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In the final analysis

Finite element analysis is helping geotechnical design to move away from empirical approaches, but experts warn that geotechnical knowledge is still essential no matter how powerful software becomes. Claire Symes reports.


Finite element analysis (FEA) is nothing new, but software development and improved soil models are helping to improve the design capabilities of the latest software packages. Application of the analysis is common in Asia and use of the technique is becoming more accepted in the UK.

While this may sound as though geotechnics is firmly moving into the computer age, many advocates of FEA are warning that numerical analysis must be carried out by engineers with sound geotechnical knowledge and an appreciation for the complex mathematics involved.

“Numerical modelling has brought the biggest change to geotechnical design in the last 25 years and there has been a rapid increase in its use,” says Mott MacDonald project director Tony O’Brien. “There are lots of different software packages with various stress/strain models available now, but examples of misuse are common and I wonder how many senior engineers are confident in checking FEA.”

This view is echoed by Buro Happold technical director Peter Scott: “Some large consultants have specialist numerical analysis groups but do they have enough geotechnical knowledge? Geotechnical knowledge is holistic and cannot be compartmentalised - modellers need to have a wideranging understanding of the topic for FEA to work effectively.”

Empirical design

While the development of FEA is taking design away from empiricism, Scott believes that understanding empirical design is still important for young engineers. “Young engineers must continue to be trained in empirical methods or FEA just becomes a black box,” he says. “Empiricism is important to help ensure that results from FEA are in the right ball park and plan for potential issues to avoid uncertainty.”

“Geotechnical knowledge is holistic and cannot be compartmentalised - modellers need to have a wide-ranging understanding of the topic for FEA to work effectively.”

Peter Scott, Buro Happold

FEA development for geotechnics started in the 1960s principally in the UK at Swansea University with Professor Olgierd Zienkiewicz. Although he published his first paper on numerical approximation to the stress analysis of dams in 1947, this was more focused on rock mechanics. One of his PhD students, David Naylor, was the first to apply FEA to geotechnics and develop mathematical models of soil behaviour.

The technique gradually evolved from basic models to more complicated models that considered more than elasticity and accounted for strength and the states the soil passes through from elastic to failure.

“It has taken a lot longer than I imagined for FEA to become accepted,” says Arup director Brian Simpson. “I thought within 10 years of the concept being introduced we would all be using it.

“The main hold up has been developing valid mathematical models of soil behaviour and use of the wrong models has damaged the reputation of FEA. Gaining the right parameters is key.”

More complicated soil models were developed as computer processing power and understanding of soil behaviour increased. “There was a lot of work behind the scenes to back analyse projects to feed information into FEA design,” says Simpson. “Collaboration was the key to development.”

In the 1970s Arup was one a of a few companies to start using FEA on projects and the first to really benefit from it was the Dubai Dry Dock scheme. In the UK the technique was used on the design of the British Library.

“Back analysis of the new Westminster Palace car park was also carried out by FEA,” says Simpson. “But the linear elastic models just didn’t fit with the reality on site where the ground was stiff when the strains were small but lost stiffness as the strains increased, so we developed new models to better fit this relationship and the first project to use this was the British Library.”

Nicholl Highway collapse exposes FEA limitations

Nicoll Highway mesh

Post-collapse analysis using FEA enabled investigators to gain a clear view of how the accident happened

One of the highest profile examples of the limitations of FEA and the potential for back analysis came with the collapse of the Nicoll Highway in Singapore in April 2004. Construction of a new deep station box and a launch shaft for the development of a new subway line caused the highway to collapse as the excavation itself collapsed with the loss of four lives.

Back analysis of the project using 2D and 3D FEA enabled investigators to find the shortcomings in the initial FEA design, as well as look at the combination of factors that led to the collapse. “There were about nine different problems with the design and construction methods on site,” explains Simpson, who was part of the team investigating the collapse on behalf of the contractor’s insurer. “If all of them had not co-existed then maybe the collapse wouldn’t have happened, but it was the combination of issues that caused the failure, not any one thing.”

The diaphragm walls for the station box and shaft were being installed through deep marine clays that were underlain by other clays with a harder alluvium at 30m below ground. The diaphragm walls were supported by two jet grout levels - one close to the base of the wall that would remain in place and another slightly higher up that was to be removed as excavation and installation of the steel struts progressed. The collapse happened as the upper jet grout level was removed.

“The excavation was modelled using Plaxis with a simple linear elastic model for clay with Mohr-Coulomb limits,” says Simpson. “But the model did not consider dilation and overestimated the undrained strength by around 40%. There was also some confusion over Plaxis guidance - which has now been revised - to use effective parameters, which was misleading for this situation.

“These problems emphasise why it is necessary to have geotechnical knowledge as well as knowledge of FEA.”

Back analysis of the collapse found that the geology of the south wall was different from the north wall and movement was noted in the south wall during the excavation. Remodelling of the design failed to take this into account and focused on using different soil parameters.

“Jet grout crushes at 0.5% to 1% strain and average strain before collapse was 2% before failure,” says Simpson. “This highlights that although strength and stress need to be considered, strain is important too.”

There were also issues on site with the construction programme differing from that planned by the FEA design. “The design planned for not more than four bays to be open without the struts being installed but eight were open at the time of the collapse,” says Simpson. “Using FEA we could model that with eight bays open, the collapse started at the third strut from the edge. But there were also some steelwork issues that contributed to this part of the failure - some of the splays on the strut pairs were missing and these took 30% of the load and led to the connection being overloaded. FEA proved useful in back analysing this failure.

“There are a number of lessons to be learnt from the Nicoll Highway collapse. The main one is that FEA is useless if the soil model used is not appropriate to the ground conditions. The model must also be updated as knowledge about the actual geology becomes known. The collapse also highlighted the importance of strains as well as stresses.”

Some of the back analysis was carried out using 3D systems which helped to highlight issues that the original 2D analysis made more difficult to see.

Improved design

Simpson continues: “With the British Library scheme we were concerned that because the excavation was deeper and bigger in volume than previously undertaken in London there were implications that could arise from extrapolating. FEA predicted a more damaging scenario for surrounding buildings than empirical knowledge would have suggested, particularly for the Underground. It allowed the design to be improved.”

In the 1980s much of the research into FEA was led by academia and led to Imperial’s development of the ICFEP model.

Scott says: “The other issue with acceptance of FEA was that it wasn’t showing any resemblance to reality and some people lost confidence, but in the 1980s there was a realisation that research did not reflect the measurements in the field. This emphasised how critical it was to have good quality site investigation data to give the right parameters for a real prediction.

“The more sophisticated the model, the better the data needs to be, but this calls for up front investment in testing. Clients want better predictions but it does cost.”

Simpson introduced another new model - the brick model - during his 1993 Rankine Lecture which considered the gradual change in soil behaviour. He compared it to pulling a series of bricks connected by different lengths of string along the ground and how the loadings would gradually change to explain the multiple kinematic hardening yield surfaces in strain space. This model has been used ever since by Arup.

Scott adds: “FEA was very much an academic tool, rather than commercial software, and this has slowed development as there hasn’t been enough money to fund development. Commercial interest has been low as the geotechnics market is relatively small. Plaxis is the most widely used commercial system and that came out of Delft University in the Netherlands. It was given industry backing that added impetus to the development.

“Plaxis has helped people gain confidence in FEA but there is a real risk that the technique could regain its bad press if the geotechnics industry is not careful. We need to focus on simple approaches to get meaningful outputs.”

Simpson says: “In the early days we had to develop our own programs, and to do that we had to fully understand the model. But now the FEA software is more available, engineers do not have to do the programming themselves so there is a risk they don’t understand what they are doing, then the software just becomes a black box and errors happen as engineers cannot evaluate if the results are credible.”

The latest versions of FEA software are making three dimensional analysis more achievable.

“I spent a lot of time using 2D analysis for 3D problems,” says Simpson. “2D is still very valid for a lot of situations and is quicker to carry out but in more complex designs, 3D increases the understanding.”

The concept for 3D FEA existed in the 1960s, but what limited its application was computing power. Software for 3D analysis only really started to be developed 10 years ago. Arup added a geotechnical element to Dyna to carry out analysis and Plaxis has added 3D to its geotechnical software, but Simpson warns that 3D analysis requires another level of expertise, and understanding the output is more difficult.

“The issue is the visualisation - maybe in the future we will have fly-through simulations but locating yourself within the model will always be a problem. We use colour and arrows to demonstrate stresses and strains now but could we use colour, sound, temperature or vibration for different levels of effective stress or pore pressure with improved visualisation techniques?”

Nonetheless, Simpson believes a lot of work is still needed to develop the mathematical models that represent soil mechanics, and the industry needs people that are skilled in geotechnics and maths to take it forward. “There is still a lot of work to be done on the influence of time but further development in permeability will be key as many of the permeability calculations currently used are still very simple.”

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