How to …

Here you may find some tips using Paratie Plus as well as some suggestions to correctly address your geotechnical problem.

How to estimate soil parameters for retaining wall analysis 

Elastic moduli for sandy soils

Elastic moduli for clays

Effective parameters for clays

Effective cohesion in clays

Mohr-Coulomb parameters for sands and gravels

How to deal with seepage analysis 

Setting up correct boundary conditions

Assessing wellpoint parameters

Selecting water table behaviour out of excavation zoen

How to assess Elastic moduli for sandy soils

The concept of Elastic modulus is  inherited from classic Theory of Structures which usually handles materials that, for a wide range of deformation, behave as linear elastic: for such materials, Elastic Modulus is therefore an appropriate parameter to describe stress-strain behaviour.

In Soil Mechanics, the concept of Elastic modulus is somehow not appropriate, since soils do  not display elastic behaviour, even at very low deformations.

For practical purposes, however, the definition of an equivalent elastic modulus is very valuable also in geotechnical engineering. The most popular way of doing is to define a secant elastic modulus Esec, which somehow approximates the behaviour of soils near to the expected deformations (see figure).

So, the general procedure is:

  1. assess the order of magnitude of expected soil deformations for the load pattern under consideration
  2. assess Esec.

However, for practical calculations, some simpler recommendations may be used, which directly give reasonable estimate of secant moduli based on ordinary soil testing results.

For retaining wall problems, a reasonable estimate for  Esec is

Esec =  (2÷3)⋅NSPT  [MPa]

(NSPT = blow count = number of blows to obtain 1 ft penetration into a borehole, using the Standard Procedure).

The unloading-realoding modulus can be set equal to around 1.5 to 2 times Esec.

Therefore, SPT testing is recommended for sands and gravels.

If static penetration test (CPT or CPTU) results are available:

Esec =  (5÷8)⋅qwhere qis the tip resistance.

Finally, it is  currently quite common to determine shear wave velocity by means of seismic tests such as Cross-Hole, Down-Hole or similar techniques. Doing so, the small strain shear modulus G0 is easily measured. A reasonable correlation with Esec is:

Esec ≅0.80⋅ G0.

(see figure at the side)

For practical purposes, it is recommended to assess Esec employing different correlations and carefully compare obtained values.

It is worth recalling that Esec for coarse soils (sands and gravels) applies to effective stress components.

Finally note that the recommendations included here apply just to retaining  wall problems, not to all the geotechnical problems that may occur in  the same soil (see next figure)

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HOW TO ASSESS ELASTIC MODULI FOR CLAYS

The definition of elastic moduli  for clay materials is even more questionable than for sands.

First of all, one has to realize whether the clay material to be analyzed behaves in drained or in undrained conditions for the load pattern under consideration.

Moreover, as in sandy soils, one has to anticipate the order of magnitude of the expected soil deformations: this is required to reasonably capture a secant modulus Esec 

Under such premises, the following suggestions may be included:

Undrained conditions

It is a very common practice to relate the undrained elastic modulus corresponding with one half of the defaormation which causes undrained failure, to the undrained shear strength Su.

 Esec  = E= Eu50 = K⋅Su

Typical values for K, for retaining wall problems, fall in between 300 and 500.

As long as Sdepends on past geological history and, in particular, on effective overburden stess, also the equivalent elastic modulus depends on the same soil parameters. In other words, the higher undrained shear strength, the stiffer the soil response.

In normally consolidated (NC) clays, S  linearly varies with depth z and is almost zero at soil surface. The same holds also for  Eu

Drained conditions

Elastic modulus for drained conditions may be somehow related to oedometric  parameters.

Virgin loading modulus, which is actually a hardening modulus, can be somehow related to the inverse of mv

Evc ≅ 0.85·(1/mv )     =0.85·(1+e0)⋅σ’v/(0.435⋅Cc)

For example, taking e0 = 0.8 , Cc = 0.25, we would obtain

Evc ≅ 14⋅σ’v

The unloading-reloading modulus EUR (which is more similar to an elastic modulus) can be selected to be higher than Evc with the same ratio as Cc/Cs . Typical values for such ratio are higher than 3.

It should be noted that drained moduli also govern undrained stiffness of clay, if the CLAY model of Paratie Plus with effective parameters is selected for analysis.

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HOW TO SELECT EFFECTIVE RESISTANCE PARAMETERS FOR CLAYS

The CLAY model in Paratie Plus requires the definition of two friction angles:

  • the critical state friction angle , and
  • a peak friction angle, which is used to linearize the failure condition near to the origin

The critical state angle φcv  an be either measured through lab testing (normally TX or DS tests) or may be related to plasticity index PI. In  the latter case, the following graph can be used. Min. percentile values are recommended, at least for low PI values (we recall that the lower PI, the lower is the clay content, so the nearer the behaviour to coarse grained soils)

The peak angle φp can be related to φcv via

tan (φ’p)  ≅ tan (φ’cv) / 1.50

It should be noted that φp must be less than φcv. See Theory Manual for details.

Finally, note that no effective cohesion is required for CLAY model used in non linear retaining wall analysis.

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EFFECTIVE COHESION ESTIMATE FOR CLAYS

When a Slope Stability Analysis is required, an effective cohesion can be assigned as well, since in this case the clay is modeled using an ordinary Mohr-Coulomb model .

Effective cohesion c’ (frequently referenced to as apparent cohesion) must be selected with very much care, according to carefully conducted lab tests.

In modern Soil Mechanics, effective cohesion is just a mathematical way to approximate a more complex soil behavior at very low confining stress levels. For this reason, such parameter is frequently critized by many Authors.

Effective cohesion is just observed in highly overconsolidated clays.

Keeping these concepts in mind, a very rough estimate of c’ can be  obtained using following equation:

c’≅ (5%-10%)⋅Su

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MOHR-COULOMB PARAMETERS FOR GRANULAR SOILS

Mohr-Coulomb parameters for coarse grained soils (sands and gravels) can be selected as follows.

Friction angle φ’

As for retaining wall design purposes, an intermedia friction angle between critical state angle and peak friction angle should be selected.

Critical state angle φcv does not depend on soil density, as it represents the friction resistance at the loosest state for soils or for soils loaded near to failure. It just depends on grain shapes and grading. Typical values for sands and gravel span between 30 and 36 deg. Paratie Plus  gives some advices through its dialog boxes.

Peak friction angle φpeak determines peak soil resistance which, however, holds just for small deformations in soils. The difference between  φpeak and φcv depends on soil dilatancy (the tendency of volume to expand during shear deformation), which in turn depends on soil density.

Paratie Plus includes some popular correlations to assess such values.

As discussed above, for design purposes, an intermediate value between φpeak and φcv should be adopted.

Typical (characteristic) angles for retaining wall analysis fall in between 30 to 42 deg . In the following table some values  are included, depending on soil relative density.

For example, consider a sand and gravel admixture. Assume φcv = 32°. Assume that, at the depth of about 8, (without water), NSPT=18 has been recorded.

We assume emax-emin=0.30 and σ’v≅19⋅8=152 kPa.

So N1=14.45 and Dr=0.455=45.5%

φpeak≅ 40° and finally φ’k≅ 38°. Note that we have applied a safety factor equal to 1.30 to (φ’peak – φ’cv).

As for slope stability problems, we should keep in mind that limit equilibrium methods currently assume that relevant deformations develop near to expected slip surfaces. This aspect should be carefully considered in selecting appropriate friction angles for such analysis.

Effective cohesion c’

The behaviour of actual soils may be better reproduced including some cohesion, which accounts for some contributions, including the following:

– undrained resistance of the clay percentage of soil mass;

– suction (negative pore pressures above water table)

– cementation.

Unfortunately, all such aspects can be hardly converted into some reliable cohesion parameter: therefore no cohesion at all should be assumed for practical design purposes.

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TYPICAL BOUNDARY CONDITIONS  IN SEEPAGE ANALYSIS

Within Paratie Plus, a seepage analysis is most often required to model water table lowering in some region.

A normal situation is represented by an underwater excavation within retaining walls. Main purpose of a seepage analysis is to give an answer to the following questions:

1 – how much water has to pumped away to sufficienty lower the water table inside excavation?

2 – which is the pore pressure distribution along each side of the retaining walls?

To obtain good answers to such questions, a seepage model should be set up correctly.

First of all a reasonable value for permeability coefficients should be assigned (note that usually horizontal permeability is higher that vertical one). Permeability coefficients should come from careful tests.

Moreover, appropriate boundary conditions must be applied. The following table may provide some guidance

 NO FLOW conditions must be ensured wherever water cannon enter the model or escape from the region or seep across. Such condition is simply accomplished by limiting the mesh to such boundaries. Hence such condition should be prescribed

  • at model bottom
  • along a retaining wall faces
  • along  a simmetry plane

Note that such condition is automatically imposed by Paratie Plus for the first two cases.

 
 FIXED head condition must be explicitly imposed where known pore pressures are requested. Along such boudaries, fluid can pass through: in other words where pore pressures are imposed, a pervious boundary is modeled. This condition is typically assigned at the far vertical edge of the model where undisturbed conditions are usually assumed. Inside excavation such condition may be used to roughly model spread pumping operations.
 Along the soil surface, a very shallow water table may emerge: so some outflow may occur. However this condition cannot occur above water table.

Such condition can be controlled via a special non linear boundary conditions offered by the seepage module.

By adding a well point, a prescribed flow condition can also be modelled.

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HOW TO DEFINE WELL POINT DATA IN A SEEPAGE ANALYSYS

A simple yet effective procedure to assess the amount of flow to be assigned to each wellpoint is outilined.

In essence two models should be used, namely:

  1. STEP 1 (model 1) – place some trenches where wellpoints are foreseen. Once seepage results are available and an acceptable water table lowering has been obtained, the amount of flow removed by a wellpoint in each positioncan be easily assessed using the Flow Inspector tool;
  2. STEP 2 (model 2): switch from trench to wellpoint for each wellpoint position; of course assign the just assessed flow quantity q for each item.

The following figure summarizes the recommended way to model dewatering operations.

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selecting phreatic line behaviour out of excavation zone

Consider this figure when selecting external water table behaviour (ASSUMPTION A  or B). In most usual situations, ASSUMPTION A is on the safe side. However the differences between the two approaches are often very small. Of course ASSUMPTION A is not applicable when there is some well point (or some trench) out of excavation zone.

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