FAQ ON PLAXIS FEM

FAQ Plaxis FEM

Below you can find answers to frequently asked questions about Plaxis FEM

Which software for fem can be used to model Maccaferri reinforced soil structures?
The following softwares can be used, among the many softwares commercially available:
- Plaxis 2D
- Plaxis 3D
- Rocscience RS2 (Phase2 9.0)
- Rocscience RS3 (2.0)
- GEO5 FEM
- ADAMA ENGINEERING OptumG2
Maccaferri often use PLAXIS 2D to model reinforced soil structures. Hence the following FAQs make reference primarily to PLAXIS 2D. Anyway the other FEM softwares above listed can be used as well and most of the following FAQs are also applicable to the other softwares.

Do I need training to properly use Plaxis to model Maccaferri reinforced soil structures?

There are many details to be considered in a FEM analysis and sometimes slight changes in the parameters might have a significant influence on the results. Maccaferri guidelines and FAQs cannot transmit the sensibility to the solution of geotechnical problems and the risk which is connected to the misunderstanding of any parameter.

Required level of expertise in working with FEM software is needed, hence Maccaferri technical guidelines cannot replace a detailed training on FEM modelling.

Professional training on FEM modelling is required before using any of the documented software for design or check purposes.

Maccaferri highlights the risks linked to distribution of wrong results, due to wrong input parameters and/or incorrect conclusions related to the misreading of output and analysis results, since underestimated risks can lead to major problems in the development of a project and requests of compensation.

Can I find guidelines to use Plaxis to model Maccaferri reinforced soil structures?

Full information about the use of PLAXIS to model Maccaferri reinforced soil structures can be found in the document: TECHNICAL GUIDELINE OF MACCAFERRI SOLUTIONS WITH FEM, Rev. 1, 12/04/2018.

Can I use Plaxis to model Maccaferri reinforced soil structures?

PLAXIS is a software for FEM (Finite Eelement Modeling) specific for geotechnical applications. Practically all geotechnical elements and structures can be modeled with PLAXIS. Maccaferri reinforced soil structures, including walls, slopes, and embankments can be modeled with PLAXIS:

Which Maccaferri reinforced soil structures can I model with Plaxis?
- TERRAMESH (WITH STEEL MESH FACING), TERRAMESH SYSTEM (WITH GABION FACING), PARAMESH (WITH GABION FACING + HIGH STRENGTH GEOGRIDS REINFORCEMENT) REINFORCED SOIL WALLS (RSW)
- MACRES REINFORCED SOIL WALLS WITH COCNCRETE PANEL FACING AND PARAWEB GEOSTRIP REINFORCEMENT
- STEEP SLOPES WITH GEOGRID REINFORCEMENT
- GREEN TERRAMESH STEEP SLOPES
- BASAL REINFORCEMENT OF EMBANKMENT ON SOFT SOIL, PILED EMBANKMENTS, EMBANKMENTS OVER VOIDS

Can I model simple and secured drapery with Plaxis?

PLAXIS modelling of simple and secured drapery is feasible, but it requires sensibility and expertise of the modeller.

In facts, the modelling of this type of solutions involve some approximation and in some cases inaccuracies. Indeed, the contact between nail and netting is neglected and even the detachment between the soil and the netting is not modelled.

Some software such as Dyna and Yade provide this advanced modelling, but other software (Plaxis, Phase2, Flac) do not consider it. For this reason, Plaxis models shall start from a deformation stage in which the contact between the soil and the netting is assured and the netting is working in tension. Another approximation is represented by the 2D models, which cannot appreciate the real distribution of the nails in all directions.

Can I model rockfall protection embankments with Plaxis?

No, Plaxis modelling is unfeasible for Rockfall Protection Embankments.

In facts, FEM modelling of rockfall solutions involves the definition of the boulder impact and material constitutive law of the elements. This is not an easy task and requires a time-consuming process.
FEM analysis of rockfall embankments was carried out in the past to evaluate the energy level capacity from a computational point of view and compare the results with the experimental tests. Other FEM softwares may be used for modelling Rockfall Protection Embankments, like Abacus Explicit, yet the costs and computational times are very high.

Which Maccaferri products for soil reinforcement can I model with Plaxis?

All Maccaferri steel meshes and steel bars, geogrids, geostrips, and woven/knitted geotextiles can be modelled with PLAXIS:

How can I model Maccaferri Geogrids and Geostrips with Plaxis?

Polymeric reinforcements are modelled in Plaxis as STRUCTURAL elements:

Available constitutive models of geogrids are:

In the new versions of PLAXIS, geogrid elements can be even modelled with Elastoplastic (N-ε) behaviour (the stress-strain curve of the material can be implemented for each product), or with Visco-elastic (time-dependent) behaviour, in which multiple stiffnesses can be inserted with a retardation time.

How to evaluate the axial stiffness EA of geogrids?
The axial stiffness of geogrids is obtained by dividing its allowable long term design tensile strength by its limite strain:

where:
- Tall is the short term ultimate tensile strength (kN/m);
- ε is the limit strain;
- RFCR is a reduction factor to allow for the effect of sustained static load (tensile creep) at the service temperature;
- RFID is a reduction factor to allow for the effect of installation damage;
- RFW is a reduction factor to allow for weathering during exposure prior to installation or of permanently exposed material;
- RFCH is a reduction factor to allow for reductions in strength due to chemical and biological effects at the design temperature
- A1 is a reduction factor to allow for the effect of sustained static load at the service temperature;
- A2 is a reduction factor to allow for the effect of installation damage;
- A3 is a reduction factor for seams and joints (if any);
- A4 is a reduction factor to allow for reductions in strength due to chemical and biological effects at the design temperature
- A5 is a reduction factor for dynamic stresses (if any);
- γM is a partial factor for the structural resistance
The short term ultimate tensile strength is obtained by tensile tests according to ISO 10319:

The stress – strain curves of Maccaferri geogrids are summarised in the following plot:

The design strength of ParaWeb geostrips is evaluated by tensile tests according to ISO 10319. Anyway the obtained value is in kN. To get a value in kN/m, the resistance of one ParaWeb geostrip have to be multiplied by the number of strips in one meter width.

The long term strength and the reduction factor for tensile creep (RFCR or A1) can be derived from creep rupture curves (for long-term applications where strain is not a limiting factor), and from isochronous curves (for applications where strain is a limiting factor).

Note that for the advanced modelling with stress- strain (N – ε) curve, tensile curves at different elapsed time (examples: 1,000 hours at the end of construction, 120 years at the end of design life) should be used: the related values can be obtained from the isochronous curves of each geogrid.

The limit strain ε related to reinforced soil structures where strain is not a limiting factor should be assumed equal to the Nominal strain at maximum tensile strength (ε = 9.0 % for Paragrid; ε = 9.5 % for Paralink)

For the limit strain ε related to reinforced soil structures and basal reinforcement where deformation should be limited, the following values are suggested:

The suggested limit strain for ParaWeb geostrips is 3 – 5 %.

Where do I find the values for determining the axial stiffness EA of geogrids?

Specific DDS (Design Data Sheet) are available for each family of Maccaferri geogrids, affording the values of the axial stiffness EA for different types of fill, both at short term and at 120 years design life, for different temperatures (typically 20°C, 30°C, 40°C).
As example, for Paragrid and Paralink at 20°C:

The tensile curves at short term, the creep rupture curves, the isochronous curves, the partial factors for tensile creep, installation damage and chemical degradation can be found in the BBA Certificate of each family of products, as example for Paralink geogrids in:

How can I model maccaferri geostrips with Plaxis?

MacRes Wall systems are composed by concrete panels and ParaWeb geostrip reinforcements.

Polymeric reinforcements are modelled in Plaxis as STRUCTURAL elements:

How can I model the interaction between geogrids or geostrips and soil in Plaxis?

The shear stress developed at the soil – geogrid interface is calculated according to the Coulomb’s shear stress criterion:

With:

The direct sliding resistance of the system may be established from the value fds = Rint ≤ 1, which is the direct sliding coefficient, determined as follows:

where:
αs is the proportion of plane sliding area that is solid;
δ is the angle of skin friction between the soil and the planar reinforcement surface;

is the coefficient of skin friction between the soil and the reinforcement.

For Paraweb geostrips αs can be modelled in the following way:

How can I model Maccaferri steel wire mesh products with Plaxis?

The steel wire mesh behaves like an extensible reinforcement and its deformability is similar to geogrid. Hence steel wire mesh products are modelled in Plaxis as elastoplastic geogrid elements.

The input parameters are the plastic load and the axial stiffness.

In the new versions of Plaxis, geogrid elements can be even modelled with Elastoplastic (N-ε)
Behaviour, where the stress-strain curve of the material can be implemented for each product, or with Visco-elastic (time-dependent) behaviour, where multiple stiffnesses can be inserted with a retardation time.

How to evaluate the axial stiffness EA of Maccaferri steel wire mesh products?

The axial stiffness of steel wire mesh products is obtained by dividing its long term design tensile strength by its limit strain:

where:

T_D = long term design strength at the end of the design life, here assumed to be equal to 120 years.
T_B = short term base ultimate tensile strength
f_creep = reduction factor due to creep = 1.0 for steel
f_m = partial material factor
f_m11 = factor relating to the manufacturing process
f_m12 = factor relating to the extrapolation of data
f_m21 = factor relating to the damage caused to the products during the installation process
f_m22 = factor relating to the effects of the environment on the products.

The value of TB for metallic reinforcement should be the ultimate tensile strength based on net cross-sectional area; for steel wire mesh products reference must be done to the testing procedures described at Par. 9.3 of EN 10223-3:2013 which considers, in the tensile test method, the specific geometrical characteristics of double twist wire mesh and the following minimum values have been found:

The partial factors adopted for a 120-year service life, for steel meshes embedded in soil with 3 < pH < 13, are:

Where do I find the values for determining the axial stiffness EA of Maccaferri steel wire mesh products?

The 120 years Long Term Design Strength (LTDS or TD) and Design Axial Stiffness EA of polymer coated steel wire mesh products according to the Annex A of BS 8006-1 and as per the BBA certificates 16/H247 Product Sheet 2 (Terramesh System), 16/H247 Product Sheet 3 (Green Terramesh) and 95/3141 Product Sheet 1 (Gabion), are equal to:

How can I model the interaction between Maccaferri steel wire mesh products and soil in Plaxis?

The shear stress developed at the soil – geogrid interface is calculated according to the Coulomb’s shear stress criterion:

The direct sliding resistance of the system may be established from the value f_ds = R_int ≤ 1, which is the direct sliding coefficient, determined as follows:

where:

α_s is the proportion of plane sliding area that is solid, 0.091 for the Terramesh System mesh.
a’ is the interaction coefficient relating soil/reinforcement bond angle with tan φ’

The following values are suggested for steel wire mesh products:

How can I model facing element in Plaxis?
Stone facing:
For Gabions, TMS and Mineral GTM stone facing, the facing is practically made up of stones; the stone facing can be modelled as a soil cluster assigning the following soil parameters:
- Unit weight: γ = 17.5 kN/m3;
  · Friction angle: φ = 40°;
  · Young Modulus = 40 MPa;
  · Cohesion, as a function of facing units height:
Welded mesh panels:
The welded mesh panels can be modelled as plate elements having the following parameters. Welded mesh panel material data set can be applied to the facing of Green Terramesh and Mineral Green Terramesh:

Concrete and Steel elements:
Concrete elements can be piles, pile caps, facing panels, foundations and shotcrete facing layers. These elements can be modelled as plate elements.
Steel elements can be driven steel piles.

In the case of concrete elements:
· Unit weight: γ = 24 – 25 kN/m3 (the latter is used in case of reinforced concrete).
· Concrete: characteristic strengths and Young Modulus are as follows:

Concrete seldom can be modelled as soil cluster. In this case, the suggested soil properties which can be used are:
· Friction angle: φ = 45°;
· Cohesion: c = 500 kPa;
· Poisson’s coefficient: ν = 0.1 – 0.2;
In the case of steel elements:
· Unit weight: γ = 78.5 kN/m3;
· Poisson’s coefficient: ν = 0.3;
· Young modulus: E = 210 GPa;

Concrete panels:
Concrete Panel material data set can be applied to the facing elements of MacRes wall system.
Concrete panels can be modelled as plate elements having the following characteristic and design parameters:

When should I use interface elements in Plaxis?

Interface elements in finite element model are used to model the contact area between two types of different material, e.g., the contact area between geogrids and the soil, between concrete and soil, etc.
This interface element, particularly in Plaxis, has two functions. The first function is to reduce the friction between the soil and the construction material in contact with the soil by introducing an interface reduction coefficient (with a value between 0 to 1). The second function is to indicate whether the interface is impermeable or permeable.
The interface reduction coefficient is not assigned to the interface element but to the soil in contact with the other elements.
Suggested interface reduction coefficient fds or Rinter have been given for geogrids, geostrips and steel wire mesh products, see FAQ about the interaction between Maccaferri products and soil.

Which procedure should be followed for analysing reinforced soil structures in Plaxis?

The following procedure should be followed.

Input steps
– Definition of the Geometry, Loads, Materials
– Generation of the Mesh
– Initial conditions
– Definition of the phreatic level
– Generation of water pressure by phreatic level
– Go to Calculate

Calculations steps
After input steps are completed, the calculation starts.
Before proceeding to the analysis, a gravity loading phase shall be carried out. This represents the initial step in which the initial in-situ pressures and stresses are defined.
Initially, when creating the finite element model, although the soil parameters has been assigned and the finite element mesh has been created, the soil body self-weight, i.e. the initial stresses, has not been counted for.
A special procedure is necessary to generate or to calculate the initial stresses within the soil body. As the name implied, initially only the original soil body exists, therefore, all the structural elements and geometry changes, e.g.: backfilling, excavation, all structural elements of the wall shall not be activated.
– Gravity Loading
– Calculation type: Plastic analysis
– Control parameters: Select Ignore undrained behaviour
– Loading input: Select Total multipliers
– Total multipliers: Define Σ-Mweight = 1

Once Gravity Loading has been defined four Calculation types can be performed:
– Plastic Analysis,
– Consolidation Analysis,
– Phi/c reduction,
– Dynamic Analysis (not covered here).

The steps and the options to be selected are:

Plastic Analysis
– Excavation phases, staged construction phases and loading phases
– Calculation type: Plastic analysis
– Control parameters: Select Reset displacements to zero
– Reset displacements to zero when needed (after excavation phases or staged construction phases to evaluate post-construction displacements and deformation)
– Loading input: Staged construction
– Define Geometry, Loads, Materials

Consolidation Analysis
– C1) Consolidation phases
– Calculation type: Consolidation analysis
– Loading input: Staged construction
– Define Time interval in days (for example 200 days)
– Define Geometry, Loads, Materials
– C2) Minimum pore Pressure
– Calculation type: Consolidation analysis
– Loading input: Minimum pore pressure
– |P-stop|: 1 kN/m2

Pseudo-static Seismic Analysis
– After Excavation phases, staged construction phases and loading phases
– a Pseudo-static seismic analysis can be carried out. For this type of analysis, in the Input Program General Settings, the Acceleration shall be defined. It is in G units in both X and Y direction. All combinations shall be done (+X +Y; +X -Y; -X +Y; -X -Y).
– Calculation type: Plastic analysis
– Loading input: Total multipliers
– Total multipliers: Define Σ-Mweight = 1 and Σ-Maccel = 1

Factor of Safety Analysis
At the end of three previously described Analysis, a Factor of Safety Analysis can be selected to evaluate the degree of stability of the solutions.
– Calculation type: Phi/c reduction
– Loading input: Incremental multipliers
– Incremental multipliers: Msf = 0.1
– In limit equilibrium analysis, the stability of walls must be analysed in three parts. The first part is the internal stability of the wall, whether the geogrids have adequate pull out and breaking resistance against the acting forces. The second part is related to wall check, whether the wall as a block has the required translational, rotational, and bearing capacity factors of safety. The last part is the global stability.
– Finite element method can only give one safety factor, the weakest one among all those generated by limit equilibrium calculation. Finite element analysis carries out the safety analysis by keeping on reducing the shear strength of the soil, until a chain plastic points (failure points) is formed and failure is triggered. The safety factor is then obtained by dividing the original shear strength parameter by the last shear strength parameter that trigger failure. This generally means the other safety factors shall be larger than the weakest safety.

What type of output can be obtained from the Plaxis analysis results?

Stresses on soil:

Stresses on reinforcing elements:
Stresses on elements shall be checked and compared to the design values. If the design value is reached the element will work in the plastic field. Usually, this option is not wanted, and the elements are preferred working in the elastic field. If the design value is reached, stronger geogrids shall be selected.

Construction settlements:
By adding construction phases, it is possible to evaluate construction settlements whether they are plastic or due to consolidation.

Post-construction settlements due to consolidation:
By Resetting displacements to zero after the construction of the Reinforced Soil Structure, there is the chance to evaluate the post-construction settlements and deformations due to live/traffic loading and consolidation.

Vertical and horizontal deformations:
Deformations and displacements are checked in Serviceability Limit States (SLS). Limiting values shall be given by the Client.

Deformations in reinforcing elements:
This part is needed to verify if the initial assumptions made on the deformation of the reinforcement are respected. By comparing the initial length of the reinforcement with the final one which is deformed, the strain of the element can be computed. In Reinforced Soil Structures, the actual elastic strains of the elements are in the range 0.5 – 1% in normal working conditions.

Potential slip surface:
Potential slip surfaces can be seen by means of the Plastic point history available in Stresses or through the Total displacements option in Deformations since excessive displacements will lead to large deformations and therefore slip surfaces.

Factors of Safety
The factor of safety can be obtained once that the Safety analysis is completed. In the Reached values option of the Phases, the Reached safety factor is displayed. This is the last value computed at the end of the analysis. The values can be even displayed in a Curve having in the X-Axis the displacements of a point and in the Y-Axis the ΣMsf Multiplier.

Which common mistakes should be avoided in designing fem solutions in Plaxis?

Plane Strain Vs Axisymmetry Model:
In case of plain strain modelling, the model in the next figure results in a long out of plane MSE wall construction. On the other hand, if axysimmetry model with rotation axis on the left-hand side is adopted, it results in a circular Island shape MSE wall.

The plane strain model means the strains can only take place in the xy plane. Along the longitudinal axis (out of plane direction) the strain is assumed to be zero, εz = 0. Consequently, the length of the MSE wall must be significantly larger than its width.

The axisymmetric model means the lateral, or more precisely, the radial strains of the model are equal in all direction, εx = εz. As the name implies the structures in the model is symmetrical along the vertical y axis and the model is rotated at the y axis, hence the model in the following figure results in a circular island shape MSE wall.

Note: in Plaxis the rotating axis is always at the left boundary.

Failure in choosing the right model of plane strain or axysimmetry will lead to incorrect output

Conclusion: Remember selecting Plane Strain model for our applications

Facing Element Modelling:
Modelling the facing with plate elements, the analysis will result in bending moment induced in the facing element as shown in the following figure. This type of modelling is developed in case of concrete facing panels and shotcrete facing.

Modelling the facing with soil cluster with the actual dimensions of the facing unit shall be done in the case of Gabion walls or Terramesh System. If water can drain through the facing element, the drainage type is chosen as drained. If water cannot penetrate through the facing element, the drainage type is chosen as non-porous. When the facing units can slip or move one another then ‘interface elements’ should be added in between units.

Conclusion:
For concrete facing elements, plate elements shall be used (MacRes and MacWall).
For all other cases, the facing shall be modelled as Soil cluster.

Initial Stress and Gravity Loading
Often the initial water pressure and the initial effective stresses of the original ground are generated through the so called K0 procedure. The K0 procedure calculates the stresses within the soil body by the following simple equation:

where σh=’ is the horizontal earth pressure at rest, K0 is the coefficient of earth pressure at rest, σv=’ is the effective vertical overburden pressure. This procedure is correct only when all the geometry of the ground surface, the ground layers, and the ground water table are horizontal.
Where the ground surface, the subsoil layer, or the ground water level is not horizontal, the Zm procedure will lead to the existence of unbalanced forces or non-equilibrium of initial forces within the soil body, which are obviously not correct. In such cases, to maintain equilibrium, there should be shear stresses developed within the soil body.
Therefore, the K0 procedure should not be used, instead a gravity loading procedure, where the shear stresses are calculated should be chosen.
The option of gravity loading and K0 procedure in the initial phase is available in Plaxis 2D version 2011 and above. For Plaxis 2D version 9 and below, the gravity loading stage needs to be done by skipping the K0 procedure. This way no initial stresses within the soil body is developed. The initial stresses of the soil body are then calculated in the calculation module of the program by selecting the first phase as plastic ‘Calculation type’, and if any of the soil layer is modelled as undrained, the ‘Ignore undrained behaviour’ option in the ‘Parameter’ tab must be selected (this is since initially, when no external load and no geometry changes is made, the soil is in a drained condition). In the ‘Loading input’ section, the ‘Total multiplier’ option is selected, and in the ‘Multiplier’ tab, key in Σ-Mweight = 1. Then the next actual construction stages are modelled.

Conclusion: Perform Gravity loading procedure for our applications if the geometry is not horizontal

How can I import data sets in Plaxis?

Steps to import reinforcements, anchor bars and HR-plates, default embankment soils, TMS, GTM and Mineral GTM facing elements and Design Approaches are presented.
• The Geogrids material set has DT products, Paraproducts, Rockfall netting products as introduced in the Technical guideline of Maccaferri solutions with FEM. The reinforcements have been modelled as Elastoplastic elements with Short/Long Term properties in case of Gravel or Sand fills.
• Anchor bars have been implemented as Elastoplastic Embedded beam rows.
• Stone fill for TMS and Mineral GTM and default soil fills have been implemented with the hardening soil model (GW – Well graded gravel, GP – Poorly graded gravel, GM – Silty gravel with trace of fines, GC – Clayey gravel, G-G – Gravel with trace of fines).
• Facing elements and HR-Plates have been implemented as Elastoplastic Plates.
• Design Approaches for EC7, NTC 18 and BS 8006 have been introduced.

To import a material data set in Plaxis:
• Click on the Show materials button
• Click on the Show global button

For reinforcements:
• Select Geogrids in the Set type command to import the reinforcement data set
• Click on the Select button at the right bottom
• The file to be selected is: GeogridMat.matdb
• Click on the chosen materials and click on the left arrow to import

For Anchor bars:
• Select Embedded beam rows in the Set type command to import the reinforcement data set
• Click on the Select button at the right bottom
• The file to be selected is: EmbeddedBeam2DMat.matdb
• Click on the chosen materials and click on the left arrow to import

For default embankment soil types:
• Select Soil and interfaces in the Set type command to import the default soil data set
• Click on the Select button at the right bottom
• The file to be selected is: SoilMat.matdb
• Click on the chosen materials and click on the left arrow to import

For Green Terramesh, Mineral GTM facing and HR-Plates:
• Select Plates in the Set type command to import the facing plate elemens data set
• Click on the Select button at the right bottom
• The file to be selected is: PlateMat2D.matdb
• Click on the chosen materials and click on the left arrow to import

To import a Design Approach:
• Click on Soil at the Top of the window
• Click on the Design approaches button
• Click on Import/Export
• Click on the Select button at the right bottom
• The file to be selected is: GlobalDesignApproaches.dat
• Click on the chosen Global design approaches and click on the left arrow to import
• For further information on the Design Approaches read the Plaxis Reference Manuals (par. 5.8.1)

FAQ Plaxis FEM

Below you can find answers to frequently asked questions about Plaxis FEM

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