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  • Published on: 7th September 2019
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The Eurocodes programme comprises several standards generally consisting of a number of

parts, and covers in a comprehensive manner the basis of structural design, actions on

structures, design of a wide range of types of structures, design of structures for earthquake

resistance, and geotechnical design. EN 1997‐1, general rules, and EN 1997‐2, ground

investigation and testing, complete EN 1997, adopted as Eurocode 7 and intended to be applied

to the geotechnical aspects of the design of civil engineering works to be used in conjunction

with EN 1990, which describes the basis of design and establishes the guidelines for related

aspects of structural reliability. In particular, EN 1997‐1 includes several sections as general

concepts, basis of geotechnical design, geotechnical data, supervision of construction,

monitoring and maintenance, fill, dewatering, ground improvement and reinforcement, as well

as a number of sections devoted to different geotechnical structures interacting with the ground.

In fact, the importance of the Eurocodes programme to design practice is actually recognised as

they are considered one of the most comprehensive suite of standards of its type in the world

developed over about thirty years of collaborative effort, further noted that they affect the work

of around thousands of professional engineers. The development of the first generation of the

Eurocodes is considered a great achievement, but the need for updating is also recognised so

that an improved generation of standards may evolve ensuring the incorporation of recent

innovations. A programme of work supported by the European Commission has been launched

to appoint experts to extend the scope of the actual versions on development of a second

generation of the Eurocodes, expected in 2020 to embrace new technologies, encouraging

innovation and ensuring the incorporation of market developments when taking into account

new societal demands. A major focus will be placed in the harmonisation and ease of use.

Meanwhile, maintenance work largely based on the feedback from the use of the Eurocodes and

on the requests for revision from public and private organisations is an essential activity to

ensure integrity involving technical improvements and amendments, resolution of questions of

interpretation, elimination of inconsistencies and misleading statements, or correction of errors.

The Eurocodes provide common rules for the design of structures and component products of

both traditional and innovative nature, moreover unusual forms of design conditions are not

specifically covered and additional expert consideration is then required. The verification

procedure is based on the limit state design concept used in conjunction with a partial factor

method, and guidance is provided for the use of design methodologies based on probabilistic

techniques. In fact, in structural design it is implicit a certain probability of failure, accepted as

Reliability-Based Analysis and Design in Geotechnical Engineering. Applications to Eurocodes.

Author:Sónia H. Marques

10

part of the real world. In a quantitative approach, reliability is a complement of the probability of

failure and may be described as the capability of a structure or a structural member to fulfil the

specified requirements for which it has been designed, the term failure interpreted with the

sense of any undesirable state. The reliability required for structures within the scope of the

Eurocodes shall be achieved by design in accordance with the standards and by suitable

combinations of appropriate measures, as for instance error reduction in design and execution

or adequate supervision and inspection. For the purpose of reliability differentiation,

consequences classes may be established by considering the consequences of failure, noted the

costs of safety measures. Normal classes are associated to designed structures under normal

variabilities and any overestimation from the use of approximate calculation methodologies

should be within reasonable limits.

Therefore, the target reliability is a parameter correspondent to a notional value subject to

optimisation to comply with the degree of uncertainty in order to develop a consistent design,

and by hypothesis is considerably different from the actual frequency of failure. In particular,

considered various constraints comprising economic interests, geotechnical engineers must

usually deal with very limited site investigation data and accordingly, handbooks of geotechnical

design tables are appreciated by practitioners so that unresolved issues may comprehend a

discrepancy of the reliability studies regarding the actual frequency of failure whereas enough

tests are very seldom available for a definite choice of the best statistical model. The guidelines

to get along with this uncertainty in geotechnical design have been achieved through a safety

factor approach coupled with the assumption of characteristic values, in other words,

representative values of parameters considered as the most adequate to estimate the occurrence

of limit states, so that when the partial factor format is first introduced, it should preferably

produce a design comparable to the resultant from the safety factor methodology, promoting the

continuity of past experience.

Considered now as exemplar the german case study, it is remarked that the implementation of

the partial factor format in the german geotechnical design practice is supported by the

continuity of acquired experience from a comparable design based on the total factor format,

although the performance of the partial factor format is related to the potential capability to

achieve the target reliability within acceptable margin of error. In fact, the endeavour on the

reliability‐based design encounters the primary target on robustness. Even though the attractive

probabilistic approach has been a research topic of interest on the german universitary system,

only a minority of professionals advocated the integration of the concept on geotechnical

standards. Thus, the traditional level of safety of the former total factor format is maintained on

the actual semi‐probabilistic partial factor format recommended by the Eurocode 7, considered

that no robust level of safety in probabilistic terms has been pursued towards standardisation in

the field of geotechnical engineering. Actually, the partial factor format through the Design

Approach DA.2* is based on a modified global safety concept, noted that different systems

associated to the same factor may have a differentiated probability of failure due to the fact that

important variabilities are disregarded. However and in accordance to the successful past

experience, the consistency of the singular global factor of safety approach is advocated in the

german geotechnical design practice, noted the important characteristic uncertainty on ground

and the high concern on human error. At a glance, it seems not possible to attain the actual

reliability from any particular model subject to imprecision, however, it is recommended to

undertake research to facilitate the integration into the Eurocodes suite of the latest

developments in scientific and technical knowledge.

Reliability-Based Analysis and Design in Geotechnical Engineering. Applications to Eurocodes.

Author:Sónia H. Marques

11

The first applications of nonprobabilistic interval analysis in geotechnical engineering have been

recently explored. In fact, the solution of practical problems in this field often requires

judgement based on limited data and interval analysis has become a research area formally

motivated by input information characterised by imprecision. Whenever no information apart

from bounds is available, intervals may be considered in the form of a model noted that they are

among the most widely used analytical tools to describe uncertainty by using nonprobabilistic

approaches. However, the application of a pure interval analysis to engineering problems may

lead to large overestimation noted that meaningful results are only obtained when a decision is

based on threshold values. A mixed approach that admits imprecise information as well as

probabilistic information is therefore desirable. For the purpose, the conventional probabilistic

approach to uncertainty may be extended to include imprecise information in the form of

intervals in order to perform a limit state imprecise interval analysis for safety assessment

presented in the format of a sensitivity analysis, wherein some parameters are implemented as

intervals and then combined with other uncertain parameters in the form of bounded random

variables. As a matter of fact, the treatment of imprecision attracted continuous interest since

the origin of probability as the science of uncertainty. Starting from only a few papers wherein

imprecise probability has been explored as a marginal alternative to precise probability, a

number of devoted works appeared with intensified frequency in the second half of the 20th

century. From first developments, imprecise probability emerged in the field of engineering by

different approaches. The key feature consists in the identification of probability bounds for

scenarios of interest with extended application in model validation, provided the ingredients for

a systematic investigation of sensitivities.

These imprecise probabilistic and interval coupled approaches are capable to be applied in the

partial factor design to Eurocode 7, considered the important impact of ground uncertainty on a

possible range of characteristic values and variabilities. In this way, a detailed analysis towards

the robustness of the partial factor design to Eurocode 7 may be pursued, noted that some

partial factors for ultimate limit state in codes of practice might have been derived by

serviceability limit state influence and the actual sustainability principles motivate a gradual

reduction in conservatism whenever possible as codes of practice are evolved. In fact, costs have

been reported in certain cases from the use of Eurocode 7 partial factors for geotechnical design

calibrated for general application. From comparison of solutions the probabilistic methods are

considered to be a very effective tool to design economic structures. In particular, considered

that geotechnical materials are among the most variable engineering materials, recent years

have seen great advances in the application of reliability techniques within geotechnical

engineering, reflecting the increased interest of the community in probabilistic methods.

It is demonstrated that the partial factor design to Eurocode 7 is not able to satisfactorily achieve

a uniform reliability level from one set of partial factors across different applications or

whenever various input parameters are considered for one case, noted that only limited

variabilities are covered by Eurocode 7. Regarding the performance of the simplified reliability‐

based design formats applied to foundations on layered soils, namely the load and resistance

factor design adopted in geotechnical engineering codes of practice worldwide, it is recognised

that regardless of the followed approach, the conventional formats are unable to achieve the

target reliability with the comparable consistency as the reported for homogeneous soils. In fact,

simplified formats have been calibrated in existing codes of practice only for the ideal condition

of homogeneous soils and there is little information about how layered soils should be

addressed. Eurocode 7 is silent in detailed provisions to guide the practical geotechnical design

in these cases, considered that the majority of bearing capacity theories involve homogeneous

Reliability-Based Analysis and Design in Geotechnical Engineering. Applications to Eurocodes.

Author:Sónia H. Marques

12

soils and the few analytical solutions for layered soils are only approximate solutions. In fact, the

multi‐layered profiles are not the exception but the norm, as structures are most likely founded

on these conditions. It is noted that bearing capacity metamodels derived by neural networks

have been considered competitive on layered soils as they significantly outperform other

methods, and in this context, neural networks are appropriate for function approximation and as

well for pattern recognition, considered the combination of different failure modes.

The limit state design concept adopted by Eurocode 7 is used in conjunction with a partial factor

methodology. The selection of appropriate partial factors on ground properties is important to

ensure the reliability of geotechnical design to Eurocode 7, as design values are determined by

applying partial factors to characteristic values. Details about the determination of geotechnical

characteristic values are then required as this topic is one of the most important due to

meaningful reliability variations. To achieve the required target reliability, Eurocode 7 does not

provide any variation in the partial factors but rather requires that greater attention is given to

other accompanying measures related to design supervision and inspection differentiation. In

this regard, checking systems frequently fail to catch errors of smaller magnitude which may

cause very important consequences of failure. Recognised some of the limitations of the

Eurocode 7 design approach, a reliability‐based design is considered a useful complementary

analysis, namely for cases wherein a correlation structure is important. In addition, it is

considered that some Eurocode 7 sections must be developed, namely applications to numerical

design. Further harmonisation is envisaged through the gradual alignment of safety levels, in

conjunction with extensive agreement of design procedures.

Characteristic features of geotechnical design include the specific knowledge of the site

conditions and the requirement for robustness considered the importance of extreme variations

for variables in causing failure and the significance of human error. In fact, adequate robustness

may provide a proper margin for variations unrelated to the primary parameters, including

moderate human error. In particular, human error is not explicitly accounted in the partial factor

design to Eurocode 7, however and given the level of understanding, the extent to which human

error is incorporated in advanced reliability analysis is a modelling decision supported by

evidence under the search for robustness, described as one of the primary requirements in a

design process accounting for uncertainty. Although there is no universal definition for

robustness, ensuring a reasonable level of safety corresponding to a reliability analysis is a form

of taking into account robustness.

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