Interrelationships between practice, standardisation and innovation in geotechnical earthquake engineering

Abstract

Construction of large civil engineering structures in seismic areas is facing real challenges. Constructions are expected to be safe, sustainable and resilient after the earthquake despite, more than often, harsh environmental conditions and significant uncertainties in the hazard conditions (geotechnical and seismic). In the case of exceptional structures, few, if any, similar structures have been constructed in the same environment, and designers may feel helpless because they cannot rely on past experience, full scale models or standards, which do not cover exceptional structures. This is a typical situation where innovation may make a project feasible. However, innovation, which is to be distinguished from research conducted by academics, must obey certain rules to be effective and accepted by the community. These features are illustrated by few examples of exceptional civil engineering structures in earthquake prone areas; these examples also serve to highlight the interrelationships between practice, standardisation, education and innovation. All these activities, although carried out by different categories of people, benefit from each other to advance the civil engineering profession.

1 Introduction

Any large civil engineering project has the peculiarity of being a prototype. While experience gained from previous works is undoubtedly useful and fundamental, each new project must take into account technical factors, such as the environmental conditions in a broad sense, but also specific non-technical factors which can have a profound impact on the design. The situation is even more critical in seismic areas because very few similar exceptional structures, if any, have actually suffered from significant earthquakes. Facing this situation, the designers may feel powerless because, on the one hand, seismic (building or bridge) codes do not cover their problems and, on the other hand, precedents are unavailable, and research has not yet progressed to a point where its results can be used. However, they must proceed and design a safe structure despite the lack of knowledge and all associated uncertainties. This is clearly the place where innovation can benefit designers. Innovation must not be confused with research: research is a long-term process, often conducted by academics, while innovation comes from an outstanding idea promoted by one person, or more likely a small group, usually drawn from practitioners. Nevertheless, practice, innovation and research do not belong to different worlds, and obviously they are interrelated and benefit from a close understanding and collaboration between the different communities. They have important implications in terms of initial formation of engineers, continuing education, code development, etc.… To be accepted by the scientific community, innovation must obey certain rules: scientific soundness, simplicity to be easily understood, due recognition of uncertainties and collaboration between concerned parties (owner, designer, checker, construction engineers); moreover, innovation should consider constraints related mainly to the available time frame for its development, safety of the built structure and, to a lesser extent, economy.

In this paper, the special nature of large engineering structures and their dependence on regulations are first briefly examined. Then, based on few examples encountered in practice, the paper attempts to highlight these different aspects and try to illustrate the domain of application and interrelationships between standardisation, education, innovation and research.

2 Characteristics of large civil engineering projects

The topic of this paper is dealing with large engineering projects in seismic areas, but some ideas are equally applicable to civil engineering structures in different environments. On the one hand, ordinary projects do not usually require innovative solutions and both cannot afford and do not warrant the related, cost and time, investment; their design usually relies on standards and past experience. On the other hand, each large civil engineering structure is unique, since each site is unique in terms of its geography, its socio-economic and natural environment, and the functions it must fulfil. Some structures may look alike, but they are never identical, and each can be viewed as a prototype. Civil engineering structures are also complex; complexity differs from complication because it involves a lot of uncertainties, particularly for structures that have significant interaction with the ground, like tunnels, dams, bridges: geology, geotechnics, hydrology, etc., contribute to these uncertainties (Cadas 1996). Nevertheless, the complexity is somewhat lesser for the structure itself which makes use of elaborate materials whose characteristics are better known and mastered. The structure is also complex due to the actions to which it may be subjected by natural phenomena like earthquakes. These are random in nature, and although large engineering structures are usually designed for earthquakes with a low annual probability of exceedance, typically of the order of 4 × 10^–4 (return period 2475 years), there is always a possibility that the design actions will be exceeded during the lifetime of the structure. This is hardly understood by the general public or media who expect a zero-risk world for these structures which are of paramount importance for safety and economy. Bridges and tunnels are critical and essential for the development of a country, and no development is possible without the infrastructure that allows circulation of goods, materials, livestock and people. They are also of the utmost importance to provide emergency access during a crisis (lifelines); finally, they are expensive and their downtime for repair may be long. To quote one example, the collapse of the Cypress access viaduct and of a single span of the Bay Bridge during the 1989 Loma Prieta earthquake, a vital link between the east and west shores of the bay, had a severe impact on the economy of the Bay Area in the aftermath of the earthquake (Fig. 1).

Fig. 1

Left: Oakland Bay Bridge—Right: Intestate 880-Cypress viaduct (Earthquake Engineering Research Institute)

These structures are truly elements required for resilient development supported by ecological, social and economic impact assessments. Due to this relatively recent evolution in the way of apprehending development, it is essential that a consensus be established for these projects which have a strong impact on social life and the natural environment.

In view of these factors, more and more is required from our essential infrastructure: we wish to make them safe, of course, but also sustainable and resilient after an earthquake. This is a true challenge because in contrast with other engineering activities, like the car and aviation industries, it impossible to test our “prototype” at full scale and for the imperfectly known environment; whereas crash tests on prototypes are common in the car industry, and aircraft test flights are performed before the airplane is used on a commercial basis. Each “new” structure would require a specific testing program, for example with a model test on a shaking table or in a centrifuge facility, which may be incompatible with the time frame of a project. In addition, scaled model tests are not free from modelling and interpretation difficulties (e.g. Madabhushi 2004). One may argue that with the increasing power of computers and with improvement of sophisticated models, model tests can be superseded by numerical analyses. Without denying the potential usefulness of numerical models, which are more easily amenable to sensitivity studies required for studying the inherent uncertainties, it should be realized that a model is a model, no matter how sophisticated it is, and represents only imperfectly the physical reality. Furthermore, running such nonlinear models (they have to be nonlinear to test the response of the structures to extreme conditions) is time consuming in terms of resourcing and not very efficient at a conceptual design stage. We will argue in the examples that simpler numerical engineering tools might be preferable, at least to start with.

3 Standardisation

A tunnel, a large bridge, a dam are unique, non-replicable works. They go beyond the purely regulatory framework applicable to current constructions and call for "rules of the art", that is to say, good practices, which result from a consensus between the professionals at a given moment and in a given geographical setting. This uniqueness and this complexity explain the value given in civil engineering to scientific education and experience, both design and construction experience. In addition, as developed later in the paper, innovation may be a key parameter in the design of large civil engineering structures. It would therefore be counterproductive for the designer to be constrained by unnecessarily restrictive regulations. Good projects are not the outcome of good regulations, and nothing can replace imagination, experience and skill. Therefore, a good standard should give room for innovation; it is ideally a document that sets the objectives of the construction in terms of performance goals, provides some prescriptive rules based on past experience and observations, and restrict the calculations rules to ordinary constructions or, at least, leaves the door open for alternative justifications. Creativity, which is a landmark of civil engineering, must not be stifled by over-stringent standards because, as shown by one of the following examples, very prescriptive rules may render the project unfeasible. In brief, the field of application of each standard must clearly be stated so that those covering ordinary constructions do not interfere with the design of exceptional structures. Equally, departures from such standards carries it own responsibilities for the designer.

4 Education and training

Capitalizing on experience is essential to ensure the sustainability of knowledge and the safety of structures, but formation and training of engineers are also vital to face our challenges. Civil engineering tasks are very diverse and are practiced in very varied conditions. To be able to develop new concepts, innovative solutions or simply to correctly apply existing concepts, the engineer needs therefore a strong scientific background and cannot, must not, rely on blind applications of recipes. Seismic building codes are evolving, and it is more important to learn the rationale behind a formula than the formula itself. Along the same lines, numerical analyses should be carried out by engineers with a solid background in numerical analysis and appropriate scientific knowledge: nothing is more unsafe than running a software as a black box. Finally, civil engineering is a discipline dominated by technology, but science always precede advances in technology. The way to reach these goals is to form educated engineers and not simply trained engineers, an objective that should be pursued in our educational system (Graham and Sivakumar 2000; Mitchell 1999). To some people this approach may look too theoretical, and not enough practice-oriented, but it is necessary to form engineers who will be able to advance our profession.

Education in civil engineering must therefore develop qualities of adaptability, inventiveness and innovation. To this end it is essential to enhance the physical perception and understanding of the behaviour of structures and make engineers aware of safety issues. Education is also the place to develop a critical sense and eradicate some simplistic ideas such as the fact that modelling would be more relevant the finer it is. We have already pointed out this tendency to rely only on sophisticated numerical analyses; where appropriate, a coarser model, provided it is developed on physical grounds, can prove to be more reliable because it is better controlled and adapted to sensitivity studies. Engineers must be aware that “we know very few things and ignore a lot” (Pierre Simon de Laplace, 1749–1827), and that models are not better than the data used to feed them. They should be conscious that uncertainties govern our projects, as we have previously noted for structures interacting with the ground or subjected to seismic hazard; the time when engineers believed that a single, probably motivated by the limited available resources, sophisticated deterministic analysis can solve their problem is clearly over, and we must realize that “Doubt is an unpleasant mental state but certainty is ridiculous” (Voltaire, 1694–1778).

5 Innovation versus research

Construction of major civil engineering works can take several years which implies that engineers follow only a limited number of projects during their professional lifes. The challenges posed by the construction of new exceptional civil engineering projects in severe environmental conditions (geotechnical, seismic) will inevitably push them to innovate but also to transpose the achievements obtained on previous projects of the same nature by distinguishing analogies and differences. There is no outdated experience in civil engineering due to technical progress; on the contrary, the successes and failures of ancient works should always be a source of inspiration.

Another fact, related to the societal aspect of civil engineering structures, makes innovation essential: the same construction, under strictly the same conditions, can no longer be approached as twenty years ago or more, so strong is the pressure from society, for good or bad reasons. Innovation is needed to meet these new demands without violating the laws of physics or leading to unreasonable expenditures. This also pleads for the solid training of engineers which gives them the strength to resist and argue convincingly.

Noting that civil engineering is a profession in which major breakthroughs are not common (bridge engineers did not go directly from a 400 m long cable-stayed span [e.g. St Nazaire in 1974 to 856 m (Normandy in 1995), or 1104 m (Russky in 2012)], innovation will usually consists in small, but significant, improvements over a previous situation. Therefore, it needs to satisfy some requirements to be accepted by the engineering community:

• Simplicity should guide the process in order to be understood by non-experts: “if you cannot explain something simply, it is because you do not understand it” (Richard Feynman, 1918–1988).

• Scientific knowledge and soundness should be the driving force.

• Validation is a key aspect; a new concept might be appealing but is of small value until it has been justified, in order of preference, by past experience (unfortunately very seldom), by physical tests and/or refined numerical analyses.

• Due consideration by the designer of construction issues and constraints because innovation is not restricted to design; significant cost savings can be generated by well-thought-out construction methods.

To fulfil this last aspect it is essential that the design team and the construction company work in close cooperation, a very common situation in France.

At this stage it is important to make the distinction between research and innovation:

• Both activities are not usually carried on by the same communities: research is mainly conducted by academics while innovation is very often the product of practicing engineers.

• Research is driven by improvement of scientific knowledge and innovation by the need to produce a specific object within a limited time frame and not necessarily with all the theoretical justifications for the truth. This aspect is clearly contained in Louis Pasteur’s address (1822–1895) to engineers: "Often engineers are bound to solve problems although on those specific issues science is not achieved. Gentlemen, you must find practical solutions, even facing uncompleted science".

• Research and innovation do not work at the same time scale: research may last for several years while innovation must answer a specific immediate problem.

• Research may require heavy resources and funding is usually provided by public agencies with no short-term return on investment. Innovation is funded by the actors of the project with an immediate objective of profitability.

These differences do not imply that both communities (academics and practitioners) should ignore each other; on the contrary, they are complementary: innovation can be guided by the products of research, and research can be inspired by an innovation, whose grounds are not fully scientifically established; in that respect, collaboration between academics and practitioners is essential during the development of a new concept to avoid big mistakes: engineering judgment may be misleading if not supported by more fundamental science, especially when working under time pressure. Finally, academics are the natural vectors for the development of an innovation. This may seem like wishful thinking as the two communities speak different languages; practitioners should accept theoretical concepts and invest in their understanding, hence the need of having educated engineers; academics should put themselves within the reach of practitioners and use a language that can be easily understood: “What we conceive well is clearly stated and the words to say it come easily” (Nicolas Boileau, 1636–1711). It is only at this price, with efforts from both sides, that civil engineering will remain a highly technological discipline and be attractive to young engineers who very often view it as an outdated, old-fashioned, activity.

To conclude on these activities, it is worth noting that research, or innovation, in civil engineering is not completely aligned with research in other disciplines.

For the Horizon 2020 research programme, the European Commission used the Technology Readiness Level (TRL) scale, originally developed for the aeronautic industry (EU 2014, ISO 2013), which is depicted in Fig. 2. From what has been said previously, it is readily apparent that research for civil engineering constructions in earthquake prone areas stops at level TRL4, possibly TRL5 if the construction happens to be shaken by an earthquake (see example in Sect. 6.1 below).

Fig. 2

Technology readiness level (TRL)

Another difference with other disciplines stems from “blue skies research”. Blue skies research has been defined as research without a clear goal and curiosity-driven science, or scientific research in domains where real-world applications are not immediately apparent (Wikipedia). Proponents of this mode of science argue that unanticipated scientific breakthroughs are sometimes more valuable than the outcomes of agenda-driven research, leading to unforeseen benefits of research that was originally seen as purely theoretical in scope. However, because of the inherently uncertain outcome and return on investment, blue-sky projects are commercially unpopular and are superseded by research perceived as being more reliably profitable or practical for civil engineering applications.

The ideas developed in the previous sections find a direct illustration in three projects in which the writer has been involved. These projects although, for some of them, having already been described in other publications, are used with a special focus on the process of innovation they were creating.

6 The Rion-Antirion bridge

Only the aspects of the design of the Rion-Antirion bridge that serves the demonstration of the topic of this paper are detailed in the following. For a complete description, the reader may refer to Pecker (2004, 2006), Combault et al. (2000, 2005).

The Rion-Antirion bridge project is a BOT (Built-Operate-Transfer) contract granted by the Greek Government to a consortium led by the French company Vinci Construction in association with seven Greek companies. The bridge is located in Greece, near Patras; it provides a fixed link between the Peloponnese and the Continent across the western end of the Gulf of Corinth (Fig. 3) and represents a critical infrastructure for the communications between both regions of Greece. The solution adopted for this bridge is a multiple span, cable stayed bridge with four main piers; the three central spans are 560 m long each and are extended by two adjacent spans (one on each side) 286 m long.

Fig. 3

Rion–Antirion bridge

The total length of the bridge, with the approach viaducts, is approximately 2.2 kms. The call for tender was launched in 1992, the contract took effect in December 1997; construction started in 1998 and completed in summer 2004; and the bridge was opened to traffic on the 11th of August 2004, five months ahead of schedule.

6.1 Environmental conditions

The environmental conditions faced by this project may figure amongst the worst ones that can be imagined in terms of geological siting, geotechnical parameters and seismic hazard.

The site has been subjected to extensive offshore soil investigations (Pecker 2004). The water depth in the middle of the strait reaches 65 m. The soil profile consists of weak alluvial strata deposited in alternate layers/lenses, with individual thickness of a few meters, of silty sands, sandy clays and medium plasticity clays with a marked spatial variability which may affect the differential settlements between the piers. No bedrock was encountered during the investigations, and based on geological studies and geophysical surveys its depth is believed to be greater than 600 m (Fig. 4). The mechanical characteristics of the offshore layers are rather poor with undrained shear strengths of the cohesive strata increasing slowly with depth from approximately from 30 to 50kN/m² at the seabed level to 100-150kN/m² at 50 m depth (Fig. 4). The shear wave velocities are also small, increasing from 100 to 150 m/s at the ground surface to 350–400 m/s at 100 m depth.

Fig. 4

Soil profile

Two scenarii were considered for the design seismic hazard of the bridge: possible occurrence of a major earthquake in the vicinity of the bridge and long-term tectonic movements. The design motion with a return period of 2,000 years is dominated by a 7.0 surface wave magnitude earthquake originating on the Psathopyrgos fault only 8.5 km east of the site. With recognition of the influence of the soil characteristics on the ground surface motion, the horizontal design response spectrum at the seabed elevation has a 5% damped response spectrum anchored at a peak ground acceleration of 0.48 g, a plateau at 1.2 g extending from 0.2 to 1.1 s and a spectral acceleration of 0.66 g at 2 s (Fig. 5).

Fig. 5

Horizontal response spectrum at sea bed level (damping 5%)

The tectonic movements take their origin in the prehistoric drift in the earth's crust that shifted the Peloponnese away from mainland Greece. The peninsula continues to move away from the mainland by a few millimetres each year. As a result, the bridge must accommodate a 2 m differential tectonic displacement in any direction and between any two piers.

6.2 Challenges

Very soon during the design stage it appeared that foundations design would be a major issue. The unfavourable geotechnical conditions with no competent layer at shallow depth, the large water depth, typical of depths currently encountered in offshore engineering, and the high seismicity of the environment represented a combination of challenges. It was also identified that the earthquake demand would govern the concept and dimensioning of the foundations. Preliminary attempts to design classical foundations (surface foundation, piles, caissons, etc.) revealed that this objective was out of reach applying usual seismic codes (e.g. Eurocode 8 or AASHTO). Piles were quickly abandoned for several reasons: the amount of reinforcement exceeded the allowable 4% value (design issues), the difficulty of realizing the structural connection between the slab and the piles in deep water (construction constraints), and the rather poor behaviour of floating piles in seismic areas as observed in Mexico City for instance during the 1985 Michoacan earthquake (feedback from observations). Caisson foundations were hazardous due to the presence of a gravel layer at the ground surface, which may create some difficulties during penetration of the caisson (construction constraints). Surface foundations were clearly impossible in view of the poor foundation bearing capacity and of the high anticipated settlements (design issues). The situation was clearly one of those identified in Sect. 1 where innovation was the only way out.

However, recognizing a problem is not solving it, and two factors contributed to the development of a successful solution. First, the contractor anticipating the difficulties decided to launch the design studies one year ahead of the contractual effective date, and this time lapse turned out to be essential to fully investigate alternative foundation solutions, to develop and to validate an innovative concept; this amount of time was worthwhile and resulted in substantial savings for the foundations. Second, a close cooperation within the design team between structural and geotechnical engineers, between the design team and the construction team on the one hand, and between the design team and the design checker, on the other hand, existed from the very beginning to give due consideration to all technical, economical and construction constraints.

6.3 Development of the foundation concept

As for any seismic design, a first important step is the definition of the required performance of the structure. This factor is probably the one that requires the closest cooperation between geotechnical and structural engineers. For the bridge this performance criterion was clearly stated in the technical specifications: for the 2000 year return period earthquake, "the foundation performance under seismic loading is checked on the basis of induced displacements and rotations being acceptable for ensuring reusability of the bridge after the seismic event". In other words, it is accepted that the foundation experiences permanent displacements after a seismic event, provided the induced displacements remain limited and do not impede future use of the bridge. Full advantage of this performance-based design criterion was taken in the development of the foundation concept: sliding of the pier is possible (and tolerated) but rotational mode of failures are prevented (and forbidden). This was translated, after a close interaction between structural and geotechnical engineers, in the following quantitative figures for design: translations can reach values of several tens of centimetres but rotations, given the important height of the pylons (see Fig. 6), must remain limited to values smaller than 0.001 radians. To the best of our knowledge, it was the first time that sliding was tolerated for a large bridge foundation under seismic loading, thereby deviating from the code requirements; if horizontal sliding was not accepted, preliminary studies have shown that design was not feasible, a clear demonstration that standards should not apply to exceptional constructions. However, it is worth noting that, at the same period the bridge foundations were designed, sliding was accepted for offshore structures in the Malampaya field (Offshore Palawan, Philippines) commissioned in 2001.

Fig. 6

Typical bridge tower and foundation reinforcement

It was quickly realized that surface foundation was the only viable alternative from a construction point of view: construction techniques used for offshore gravity base structures are well proven and could easily be implemented for the Rion-Antirion bridge. The problems posed by the poor soil conditions still remained to be solved. In order to alleviate potential damage to the structure due to the adverse environmental conditions and to carry the large earthquake forces brought to the foundation (shear force of the order of 500MN and overturning moment of the order of 18,000MNm for a vertical buoyant pier weight of 750MN), the innovative foundation concept finally adopted consists of a gravity caisson (90 m in diameter at the seabed level) resting on top of the reinforced natural ground. The ground reinforcement (Fig. 6) is composed of steel tubular tubes, named inclusions, 2 m in diameter, 20 mm thick, 25-30 m long, driven on a grid of 7 m × 7 m to 8 m × 8 m below three of the four foundations. The total number of inclusions under each foundation is therefore of the order of 150. In addition, a gravel bed layer, 2.8 m thick, is laid on top of the inclusions just below the foundation raft with no structural connection between the raft and the inclusions heads.

The behaviour of this foundation scheme is clearly different from that of piles and the first question raised by Prof Ralph Peck, member of the checker’s team, was, “where such a scheme has been implemented?”. At that time nowhere, it was obviously a prototype, but the author remembers his unrespectful reply to the question, “if we always look for a precedent, the Eiffel tower would have never been built”.

The answer was obviously not sufficient to satisfy the checkers’ team (P. Taylor, R. Peck, R. Dobry, N. Priestley, M. Calvi and F. Siebel), and robust arguments and justifications had to be developed. These developments exactly followed the steps outlined in Sect. 5 with a gradual approach required for an innovative concept:

• Preliminary design of the concept with simple explanations and scientific grounds. As mentioned previously major breakthroughs are not common in civil engineering, and new solutions are built on existing ones. The starting point was the results established for the seismic bearing capacity of a shallow foundation (Pecker-Salençon 1991, Salençon-Pecker 1995a, 1995b, Paolucci and Pecker 1997) combined with those established for the stability of nailed slopes (de Buhan and Salençon 1993). All these theoretical results are established using the yield design theory (Salençon 1990, 2013) which requires only the strength parameters of the constituents of the system (nails, soil, interface). Additionally, it is easily amenable to parametric studies and requires limited computer demand. The results of the nailed slopes were extended (a) to shallow foundations and (b) to include the contribution of the shear resistance of the inclusions, a feature that nails do not possess (Salençon and Pecker 1999). This approach lends itself to a simple visualisation of the surface of ultimate loads (the foundation bearing capacity, Fig. 7) in the loading space parameters (shear force, vertical force, overturning moment and soil inertia forces). In addition to the clear benefit of the inclusions, shown by the expansion of the ultimate surface from the blue line to the red line (Fig. 7a), this visualisation explains both the capacity design philosophy implemented with this scheme and the simple way to design the inclusions layout. The capacity design philosophy (Paulay 1993) is extended to the foundation (Pecker 1998) with the gravel layer being the yielding element (equivalent to the plastic hinge in structural design) and the soil reinforcement with the inclusions providing the overstrength. The plastic hinge is activated if during the loading sequence the point representing the loading parameters reaches the ultimate surface along the vertical red line of Fig. 7a (point A), the height of which is larger as the inclusions spacing is smaller (Fig. 7b). Since the deck is not connected to the pylon (Sect. 6.4) the pier is very stiff and behaves as a rigid body with a moment M at its base proportional to the shear force V: M = Vh with h being the elevation of the centre of gravity; therefore, during the earthquake the point representing the loads moves more or less along the dashed line of Fig. 7b. The inclusion spacing is then determined by requiring that point A be located on the vertical line.

• Experimental validation with scaled models tested in the centrifuge facility in Institut Gustave Eiffel, formerly Laboratoire Central des Ponts et Chaussées (Garnier and Pecker 1999). Soil was brought from the site to the laboratory, reconsolidated in the bucket and inclusions placed by hand with sand and foundation on top (Fig. 8). The model was centrifuged at 100 g and the specimen loaded cyclically and monotonically up to failure (direct loading with a jack was applied to the foundation because at that time the in-flight shaker was not yet available). Comparisons of the predicted failure loads calculated with the yield design theory and of the measured failure loads were convincing enough to proceed with the design (Fig. 9). Furthermore, the foundation scheme was shown to be capable of dissipating a significant amount of energy under cyclic loading.

• Final design with sophisticated nonlinear finite element models (FEM, Fig. 10) with the software DYNAFLOW (Prevost 1985, 2008). These numerical analyses were intended to confirm the concept and also to provide estimates of the load deformation curves under monotonic loading which are used for the seismic soil-structure interaction (Sect. 6.5).

Fig. 7

Left: Cross section of the surface of ultimate loads for given vertical force and soil inertia force; Right: influence of inclusions spacing

Fig. 8

Left: Centrifuge facility at LCPC—Right: View of the soil model with inclusions

Fig. 9

Left: Comparison of measured failure load in the model with the numerical prediction—Right: View of the inclusions at failure

Fig. 10

Finite element analyses of the foundation. Top: view of FEM at failure; bottom: comparison of the FEM analyses (diamonds) with the failure surface calculated from yield design

In addition, the finite element runs used for the energy analysis confirmed the high potential for energy dissipation of the foundation scheme under cyclic loading: for the smaller loops almost all energy is dissipated in the soil, while for the largest loops about half of the energy is dissipated by horizontal sliding at the raft-soil interface. Damping ratios computed from the corresponding static backbone curves assuming Masing criterion are about one half of those obtained from the loops (Dobry et al. 2003). For horizontal force-displacement, the damping ratio range using Masing was 24–30% compared to 42–59% obtained from the loops. For rocking moment-rotation, the range of damping ratios using Masing was 12–29% compared to 31–44% obtained from the loops. This latter analysis is the outcome of the intense collaboration between the checker’s team (Dobry, Mavroeidis, Zeghal, Gohl, Yang) and the designer (Pecker), a condition that has been indicated as essential in the development of innovative concepts.

6.4 Tectonic movements

In order to accommodate the large differential displacements between piers, induced by a potential fault offset in the middle of the straight, the solution has again been inspired by a previous project, the Vasco da Gama bridge in Lisbon. The deck is fully suspended over its whole length (2.2 km) through the cables without any structural connection to the pylons; in case of differential displacements no force is actually transmitted to the pylons. However, to prevent movements of the deck under small amplitude loading induced by wind, traffic or small earthquakes a strut maintains the deck in place. For large amplitude loading the strut breaks and the deck is set in free vibration with energy dissipation provided by four huge custom-made dampers (capacity 3500kN each, stroke ± 1.75 m, speed 1.25 m/s), which also prevent impacts with the pylons’ legs (Fig. 11).

Fig. 11

View of the struts and dampers from under the deck

6.5 Soil-structure interaction analyses

With the poor soil characteristics and the mass of one pylon it became readily apparent that soil-structure interaction (SSI) cannot be ignored. However, given the continuous length of the deck, the whole structure should be treated in a single model. Several approaches can be contemplated including a global FEM including the four pylons, the deck and the surrounding soil; this approach was clearly out of reach even at the final design stage because several elements in the model exhibit a nonlinear behaviour (soil, cables, foundation interface) and numerous parametric studies were required to cover the uncertainties. Another classical alternative would be to remove the soil model, to replace it with the so-called foundation impedances and to carry out a multistep dynamic analysis (Kausel 2019). One of the main limitations of the multistep approach is the assumption of linearity of the system for the superposition theorem to be valid; some non-linearities, such as those related to the propagation of the seismic waves, can be introduced, but the non-linearities specifically arising from soil-structure interaction are ignored. Those non-linearities may be beneficial and tend to reduce the forces transmitted by the foundation to the soil and therefore decrease the seismic demand (Pecker et al. 2014). In that situation, uncoupling the demand from the capacity is no longer valid: as the foundation yields the forces are modified and further yielding is governed by the new forces. The inconsistency introduced by checking the foundation capacity for the forces derived from an uncoupled analysis was quickly highlighted and led to impossible verifications; again, a code approach was not appropriate and something else has to be developed. Therefore, it was decided to implement a more realistic approach, inspired by Paolucci (1997), which closely reflects the physics of the interaction. Giving up the mathematical rigor, an engineering approximation, in the same spirit as the multistep approach, can be achieved by sub-structuring the supporting medium into two sub-domains (Fig. 12):

• A far-field domain, which extends a sufficient distance from the foundation for the SSI non-linearities to be negligible; non-linearities in that domain are only governed by the propagation of the seismic waves.

• A near-field domain, in the vicinity of the foundation, where all the geometrical and material non-linearities due to SSI are lumped.

Fig. 12

Concept of macro-element

The exact boundary between both domains is not precisely known, but its location is irrelevant for practical purposes. This concept of far-field and near-field domains can be easily implemented if one assumes that the degrees of freedom of the foundation are uncoupled: the far-field domain is modelled with the linear (or equivalent linear) impedance functions whereas the near-field domain is lumped into a non-linear macro-element. A simplified rheological representation of this sub-structuring is shown in Fig. 13: the macro-element is composed of a finite number of springs and Coulomb sliders which are determined from curve fitting to the non-linear force–displacement (or moment-rotation) backbone curve, computed for instance with a static finite element analysis (static pushover curves). Damping in the near-field domain arises only from material damping and obeys Masing's law, which has been shown to be conservative (Dobry et al. 2003); damping in the far-field domain is of the viscous type.

Fig. 13

Simplified rheological model for the macro-element

Again, validation of this new modelling approach is essential and follows the various steps described in Sect. 5: it is based on the results of the centrifuge tests (for damping) and then a comparison of the results of this simplified dynamic rheological model with those obtained from a rigorous dynamic finite element analysis of a single pylon, including all the nonlinearities mentioned previously. Figure 14 compares the overturning moment at the foundation level of the bridge pier foundation computed with both approaches: not only the amplitudes are correctly matched but also the phases are preserved.

Fig. 14

Comparison between finite element analysis and the nonlinear rheological model for the foundation

The simplified model has been subsequently used by the structural design team for all the seismic analyses of the bridge. It allows for the calculations of the cyclic and permanent earthquake displacements. The seismic demand at the foundation level is significantly reduced with a shear force of the order of 500-600MN and an overturning moment of 18,000MNm, which can be accommodated by the reinforced soil foundation.

6.6 Outcome of the project in terms of research

In the previous sections the development of an innovative concept has been described as the result of a progressive approach starting from the observation of the impossibility of satisfying the code design requirements for classical solutions, building up on existing solutions to develop a new idea and finally justification and validation of the new concept. However, it has also been noticed that due to time and budget constraints of the project, fully rigorous and scientific proofs cannot be developed, and that short-cuts have to be taken. This is a typical situation for civil engineers in an innovative approach: they have to make the best possible choice with engineering judgment and the elements at hand (see Pasteur’s address). Nevertheless, this is also a turning point where innovation may be a source of inspiration for more fundamental research. In fact, all the concepts developed previously found a natural development in several publications by researchers and PhD theses:

• Many researchers have recognized and pointed out the beneficial role of nonlinear foundation behaviour either from model tests (for instance Gajan et al. 2005; Shirato et al. 2008; Heron et al. 2012), or from numerical studies (among others Kutter et al. 2003, Anastasopoulos et al. 2010, Pecker and Chatzigogos 2010, Pecker et al. 2014).

• This beneficial effect can be used to protect the foundation and the structure provided the paradigm of no foundation damage under seismic loading is relaxed. For important structures this possibility has now received a wide attention in the engineering community (Deng et al. 2012) and has been popularized by Gazetas (2015). This new procedure of designing foundation, accepting uplift and permanent displacement of foundations has even been introduced in recent standards (ASCE/SEI 41-17 2017, CEN/TC250 2021).

• The reinforced foundation scheme has motivated the development of advanced numerical tools which provide not only the ultimate loads of the system, as the yield design theory does, but also the complete stress–strain behaviour up to failure (Hassen and de Buhan 2004, 2005; Hassen et al. 2007). This tool is based on a multiphase model for the elastoplastic analysis and design of soil structures reinforced by stiff linear inclusions, where shear and bending effects are taken into account. A FEM-based numerical tool, incorporating a plasticity algorithm adapted to this multiphase model, has been developed with emphasis on the crucial role played by the shear and flexural behaviour of the inclusions. The decisive advantage of the two-phase model is worth noting: the direct implementation of the finite element method on the reinforced zone does not require a refinement of the mesh to capture the complex interaction between the inclusions and the soil; the element size in the reinforced zone is in no way different from the size that would be adopted in the absence of reinforcement. As an illustration, Fig. 15, taken from Hassen and de Buhan (2004), presents the stability analysis of a slope in the form of a curve showing the evolution of an increasing proportion of the weight applied to the structure (load factor) as a function of the displacement of a point located at the top of the slope. The slope has been reinforced in its central part by a group of steel vertical tubular piles of radius R = 1 m, thickness e = 0.02 m and length equal to the thickness of the soft superficial layer H = 13 m; the reinforcing inclusions are placed into the soil mass following a regular square mesh of s = 5 m spacing. The flexible piles are those in which shear and flexural effects are ignored, and the rigid piles are those in which these effects are considered. It is clearly shown that, for the latter model, the ultimate load is about 20% higher than the prescribed loading, thereby ensuring the stabilization of the slope under its own weight. The results confirm that the shear and flexural properties of the reinforcements play a decisive role in the global response, which has important consequences in terms of engineering design methods and optimization procedures applied to this kind of reinforced soil structures.

• The macro-element concept has received much attention and has been extended, for shallow (strip, rectangular or circular) foundations, to more general situation introducing the coupling between the various degrees of freedom of the foundation, taking into account uplift of the foundation and soil yielding (Cremer et al. 2001, 2002, Chatzigogos et al. 2009, 2011, Figini et al. 2012, Grange et al. 2009). It has also been recently extended to pile foundations (Correia 2011; Correia et al. 2012; Pérez-Herreros 2020). The macro-element, which can be viewed simply as an extension of the concept of linear foundation impedances to the non-linear range, must be described by a constitutive law selected in such a way as to ensure that the response of the system, examined at the mesoscale, correctly reproduces the features of the actual response of the model. This is an essential remark, since the passage from the local scale to the meso-scale wipes out all characteristics of the local scale (e.g., stresses and displacements at any point in the soil domain near the footing) except for those that are deemed essential for the overall behaviour of the global model. The features of the system to be retained at the meso-scale model are usually represented through a number of “generalized stress” variables and by the corresponding “generalized strain” variables according to the type of examined problem. An illustration of the capability of the macro-element model is depicted in Fig. 16 where the results of the numerical simulation are compared to experimental tests carried out on a shaking table (Combescure and Chaudat 2000). This concept is very efficient for SSI analyses since the number of degrees of freedom of the system is dramatically reduced; the macro-element has, at most, six degrees of freedom. It is gaining more and more popularity and starts to be used for actual projects. The author has personally used one of these formulations for the study of a gravity caisson quay wall.

• Another critical aspect in the design of the Antirion approach viaduct of the bridge, which has not been addressed above, is the impact of a massive liquefaction of the slope on the pile foundations. Again, thanks to the excellent collaboration with the checker, the results obtained in the centrifuge facility at Renssaler Polytechnic University (RPI) for the study of the impact of lateral spreading on structures have been used to estimate the soil pressures exerted on the piles by the liquefied soil (Dobry and Abdoun 2001). This was done to the satisfaction of all parties, but clearly a more sophisticated approach combining experiments and numerical models would have been warranted. This lack of theoretical approach provided a topic for a PhD thesis aiming at simulating the lateral spreading of a liquefied soil mass along with evaluating its impact on neighbouring structures by calculating the lateral pressures exerted by the liquefied ground (Montassar 2005; Montassar et al. 2009). Unlike others studies the soil is not modelled as a viscous fluid but as a more realistic viscoplastic Bingham material, which exhibits both residual shear strength and viscous properties. Figure 17 presents the results of a posteriori simulation of the liquefaction of the slope on the piles of the approach viaduct.

Fig. 15

Stability analyses of a slope reinforced with inclusions (Hassen and de Buhan 2004)

Fig. 16

Calibration of the non-linear foundation macro-element proposed by Figini et al. (2012)

Fig. 17

Top: Simplified sketch of the Antirion approach viaduct problem and deformed mesh at 30 s—bottom: drag force profiles at different times (Montassar et al. 2009)

6.7 Bridge response during an earthquake: the TRL5 stage

It has been noted that the TRL5 stage can very seldom be experienced by our civil engineering projects because they are prototypes and the relevant environment, i.e. earthquake shaking, remains exceptional. However, the Rion-Antirion bridge is one exception, noting however that the recorded event was less damaging than the design earthquake.

On 8 June 2008, at 15:25 a strong earthquake with a moment magnitude M_w = 6.5, named “Achaia-Ilia”, occurred in Greece. The focal depth was estimated to be around 30 km and the epicentre was located at a distance of 36 km SW from the Rion-Antirion bridge (Fig. 18). The maximum on-shore acceleration was 0.127 g recorded on Rion in the transverse direction to the bridge. The deck experienced the most intense shock during the earthquake: the acceleration exceeded 0.5 g, while the displacement amplitude reached 27.7 cm. The expansion joint movement at the extremities of the bridge did not exceed 14 cm in range. Based on the recorded free-field motions, the return period of this event was estimated to be of the order of 100 years. A video showing the behaviour of the bridge during the earthquake will be shown during the oral presentation (Fig. 19).

Fig. 18

Epicentre location and bridge site

Fig. 19

Video of the bridge response during the earthquake

The bridge is equipped with a complete monitoring system capable of collecting high frequency data at critical elements of the structure during a seismic or wind dynamic event and is subjected to periodic topographical surveys. From the analysis of the data collected during the event and the thorough inspections performed after, it was confirmed that the behaviour of the bridge was well within the serviceability limit states, without permanent damages (Papanikolas et al. 2010).

The visual post-earthquake inspections confirmed the good overall condition of the bridge. No structural damage was observed even though the seismic event was strong. The lateral, sacrificial strut elements failed as predicted from the design for a significant earthquake in order to prevent structural damage, thus activating the dissipation system (Fig. 19). They were replaced after the earthquake. Given the acceleration amplitude on the foundation (less than 0.15 g) no sliding took place along the gravel bed.

After the earthquake a complete geometrical monitoring was conducted in order to check if tectonic movements or settlements had occurred during the earthquake. It is important however to mention that just before the earthquake the scheduled geometrical monitoring campaign had been completed, allowing for an accurate evaluation of the earthquake-induced displacements (Table 1).

Table 1 Foundation settlements (mm)

Results presented in Table 1 show that:

• The total settlements from foundation landing were in the expected range of calculated values.

• The earthquake-induced settlements represent 5% to 10% of the total settlement.

• Back calculations of the earthquake-induced settlements from the recorded motions were within the expectations.

6.8 The Rion-Antirion bridge: a precedent in earthquake foundation engineering

At the time of design, at the end of the twentieth century, the design concept for the foundations was completely innovative and required a lot of intellectual and financial investment to convince all involved parties. This investment was worthy because this project paved the path for more recent ones. To the best of the author’s knowledge, two major long suspension bridges and one nuclear waste storage building replicated the same concept.

The Osman-Gazi Bridge (Izmit Bay suspension Bridge), approximately 50 km east of Istanbul, crosses the Marmara Sea with a main span of 1,550 m in close proximity to the North Anatolian fault (Fig. 20). This bridge, the fourth longest span bridge in the world, was opened on 1 July 2016. The Owner is NÖMAYG / Nurol-Özaltin-Makyol-Astaldi-Yüksel-Göçay and the Contractor is IHI Infrastructure Systems CO., Ltd with COWI as bridge designer.

Fig. 20

Izmit bridge (Turkey) and its foundation

The bridge site is located in a highly seismic region. The non-collapse earthquake has a return period of 2,475 years and a peak ground acceleration of 0.87 g.

The ground conditions and the magnitude of loading were similar to the conditions for the Rion-Antirion Bridge in Greece. The characteristics in both cases are: deep water (40–65 m), deep soil strata, weak alluvial deposits, soil strength increasing with depth and strong seismic activity with large tectonic movements. Despite being a cable stayed bridge, the Rion-Antirion bridge with its extensive physical and numerical modelling and its successful behaviour during an earthquake, served as a basis to transpose the foundation concept to the tower foundations of the Izmit Bay Bridge (Steenfelt et al. 2015). A schematic view of the foundations of one tower is depicted in Fig. 20.

The 1915 Çanakkale Suspension Bridge spans the Dardanelles strait, about 10 km south of the Marmara Sea (Fig. 21). With its main span of 2023 m, it is the longest suspension bridge in the world which was opened to traffic on March 18, 2022. The bridge's tender project was designed by Tekfen Construction and detailed designed by COWI and PEC (Pyunghwa Engineering Consultants in South Korea, for cable design and approach bridge design packages only). Arup and Aas-Jakobsen participated in the project as Independent Design Verifier (Phil 2022).

Fig. 21

1915 Çanakkale Bridge and its foundation

The bridge is located ~ 20 km from the North Anatolian Fault, a plate boundary between the Anatolian and the Eurasian plate, and, as such, has the potential to experience significant earthquakes. The non-collapse earthquake has a return period of 2475 years and a peak ground acceleration of 0.7 g. The bridge foundations include two main towers for which a hybrid gravity/pile inclusion foundation solution like the one adopted for the Izmit Bay Bridge (Steenfelt et al. 2015) and the Rion-Antirion Bridge was selected (Giannakou et al. 2019). The foundation consists of a gravity caisson foundation resting on top of reinforced soil with steel tube inclusions. A gravel bed is placed below the base of the caisson (Fig. 21).

Two-dimensional non-linear dynamic numerical analyses were conducted to evaluate the tower performance using advanced soil constitutive models which were calibrated to capture liquefaction triggering and post-liquefaction accumulation of shear deformations. The advanced numerical analyses captured the important liquefaction-related mechanisms of the adjacent slope, allowing for a rational and reliable prediction of tower performance. Results indicated limited tower deformations even under the “worst-case” scenarios.

The nuclear waste storage building of ICEDA (Installation de Conditionnement et d'Entreposage de Déchets Activés), the purpose of which is to package and store various categories of radioactive waste, is located on the Bugey site in France near Lyon (Vandeputte et al. 2011; Okyay et al 2012). The site is located in a seismic area for which the design earthquake has a peak ground acceleration of 0.24 g. Due to the poor soil conditions with a clay layer, 35 m to 55 m thick, overlying a stiff Molasse, the building is founded on 300 reinforced concrete inclusions reaching the Molasse (Fig. 22).

Fig. 22

Construction of the ICEDA foundations

Extensive nonlinear finite element analyses were carried out with the software DYNAFLOW (Prevost 2008) which were peer reviewed and led to approval by the French Nuclear Safety Authorities (Fig. 22).

7 The 3^rd Atlantic Bridge (Panama)

The Panama Atlantic Bridge (Fig. 23), constructed by Vinci Construction Grands Projets, is the third bridge across the Panama Canal on the Atlantic side, north of the new locks of Gatun (Joly et al. 2017). The total length of the crossing is approximately 3 km with a cable-stayed bridge 1,050 m long with a central span of 530 m and two access viaducts 1,125 m and 906 m long. The bridge was completed in 2019. It is located in a highly seismic area for which the design ground motion is defined by a return period event of 2,475 years with a peak ground acceleration on rock equal to 0.57 g and a 5% damped spectral acceleration at the plateau of 1.3 g. The applicable standard for design was AASHTO “LRFD Bridge Design Specifications”

Fig. 23

Atlantic bridge

The site conditions at two piers of the access viaducts were particularly difficult with a 10 m thick hydraulic fill layer over a layer of very soft clay, 12 m thick, called Atlantic muck, resting on top of stiffer materials ranging from a residual soil to a weathered and soft rock (Fig. 24).

Fig. 24

Soil profile and shear wave velocities at the location of two piers of the access viaduct

7.1 Challenges

The Atlantic Muck exhibits a shear wave velocity of 60-80 m/s and the underlying layers a shear wave velocity of 500 m/s up to 800 m/s. This special configuration creates large displacements and deformations in the soft layers which induce large kinematic bending moments in piles. The seismic bending moments and shear forces induced in the piles at the interface between the Atlantic Muck and the residual soil led to a reinforcement ratio exceeding 4%, the upper acceptable limit according to the AASHTO standard.

7.2 Foundation concept

The solution which has been eventually adopted was inspired by the success of the foundations of the Rion-Antirion bridge (Pecker 2018). Non-linear foundation behaviour and particularly the beneficial effect of foundation uplift to reduce the overturning moment is now commonly accepted. Therefore, the idea consists in relying again on a shallow foundation not anchored into the ground, which implies suppressing the piles below the footing. Given the really poor quality of the Atlantic Muck, soil reinforcement was not feasible, and the need to provide a competent seating for the foundation is realized by substitution of the soft clay by a massive (unreinforced) concrete block between the base of the footing and the top of the soft rock. Protection of the foundation is achieved with a 18 m diameter peripheral wall which carries a large part of the kinematic forces induced by the soil displacements and limit the kinematic forces acting on the foundation (Fig. 25).

Fig. 25

Layout of the foundations

The wall is constructed with secant piles anchored in the rock formation, working like individual cantilever beams without hoop connections. A peripheral annular beam at the top of the wall ensures the continuity between the piles and stiffens the wall. No mechanical connection exists either between the footing and the underlying concrete block or peripheral wall, or between the concrete block and the rock (Fig. 26).

Fig. 26

View of the foundations during construction

The sequential construction of the foundation involves realization of the piles, linkage of the piles with the annular top beam, underwater excavation and pouring of the concrete, dewatering and construction of the footing and pier.

Very detailed 3D nonlinear finite element analyses were run with the software DYNAFLOW (Prevost 2008) to calculate the foundations displacements (rocking, uplift), the forces induced in the protecting wall, annular beam and footing. For instance, the uplifted area of the footing does not exceed 15% of the cross section (Fig. 27). Compared to a classical shallow foundation, the only drawback is the inability to benefit from slippage because the foundation is blocked horizontally against the peripheral wall. Nevertheless, the moment reduction due to uplift and the limitation of the kinematic forces were significant and sufficient to make the design feasible.

Fig. 27

Uplifted foundation area during earthquakes (7 simulations with time histories Acci-H1)

7.3 Outcome of the project

This project did not really motivate additional research as the Rion-Antirion bridge did, but the concept of an uplifting foundation benefited from this previous experience and provides another example of this new trend in foundation design.

8 Prefecture of Fort de France (Martinique)

The new Prefecture building in Martinique (French Caribbean islands) is located on top of loose cohesionless deposits, 9 to 17 m thick, resting on top of a soft rock layer exhibiting a marked slope towards the sea. According to the French seismic regulations, the project has to be designed for a surface peak ground acceleration of 0.36 g associated with a 7.5 magnitude earthquake.

8.1 Challenges

The site being near the coast, the water table is at 1 m depth, and the soft soil deposits are prone to liquefaction with certainly lateral spreading taking place. The objective of the foundation design was two-fold: if possible, utilise a surface foundation to minimize the cost and duration of construction, and prevent the adverse effects of lateral spreading.

The contractor, Solétanche–Bachy, proposed a deep soil mixing improvement (Benhamou and Mathieu 2012) that proved successful during the 1995 Yoko-ken-Nanbu earthquake. The 14-story Oriental Hotel, located on a pier in Kobe, was founded on piles protected by a deep soil mixing (DSM) grid, and it survived the earthquake without damage to its pile foundations or evidence of liquefaction within the lattice, despite large liquefaction-induced deformation of the surrounding untreated quay walls (Namikawa et al 2007). The same type of lattice type soil improvement with deep mixing was replicated in Fort de France using the Geomix® technique, which is a DSM technique based on the Hydrofraise technology combined with Cutter Soil Mixing (CSM) principles (Benhamou and Mathieu 2012). Figure 28 (left) shows the geometry of the Geomix grid: each panel is 6 m long, 19 m deep and 0.5 m thick. A total area of 1,440m² has been treated. Figure 29 presents a view of the site during construction.

Fig. 28

Lattice type soil improvement with deep mixing

Fig. 29

View of the foundation during construction

On top of the grid a gravel layer was placed on which the building was founded with a direct foundation. The role of the gravel layer was to prevent “hard points” that may damage the building raft due to differential settlements.

As mentioned previously the purpose of the soil improvement was essentially to prevent lateral spreading. Simple hand calculations were used to demonstrate that, given the in-plane dimensions of the overall caisson (36 m by 40 m), this is easily achieved with the overall caisson being stable under the pressure applied on its periphery by the liquefied laterally spreading soil. Pore water pressure build-up within the cells is limited by the stiffness of the caisson, which prevents the development of high shear strains in the soil; furthermore, induced pore pressures do not represent a real threat since the raft is founded on the lattice grid and designed to be supported only on the caisson’s walls. Strength checks of the panels’ resistance indicated that an unconfined compressive strength of 1 MPa was sufficient to ensure the stability; static settlements were less than 2 cm.

8.2 Outcome of the project in terms of research

The project described in the previous section does not constitute an innovation per se; it just took advantage of an existing solution that proved its efficiency during earthquakes. However, it was implemented in that case with the restricted goal of preventing damage due to liquefaction-induced lateral spreading. No in-depth study was dedicated to the pore water pressure build-up, or even liquefaction, within the cells because the foundation was totally supported by the trenches. In view of the increasing use of soil mixing technique in urban areas, particularly since 1990 (Fig. 30), numerous research projects were undertaken worldwide to quantitatively assess the performance of this technique. In the following, we will focus on the improvement technique based on a lattice type soil mixing technique (DSM lattice).

Fig. 30

Volume of treated soil by soil mixing (after Tokunaga et al. 2015)

Since this technique shows promising perspectives due to the progress of technology, a research program based on experimental centrifuge testing and advanced numerical analyses was launched by the Fédération des Travaux Publics (FNTP) and Solétanche–Bachy (SB) to develop design guidelines for this technique (Pecker et al. 2020). It was motivated by the limited number of existing design guidelines (Bruce et al. 2013 for North America, Kitazume and Terashi 2012 for Japan) and the limitations of recent studies (e.g. Gueguin et al. 2013, Nguyen et al. 2013). These last two studies have the merit of shedding more light on the overall behaviour of lattice trenches, but the conclusions are based on an elastic behaviour of the soil. For instance, based on the theory of homogenization, Gueguin et al. (2013) established analytical relationships providing upper bound and lower bound estimates of the relative stiffness, G_L, of the soil improved by a lattice type deep soil mixing to the soil stiffness, G_S, as a function of the replacement ratio η defined as the ratio of the area of improved soil to the total area (Fig. 31). Although based on the theory of elasticity, the figure clearly shows the superiority of the lattice scheme with respect to a unidirectional trench loaded transversally or to an isolated column.

Fig. 31

Shear modulus of a reinforced soil for different configurations: lower bound-dashed line; upper bound: dotted line

A grid pattern of DSM walls acts as a confined shear box, which can provide additional shear stiffness and strength for sites to withstand liquefaction. An increase in stiffness results in a decrease in the average (across the improved cell) induced shear strain which turns into a decrease in excess pore water pressure build–up. One important finding of the two mentioned studies (Gueguin et al. 2013; Nguyen et al. 2013) is the demonstration that the commonly used assumption of shear strain compatibility between the soil and the caisson does not hold (Fig. 32).

Fig. 32

Shear strain in the improved soil; left: strain compatibility; right: actual strain

Nguyen et al. (2013) investigated the behaviour of soil deposits treated with DSM grids using three-dimensional linear elastic finite element analyses of unit cells. Parametric analyses are performed for a range of geometries, relative stiffness ratios, and dynamic loadings demonstrating that shear stress reductions are less than predicted by the assumption of shear strain compatibility. Their results are interpreted in terms of a cyclic stress ratio (CSR) reduction factor defined as the reduction of the cyclic stress ratio of the improved soil over the same quantity for the unimproved soil.

The previous attempts to quantify the efficiency of the ground improvement technique based on lattice-shaped DSM trenches are classical stress-based approaches adapted from the state-of-the art methodology used in free-field conditions. It consists essentially in evaluating the reduction in the earthquake induced shear stress in the enclosed soil and to compare it with the one in free-field. In Pecker et al. (2020) a more fundamental strain-based approach is attempted to reflect the fact that shear strain is a more fundamental parameter than shear stress when the tendency of the soil skeleton to undergo volume changes is evaluated (Dobry et al. 1982; Dobry 1985; Dobry and Abdoun 2015). As quoted from Dobry and Abdoun (2015):

Results of undrained cyclic strain-controlled tests in the laboratory supplemented with field measurements show two important practical advantages of using γ_c instead of CSR = τ_c/σ'_v0 to characterize the pore pressure response of sands to cyclic shear loading. The first advantage is the existence in both clean and silty normally consolidated sands of a threshold shear strain, γ_tv ≈ 0.01%, necessary to start the pore pressure build-up. The second advantage is the fact that in cyclic strain-controlled undrained tests, the curve of excess pore pressure ratio, r_u = Δu/σ'_v0 versus applied γ_c after a given number of cycles, n, is remarkably stable.

Therefore, as a result, whether strain–controlled or stress–controlled tests are used, the generation of pore pressure is more uniquely related to γ_c. Only the main results of this study are briefly outlined in the following sections, skipping all the calculation details which are provided in Pecker et al. (2020).

8.2.1 Design procedure

The first step of the proposed design procedure consists, given the magnitude of the earthquake, in estimating the shear strain γ_cl corresponding to liquefaction triggering. This is presented in Sect.  8.2.2.

The second step consists in calculating the maximum free-field induced shear strain γ_S either from a site response analysis or from a simplified procedure. The equivalent average shear strain < γ_S > in the reinforced soil is estimated from a relationship involving the maximum free-field shear strain and the geometrical and mechanical parameters of the system (Sect. 8.2.3).

If < γ_S > is less than γ_cl, liquefaction is not triggered, in an average sense, within the DSM cells and the pore pressure increase can be estimated from any appropriate statistical relationship relating pore pressure to cyclic shear strain (e.g. Cetin and Bilge 2012). If not, either a specific finite element analysis needs to be carried out to compute a more accurate value of < γ_S > or the original design needs to be modified by decreasing the cell width, increasing the DSM modulus, etc.…

8.2.2 Definition of the shear strain triggering liquefaction

The first step in the methodology, i.e. the development of a relationship between cyclic resistance ratio (CRR) and the shear strain γ_cl corresponding to liquefaction triggering, is a key issue to link the cyclic stress approach currently used in liquefaction triggering evaluations with the cyclic strain approach. This development has been carried out by Dobry and Abdoun (2015) for earthquakes with magnitude 7.5. Their derivation starts from the liquefaction resistance chart based on the shear wave velocity and an assumed variation of the secant shear modulus with shear strain (modulus reduction curve). Their calculations carried out for a range of values of the input parameters K₀ (at rest earth pressure ratio) = 0.5–0.6, $\sigma_{v0}^{^{\prime}}$ vertical effective stress) = 50–100 kPa, V_S (shear wave velocity) = 100–180 m/s lead to a remarkable constant value γ_cl = 3 × 10^–4 for the liquefaction triggering shear strain. The same methodology has been applied in Pecker et al. (2020) to other magnitudes by correcting CRR by the range of magnitude scaling factors (MSF) recommended in Youd et al. (2001):

$$\frac{{10^{2.24} }}{{M_{{\text{w}}}^{2.56} }} \le {\text{MSF}} \le \left( {\frac{7.5}{{M_{{\text{w}}} }}} \right)^{3.3}$$

(1)

Results of γ_cl versus moment magnitude M_w are plotted in Fig. 33. For each magnitude the symbols correspond to different estimates of the input parameters (K₀, σ'_v0, V_S, MSF) in the range defined above. The solid line represents the best estimate of the shear strain triggering liquefaction in the field; the two dashed lines correspond to upper and lower bound estimates. Use of the best estimate curve is recommended, but the methodology remains unchanged if more, or less, conservative estimates of γ_cl, represented by the dashed lines, are used. The best estimate curve for γ_cl, in percent, can be approximated by Eq. (2):

$$\gamma_{{{\text{cl}}}} = \frac{{0.113M_{{\text{w}}}^{2} - 1.596M_{{\text{w}}} + 5.711}}{{M_{{\text{w}}} - 5.343}}$$

(2)

Fig. 33

Shear strain versus moment magnitude at liquefaction triggering

The curve(s) in Fig. 33 are based on the finding that γ_cl for magnitude 7.5 earthquakes is equal to 3 × 10^–4. As clarified by Prof Dobry (personal communication) that conclusion is applicable to loose, uncompacted fills (and by extension to loose, very recent sedimentary deposits). These loose, uncompacted fills and loose recent sedimentary deposits in fact control the location of the liquefaction curve for low values of V_S1 (and also control the locations of the curves for low values of penetration resistance in CPT and SPT liquefaction charts). For denser, aged, overconsolidated, etc., sand deposits having larger values of V_S1 (and larger values of CPT and SPT in the penetration charts), the strain needed for liquefaction is greater (0.3–0.6%, Point B in Fig. 7 from Dobry-Abdoun 2015). Nevertheless, from a practical viewpoint, most of the cases of soil improvement will correspond to loose, uncompacted fills or recent loose natural deposits; if the shear strain for triggering of liquefaction increases for a dense sand compared with Fig. 33, the use of the mean curve constitutes a conservative approach even if it is replaced by the upper bound curve. So, Fig. 33 may be too conservative for denser deposits, but it will never underestimate the danger of liquefaction.

8.2.3 Calculation of the induced shear strain in the reinforced soil

To assess the efficiency of the soil treatment, the average (at a depth across a horizontal cross section within the cell) earthquake induced shear strain is compared to the shear strain required to trigger liquefaction. As pointed out by previous analyses based on analytical solutions (Gueguin et al. 2013) or on numerical analyses (Nguyen et al. 2013), both assuming linear-elastic behaviour of the reinforced soil, this average shear strain < γ_S > cannot be calculated on the assumption of shear strain compatibility between the reinforcement and the enclosed soil. It is a function of the geometrical dimensions of the reinforcement, the replacement ratio, the ratio of the DSM modulus to the soil modulus, the free-field induced shear strain, etc. Based on numerous dynamic non-linear finite element analyses, conducted with the software DYNAFLOW (Prevost 2008), and dimensional analyses (П theorem, Vaschy 1892, Buckingham 1914), < γ_S > is written:

$$\left\langle {\gamma_{S} } \right\rangle = \lambda \left( {\frac{{G_{{\text{T}}} }}{{G_{1} }}} \right)^{{\theta_{1} }} \left( {1 - \eta } \right)^{{\theta_{2} }} \left[ {{\text{tanh}}\left( {\frac{B + e}{{H_{T} }}} \right)} \right]^{{\theta_{3} }} M_{w}^{{\theta_{4} }} \left( {\frac{{G_{S} }}{{\rho_{S} H_{S} {\kern 1pt} pga}}} \right)^{{\theta_{5} }} \left( {1 - \frac{{H_{{\text{T}}} }}{{H_{{\text{S}}} }}} \right)^{{\theta_{6} }} \gamma_{S}^{{\theta_{7} }}$$

(3)

With the following notations (see Fig. 34):G: soil shear modulus $G = G_{1} \left( {{{\sigma^{\prime}_{{m}} } \mathord{\left/ {\vphantom {{\sigma^{\prime}_{{m}} } {p_{{a}} }}} \right. \kern-0pt} {p_{{a}} }}} \right)^{0.5}$ with σ’_m : mean effective stress and p_a a reference stress (atmospheric pressure), G_S: shear modulus calculated at mid-height of the soil column, ρ_S: soil mass density, H_S: total height of the soil column, G_T: shear modulus of the DSM walls, H_T: height of soil improvement, e: thickness of the DSM wall, B: spacing of DSM walls, A: total plan area (sum of area of soil and walls) = (B+e)^2 ,A_C: area of improved soil by DSM = 2Be+e^2 ,η: replacement ratio defined as A_C/A, γ_S : free-field shear strain, M_w: earthquake magnitude, pga: free-field peak ground acceleration, θ_i : fitting parameters determined by the least square method.

Fig. 34

Geometric definition of DSM grid

The following numerical parameters have been investigated through nonlinear dynamic finite element analyses both for the free-field and for the reinforced soil:

• The soil mass density ρ_S is fixed at 2.0t/m³.

• G₁ takes values of 75 MPa, 90 MPa, 110 MPa.

• The soil column height H_S is fixed at 30 m.

• The height of treatment H_T takes values of 10 m, 15 m, 20 m.

• The shear modulus of the trenches G_T takes values of 1125 MPa, 1700 MPa, 2000 MPa.

• The grid spacings takes values of 4 m, 6 m and 8 m and the trench thicknesses 0.4 m, 0.6 m, 0.8 m and 1.0 m.

• Earthquake magnitude M_w = 6.0, 6.5, 7.0 represented by a set of 10 natural records for each magnitude.

• Outcrop free-field acceleration at depth H_S (different from parameter pga), 0.5 m/s², 2.5 m/s², 3.5 m/s², 4.5 m/s²; pga is an output of the free-field site response analyses.

• The free-field shear strain γ_S is calculated from the free-field site response analyses.

The non-linear model is the elastoplastic multi-yield constitutive model developed by Prevost (1985). The DSM trenches are modelled with an elastic behaviour.

Prior to the numerical analyses, the calculation model and the soil parameters have been calibrated by comparison with centrifuge tests carried out in the Institut Gustave Eiffel (formerly LCPC then IFSTTAR) facility in Nantes. For illustration purpose, one example of the simulation of one centrifuge test is provided in Fig. 35.

Fig. 35

Cross section of the centrifuge model test with the DSM grid and comparison with numerical simulation

The strain was found to increase almost linearly with depth along 90% of the reinforcement height; it can therefore be linearly interpolated/extrapolated between the value at the surface and the value at mid-depth for all depths between the surface and 0.9H_T. In the remaining 10% of H_T, the value at the base should be used. Based on these findings three depths have been analysed and the average shear strain calculated in a horizontal cross section within the cell; the best fit parameters are listed for each depth in Table 2.

Table 2 Parameters θ_i in Eq. (3)

The calculated average shear strain in a given horizontal plane is compared to the one predicted with Eq. (3) in Fig. 36. A satisfactory fit is achieved with a correlation coefficient of 0.96.

Fig. 36

Comparison of calculated versus predicted (Eq. 3) average shear strain

8.2.4 Conclusions

To conclude, this example, the purpose of which is not to outline in the present paper all the results and the detailed methodology, has been presented to illustrate how an actual project may be a source of motivation and inspiration for design-oriented research that leads to the development of guidelines to be used for future projects. Obviously, as mentioned in the introduction of the paper the time frame required to conduct this research is not compatible with an “ordinary” construction project, in contrast to the Rion-Antirion bridge project. However, its outcomes may lead to significant savings in the future: the evaluation of the pore water pressure induced in the cells may allow a direct foundation of the building on the soil without the need to bridge between the walls.

9 Conclusions

The purpose of this paper was not to present new developments related to earthquake design of foundations for civil engineering structures, except maybe for the design of DSM lattice type improvement, but to tentatively share, on the basis of more than 40 years of experience, some general views on the interrelationships between several activities of an engineer: education, training, practice and innovation. With the increasing complexity and expectations for our structures, I have attempted to demonstrate that innovation is the key factor for the design of special structures subjected to severe requirements. Although civil engineering relies heavily on past experience, advanced numerical tools and standards, many situations cannot be solved with a simple blind application of these features. Use of precedents and strict applications of standards may render the design of the structure impossible, because any important structure is a prototype, and standards are not established for exceptional structures. I argued that standards should not be applicable to such structures, and that one should leave the door open to the creativity of engineers. However, innovation must be framed to be understood and accepted by the engineering community: simplicity, scientific roots, validation are the key parameters. It has been noted that these requirements may be incompatible with the time frame devoted to a project and necessity leads the engineer to rely on his or her own judgment and simplified justifications. Nevertheless, scientific rigour must not be neglected in favour of efficiency, and one way to satisfy this necessity is to increase the collaboration between scientists and engineers. To achieve this collaboration scientists must put themselves within the reach of engineers and engineers must be educated and possess a strong scientific background, gained in their initial formation but also along their lives. Both communities benefit from this interaction: during the innovation phase (short time scale) the scientist is a guaranty of the merits of the innovation and later on innovation may be a source of inspiration for research (long time scale). Several examples drawn from actual projects have illustrated these aspects and proved to benefit everyone including the social community provided everyone accepts to move forward and to get out of his comfort created by precedents, standards, etc. We should be confident in our capabilities to innovate and give ourselves the means to achieve it.

“It's not because things seem difficult that we do not dare, it's because we do not dare that they seem difficult” (Seneca The Younger, 4BC-65AD).