Geotechnical Analysis. A decision-making process and soil-structure interaction project. COGAN.
Setting up a geotechnical numerical model and adding Structural elements in geotechnical numerical model. A learning experience from COGAN, a Leonardo da Vinci European Transfer of Innovation project. Improving competency in geotechnical numerical analysis.
Inspired by COGAN EU. Competency in Geotechnical Analysis
Our personal, individual attitudes toward engineering and toward society have potential impact on our country’s future. However small that impact, each of us should try to make it for good. — Dr. Peck.
Section 1 / setting up a geotechnical numerical model, from planning the analysis to reporting the results at the end.
Section 2 / modeling structural elements, including the different element types and modeling concrete and steel materials. Deriving input parameters and interpreting output for structural elements in plane strain and axisymmetric models.
Accompanied by Dr. Peck’s Quotes from Peck.geoengineer.org
Section 1 / Setting Up a Geotechnical Numerical Model
1. ANALYSIS PLANNING
1 Is Numerical Analysis (NA) needed?
t vs $ needs to be JUSTIFIED
Potential for greater ECONOMY in overall design
Complex ground behavior, soil-structure interaction, time effects, observational approaches in the DESIGN
2 Aims of the NA
VERY important for analysis planning
DOCUMENT/AGREE the aims
3 Information gathering
HISTORICAL information
EXISTING structures and infrastructure (design team, methods, anticipated program)
4 Site investigation planning > NAFEMS
Site characterization and ground model > GROUNDMODELS
Parameters testing / in-situ or/and laboratory
Interpretarion
5 Selection of software
The most suitable
Know its strengths and weakness
Verify it works
6 Interface with design process / VITAL for work during and after the design
Outputs to meet needs of follow-on designers
who would use the results, what the engineers need, methods should be clearly explained
Assumptions and methods clearly explained
why the technical,economical, environmental and social issues
Implications of your outputs and recommendations
Regular communication
Keep updated on design changes
Monitoring requirements
Will the analysis produce appropriate outputs
2. GEOMETRY SIMPLIFICATION
Simplifying the outside world around your area of interest, simplifying the geometry of the particular structure you are analyzing and also simplifying construction sequences.
As always, when you interpret the outputs, remember the assumptions you have made in the analysis and consider how these may have affected the outputs and how the outputs should be interpreted.
3. PLAIN STRAIN AND AXISYMMETRIC ASSUMPTIONS
Project example: basement excavation in layered strata
- excavation is supported by the basement walls
- Some of the walls are supported with inclined struts
- complex geometry with non-orthogonal corners and a step in the basement floor
- point loads inside the basement and some line loads outside
- bearing piles
- ground anchor supporting a basement wall along one side of the basement
A 3D model of the real project would take many resources to set-up (time, computational power, learning curve) and then analyze all that geometry. Instead, you could analyze one or more 2D plane strain sections of that basement and still obtain all the outputs we need with sufficient accuracy.
There’s nothing wrong in principle with analyzing a 2D plane strain model to represent a 3D problem. It does provide sufficiently accurate outputs in many situations.
Plane strain means that all strains are in the plane of the analysis — there is no strain in any direction away from the plane.
The best way to visualize that is to extrude the plane strain model perpendicular to the plane.
RECOMENDATIONS
- Contiguos piled wall > having a uniform section is probably a reasonable approximation even for a contiguous piled wall because the piles are very close together.
- Bearing Piles > they can be simulated just like the basement walls. Instead of discrete piles spaced put with soil between, they could be simulated as a regular basement wall.
- Inclined Struts > instead of having a spacing between them, they are actually providing continuos support to the basement wall.
- Ground Anchors > this is more difficult to simulate the anchor/soil interaction. And the ground strata. they are all assumed to be horizontal in the direction perpendicular to the analysis plane.
- Loads > a point load in plain strain is a line load perpendicular to the analysis plane. A line load outside the excavation is actually simulated as an area load.
Of course, there is the need to be careful with input parameters and interpreting outputs for those pile/struts/anchor elements and loads to take those simplifications into account.
Compare a simplified plane strain model with the original 3D representation.
What is important is to understand and visualize the geometric assumptions and remember them when selecting the input parameter and interpreting the outputs. The input parameter can vary for soil and rock cases.
What is around the project and geometrical assumption
- There is a shaft excavation which, die to its circular shape on plane, possesses axis-symmetry
- 3Dimensional view of the ground
- the embedded retaining wall that will support the shaft excavation
- A pair of struts near the top to support the walls and another pair near the base of the excavation
- The form the shaft, the excavation will follow the Top/Bottom procedure
- There is a footing foundation with an applied load near the shaft, and it would be required to analyze/predict the effect of that foundation on the shaft walls
2D AXISYMMETRIC ANALYSIS
- A section from the axis symmetry down the centre of the shaft out through the footing will be taken
- There is a section with the shaft wall, struts, footing and its point load
image
What are the assumptions in the 2D axisymmetric model?
- All strains are in the plane of the analysis and there is no strain in any direction away from the plane
- The conditions (geometry, loads, etc) are all assumed to be the same in the direction perpendicular to the analysis plane, but…
- In the circumferential direction around the vertical axis of symmetry they are not. The retaining wall looks ok, but the struts are now solid discs or slabs rather than the actual linear struts
Comparing the 3D model with the 2D axisymmetric assumption:
- Carefully specify the input parameters fro the struts and interpreting the ioutputs
- As far as the footing is concerned, a 3D analysis would be more accurate in this case
- Compare the analysis results using a 2D software, with and without the ring footing.
- Use the engineer/experts judgement to asses the real effect on the wall
4. LOCATING BOUNDARIES
Guidance on where to locate the boundaries in the analysis model.
How far from the place of interest should they be placed?
If they are too close the boundary effects may start to affect the results. If they are too far they will become unncessarily large and lead to long analysis times.
example > loaded spread foundation
- A load is applied
- Changes of stress and strain are predicted by the model. The bulb lines, represent the approximate spatial extent of different levels of stress and strain changes in the model
- Vertical and horizontal boundaries are placed so far away from the area of interest that no significant deflection would be expected to occur there.
- The boundaries are located about 3 times the size of the loaded area away from the area of interest (general rule of thumb for a first guess)
Be careful with the boundary effects, if the boundary is too close (horizontally and vertically) can affect the results.
The case of a hard bed rock. The only occasion where a shallow boundary should be use, is where a very stiff and strong layer compared with the stiffness and strength of the ground are of interest existed in reality at this level. This is the case of a hard bed rock or dense granular soil underlying a softer soil layer, since the strains in this material would be insignificat compared to the strains in the are of interest, and if the rock base is extended and not a localized feature.
Test whether the boundaries of a selected model are in a suitable location. Plot the output that are critical to the analysis and that boundary effects does alter the results.
Plot the output of the model, to analyze boundary effects. Make a sensitivity analysis.
Eliminate boundary effects but still to have an economical model in terms of analysis times.
5. FIXITIES AND AXES OF SYMMETRY
All models need some kind of fixity in space for the model to be in equilibrium under its self weight and under applied loads and displacements to the model.
Remember 2D fixity to 2D model and a 3D fixity for a 3D model.
Standard fixative for 2D plain strain and axis symmetric analysis, as well as 3D analysis where the horizontal displacement is fixed in both horizontal axis direction
Vertical boundary > impose a zero horizontal displacement to represent the restraint from the adjacent ground that is excluded from the model. Allow vertical displacement, this is essential because the ground must be allowed to apply its own self weight without any vertical support of the sides in order to generate realistic stresses within the ground.
Example > excavation with horizontal ground strata, supported by embedded walls and straps near the top spanning between the walls, an arbitrary basement slab and some applied loads. Clearly there is an axis of symmetry in the middle of the excavation, so the section looks the same on each side.
The workload can be reduced by setting up and running the analysis only in one side of the axis of symmetry of the model, without any significant change in the outputs.
The displacement fixity are the same for the horizontal, but in the vertical a displacement must be allowed. On a plane of symmetry in a 3D analysis, it need a fix for the displacement in the horizontal direction perpendicular to the plain of symmetry.
Having structures intersect a model boundary away from the area of interest is unusual, but having structures intersecting an axis of symmetry is more common.
An additional displacement fixity to be considered if we are simulation bending up the slab structure, then a rotational fixity must be imposed at the axis of symmetry to simulate the equal and opposite moment reaction from the structure on the other side of axis of symmetry. Without that, a freedom of rotation in the axis of symmetry would be representing an actual hinge. So, for the basement floor slab there we need to impose a rotational restraint.
But since the structure is simulating an axial load only and not bending, there is no need to impose a rotational spring spring there, just the horizontal displacement of the city.
Finally, there is the complete set of boundary displacement fixatives for a numerical model. It does not actually change when we have an axis of symmetry.
6. ELEMENTS AND MESHING
Common mesh generation elements in the FEM and FDM (finite element and finite difference method) the geometry is divided up into a number of elements forming a mesh group.
- Vertex node to each element with a linear variation of displacement across the element
- Mid-sided nodes allow curved edges to the elements
- Higher order elements have been introduced with multiple nodes and more precise quadratic variation of displacement across the elements. Requires more power! but with the actual CPU and GPU available, we can now use this.
Typical 3D elements
1D elements and also for shell elements within 3D models, the number of nodes along their length must match the number of nodes along the sides of the elements to which they are connected to, so that no nodes are left disconnected.
Study of soil-structure interaction.
Interface elements
Due to the big difference in stiffness between structural materials and soil, there is often relative movement between soils and structures which in turn affects the stress rate state in the soil. In order to allow relative movement, an interface element is required between the soil and structure. The nodes on each of the interface element are coincident because the structure and soil are in contact.
- The interface element usually has zero tensile strength allowing the interface element to extend, and the soil and structure to separate. It is important to check how the program handles cases where there is the case the soil and structure may re-establish contact.
- Friction criterion defining when there is shear deformation across the element and sliding between the soil and the structure.
It is often difficult to obtain the parameters needed for the interface elements, particularly the stiffness parameters. It is worthwhile performing a parametric study and then make a judgement about installing interface elements to check that everything works due to the additional complexity introduced by including interface elements.
When generating a mesh of elements keep a balance between: low number of elements to reduce analysis times / sufficient small elements to provide precise outputs
A compromise is achieved by grading the mesh so that the element size changes in different areas of the model.
Mesh grading
When large stress and strain changes very rapidly over a short distance, this is where the smallest elements are required because of the high gradients of stress and strain. To have the most efficient mesh, run the analysis twice with slightly different meshes until a change is noticed.
Aspect ratios & distorsion
Inspect the created mesh for any excessively distorted elements.
- GOOD: proportioned elements with aspect ratios close to 1 (ratio between longest/shorter dimension in the element)
- BAD: High aspect ratios or twisted so that element sides cross over each other. AVOID / 2D analyses are particularly sensitive to excessive aspect ratios.
RECAP
L1 Annalysis planning
When to perform a Geotechnical Numerical Analysis is very important. Usually when there is the need for cheap and quicker solution or review, the GNA should be avoided, since numerical analysis usally takes longer and is so more expensive than conventional methods.
L2 Geometry simplification
When setting up a GNA model, the aims of the analysis should be defined. This should be done first since all the other decisions are made to meet these aims.
For every project, there is still the need to obtain historical information about the site when a new construction is going to be simulated with FEM.
We can be sure that a simplification to the analysis model geometry has not significantly affected the outputs by running the analysis with and without the simplification and heck if the outputs have changed.
L3 Plane strain and axisymmetric assumptions
- A pile raft can only be modelled realistically in 3D.
- Only single piles can be modelled in axisymmetry.
- Only xxxx can be modelled in plain strain.
L4 Locating boundaries
The best location for the vertical boundaries of a model can be found by locating the shortest distance from the area of interest where there are no boundary effects on the requiered output.
L5 Fixities and axes of symmetry
When modelling a beam that is interseced by a model bondary, the following displacement fixities should be taking into account. Rotational in all directions and horizontal displacement (perpendicular to the plane boudnary)
L6 Elements and meshing
Usual features on interface (slip) elements:
- they allow transfer of compressive stress across the element.
- they allow separation between materials under the tensile stress.
- they allow sliding between materials according to a friction criterion.
The smalles elements requiered in a mesh are where the highest gradients of stress and strain can occur. For accurate results, the smallest slements are needed where the stress and strain changes rapidly over short discantes.
How to know when the whether the mesh is influencig outputs? Checking the outputs with two similar meshes to compare if there is a difference.
7. Constitutive Model Selection
Previously
- Establishing the Ground model. This charaterises the ground into a number of zones or layers.
- Documenting the aims of the analysis model
- The ground model has to be combined with the aims of the analysis to consider which aspects to the ground behaviour are goind to be the of the most influence on the required outputs.
This is called prioritising the aspects of ground behaviour bacause no constitutive model can recreate every aspect of ground behaviour.
Recommended steps
- Identify the critical aspects of behaviour and then
- Plan the parameter testing to measure this behaviour and
- Choose a constitutive model that recreates the critical behaviours accurately.
For example, if strentgth anisotropy is considered a priority aspect of a ground behaviour, a parameter testing would be needed to measure anisotropic strength and choose a constitutive model that includes anisotropic strength.
Critical aspects of ground behaviour are different for each structure type. It depends on many factors.
- Structure type
- Loading
- Construction methods
- Ground conditions
Always refer to case studies of simmilar numerical analyses in similar conditions to compare certain parameters that other engineers have found critical.
Constitutive models:
- Provides the stress-streain relationship
- First order/basic models: Linear elastic models (tipically used for structure materials in geotechnical analysis) and linear elastic perfectly models (usually with a Mohr-Coulomb failure criterion for geo-materials)
- These models will provide acceptable and accurate predictions for some cases.
- In other cases, they will exclude critical aspects of ground behaviour such as stress and strain-dependancy of stifness, anisotropy, creep behaviour, and so on.
- Choose the simplest model that includes these priority aspects.
- Do not intriduce innecessary complexity.
8. Initial Stress
For a geotechnical analysis there is the need to establish in situ stresses at the beginning of every project.
When simulating stress conditions:
- the stress in the ground arising from its self-weight is usually by far the largest stress
- the behaviour of soil and to a certain extend rock (they are fictional materials) is governed by the stresses within the ground
- advanced constitutive models may require other initial parameters in addition to in situ stress, such as stress history
- is very important to get the initial stress right
Example 1 > a genereric ground profile with layers, saturated with groundwater up to the ground surface
- if all the layers happen to have the same density, the profile of vertical stress will be straigth. In layers of different density the profile would have a different slope in each layer . sigma_v =gamma*z
- under hydrostatic conditions, the pore water pressure is also easy to calculate which leads to the vertical effective stress. sigma_v’=sigma_v-u
- the horizontal stress is calculated from the in situ earth pressure coefficient or stress ratio Ko. sigma_h’=Ko*sigma_v’
- Ko is calculated from Jaky’s formula in consolidated conditions N-C Ko=z-sin(phi’)
- in over consolidated conditions, due to this effects of a eroded way ground over a geological time to get to the present day ground level., the horizontal stress can no longer be stimated from Janky’s formula. Ko varies with depth, being particularly high near the ground surface.
There are 2 methods of setting up the initial stress in a numerical model:
FIRST > especify the initial sterss as input to the analysis. one way is to calculate the stress by hand and input those into the program or the software will calculate them automatically based on the levels of the layers, their densities, specified Ko values and groundwater values.
When the program calculates the stresses, they are not being calculated by numerical analysis but being provided by a parallel code which then input the initial stress to the analysis program.
This method is acceptable for horizontal ground layers where the stress are likely to be homogeneous across the domain of the model.
When there is a sloping ground surface this method can still be used but the analysis would be started with a horizontal ground surface and then adding or removing elements in stage by stage case to create the slope effect.
Where ground layers of different density are sloping, the initial stresses will not be homogenous and it would be too hard to specify the initial stresses everywhere manually. This is where the second method comes in handy to stablish the initial stresses.
SECOND > The gavity switch-on method, is called like that because the analysis starts without gravitational acceleration.
In the first stage of the analysis gravity is activated and the self-weight of the ground is activated based on specified density. Then, the initial stresses are calculated by the numerical analysis method. The vertical stress is determined from the especified ground density, but the horizontal stress cannot be calculated from a specified Ko value. In this method the horizontal sterss can be manipulated by the specified Poisson’s ratio fro the ground but it may not be possibleto achieve high values of horizontal stress due to the restrictions on Poisso’s ratio values.
These two methods generally establish the initial stresses in natural and ideal conditions. Constructions or groundwater changes produce stress changes in the soi and this would have to be simulated in order to sestablish the present stress state before continuing to simulate the planned construction activities.
For advanced models which are stress path and stress history dependant, is very important to have into consideration how stress have changed in time and know greoundwater and human-made changes. For example, a stress path reversal may result in different predictions form a case where the stress path continued along the same direction.
9. Construction Methods
Numerical Analysis need to consider the construction methods. Since the methods of construction influences the ground behavior and hence must be incorporated into the analysis.
Compaction: will not normally be attempted since is quite complex.
