region that is partly located in the tension zone,as illustrated in Figure 7.17.The left hand side of the ellipse crosses the p′⁃axis at a value of c cotφ.In order to maintain the right hand side of the ellipse(i.e.the cap)in the‘pressure’zone of the stress space,the isotropic pre⁃consolidation stress pp has a minimum value of c cotφ.This means that entering a cohesion larger than zero may result in a state of over⁃consolidation,depending on the magnitude of the cohesion and the initial stress state.As a result,a stiffer behavior is obtained during the onset of loading.It is not possible to specify undrained shear strength by means of high cohesion and a friction angle of zero.Input of model parameters should always be based on effective values.Please note that the resulting effective stress path may not be accurate,which may lead to an unrealistic undrained shear strength.Hence,when using Undrained(A)as drainage type,the resulting stress state must be checked against a known undrained shear strength profile.
(3)Friction angle
The effective angle of internal friction represents the increase of shear strength with effective stress level.It is specified that in degrees,zero friction angle is not allowed.On the other hand,care should be taken in the use of high friction angles.It is often recommended to useφcv,i.e.the critical state friction angle,rather than a higher value based on small strains.Moreover,using a high friction angle will substantially increase the computational requirements.
(4)Dilatancy angle
For the type of materials,which can be described by the Soft Soil model,the dilatancy degrees is considered in the standard settings of the Soft Soil model.
(5)Poisson's ratio
In the Soft Soil model,the Poisson's ratio v is the well⁃known pure elastic constant rather than the pseudo⁃elasticity constant as used in the linear elastic perfectly⁃plastic model.Its value will usually be in the range between 0.1 and 0.2.If the standard setting for the Soft Soil model parameters is selected,then vur=0.15 is automatically used.For loading of normally consolidated materials,Poisson's ratio plays a minor role,but it becomes important in unloading problems.For example,for unloading in a one⁃dimensional compression test(oedometer),the relatively small Poisson's ratio will result in a small decrease of the lateral stress compared with the decrease in vertical stress.As a result,the ratio of horizontal and vertical stress increases,which is a well⁃known phenomenon in overconsolidated materials.Hence Poisson's ratio should not be based on the normal consolidated K⁃value,but on the ratio of the horizontal stress increment to the vertical stress increment in oedometer unloading and reloading test such that
(6)K⁃parameter
The parameter M is automatically determined based on the coefficient of lateral earth pressure in normally consolidated condition,K,as entered by the user.The exact relation between M and K
is as follows(Brinkgreve,1994):
The value of M is indicated in the input window.As can be seen from Eq.7.58,M is also influenced by the Poisson's ratio vur and by the ratioHowever,the influence of
is dominant.Eq.7.58 can be approximated by