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
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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
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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
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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.