Design is defined as the act of conceiving

and producing a plan or model before

construction. The time requirement for

human thinking does not feature in

technological evolution, which is quite

prevalent in numerical modelling for

geotechnical applications. Finite Element

Method (FEM) modelling is a numerical

procedure to determine the stresses and

strains within a complex engineering

problem that can combine structures, soils

and civil infrastructure. This form of

numerical modelling for soil-structure

interaction problems is not a new concept;

however, the widespread prevalence of FEM

for geotechnical design has only recently

been made possible by technological

improvements in software and hardware.

In particular, the user interfaces have

been simplified dramatically allowing

“nonspecialists” access into this once

specialized field. On one hand, this should

be viewed as a highly positive occurrence,

as it facilitates improved accuracy in the

mainstream geotechnical calculations

undertaken for infrastructure and

construction projects. For example, using

advanced numerical techniques, we can

now predict with a high level of accuracy

the impact of new basement construction

on adjacent building foundations and

underlying pipe networks. On the other

hand, we always need to consider if the

accuracy stated within our technical

deliverables reflects the actual accuracy of

such analysis approaches.

Limitations and AssumptionsWhile these techniques open up new

possibilities in terms of engineering

design, it is critically important to

understand the limitations of such

geotechnical software and to be cognisant

of the inherent assumptions in the design

process. Every engineering challenge

brings its own unique assumptions;

FEATURE ARTICLE

DEEP FOUNDATIONS • JAN/FEB 2017 • 69

AUTHORS Paul Doherty, Ph.D., and John O’Donovan, Ph.D., C.Eng., MICE, Gavin & Doherty Geosolutions Ltd.

The past decade has seen technology

improve at an exponential rate, and while

civil engineering occasionally appears slow

to adopt the most recent advancements in

IT, the impact on our industry is impossible

to ignore. Computing power is at a point

where the average smart phone contains

more technology than a supercomputer

from 15 years ago! Data storage and

processing ability is at an all-time high. We

now operate in an environment where day-

to-day communications occur in real-time

regardless of geographical location of the

people involved or of the technical

complexity of the subject concerned. The

major disadvantage of this process is that

with technology changing dramatically,

our expectations also increase and, as a

result, the design/engineering queries are

expected to be resolved instantaneously,

leaving little room to think about the

underlying problem!

Numerical Modelling in Geotechnical Engineering

A flood prone river modelled in the second case study

70 • DEEP FOUNDATIONS • JAN/FEB 2017 DEEP FOUNDATIONS • JAN/FEB 2017 • 71

A.

B.

C.

(A.) Initial failure points close to shaft wall toe, (B.) development of slip circle into the gravel aquifer and (C.) full base failure through heave of the soil over-lying the gravel aquifer

To achieve confidence in the accuracy of

the predictions of soil stresses and the

resulting soil movements that are

generated, it is critically important to

calibrate the soil model employed in any

numerical analysis. This calibration exercise

typically involves simulating a number of

laboratory and, possibly, field tests within

the FEM environment to determine a

synthetic soil response curve that can be

compared to the real experimental results.

The parameters are typically varied until a

reasonable match is achieved between the

laboratory and simulated soil test results.

This is an iterative process as the same

parameters are then used to simulate

additional laboratory experiments tested

under different conditions. The soil

material parameters are adjusted until a

reasonable match is seen with the full suite

of laboratory tests. This calibration exercise

can lead to improved understanding of the

advantages and disadvantages of different

constitutive models. Typically, as the

constitutive model becomes more complex,

the calibration time required to determine

each of the required parameters becomes

longer. A balance should always be struck

between introducing complexity to a FE

model and the accuracy of the output

required. This balance should be informed

by considering what the FE results will be

used for. For example, a nonlinear soil

model may be required to satisfy tight

movement criteria while underpinning a

structure that is sensitive to deformation,

whereas a linear soil model may suffice for

other applications where movement criteria

are less critical.

Case Study - Deep Access Shaft for Tunnel ConstructionGavin & Doherty Geosolutions (GDG) was

commissioned with the analysis of a series

of deep access shafts used to construct a set

of tunnels for a new sewer network under a

major North American city. The soil

stratigraphy consisted of interbedded

glacial till layers of silty clay with a range of

plasticity values. The clay layers were

underlain by an open gravel deposit, which

was also a high-pressure aquifer with

artesian conditions, and, therefore, base

heave blow-out at the bottom of the shaft

was a serious concern during construction.

The shafts, which ranged from 25 to 38 m

(82 to 125 ft) in depth, were constructed

using a secant piled starter wall over the

upper 18 m (59 ft) and a structural shotcrete

wall over the lower reaches of the shaft. In

the permanent condition, the base heave

would be resisted by a permanent concrete

however, three general assumptions

common to every soil-structure numerical

model are considered below.

One of the first steps in any soil-structure

interaction problem is to quantify the in-situ

stress regime, i.e., to determine what the

stresses are in the ground prior to con-

struction-induced changes to the stress

regime due to loading (e.g., foundations) or

unloading (e.g., basement excavation). The

in-situ stresses include the vertical and

horizontal stresses, as well as the pore pres-

sures. The vertical stresses can be derived

from the stratigraphy of the site and the

density of the various materials present;

however, the lateral effective stress is a much

more complicated parameter to quantify

accurately. The lateral effective stress is

influenced by the stress history and past

geological events, such as glaciation. A K0

parameter, which is the ratio of the vertical to

horizontal in-situ stress, is often used as an

input in numerical modelling software, and

this parameter can have a dramatic impact

on the results of FEM analyses. Laboratory

tests and correlations from field tests have

been developed to quantify this parameter

and these can be used to select an appro-

priate K0 value for input in the soil-structure

interaction analysis. Further consideration

should be given to the variability of the value

of K0 within a stratum as it may be

influenced by local properties, such as soil

fabric, particularly in cohesionless material.

One of the next steps in the modelling

process is to determine whether the material

is likely to behave as undrained or drained.

This is a critical question as soil material may

behave very differently depending on the

assumption adopted. Undrained behaviour

does not allow for volume changes or the

dissipation of excess pore pressures, and,

therefore, this typically represents a short-

term response to loading/unloading. By

contrast, drained behaviour represents the

fully-equalised conditions where the pore

pressures remain at their in-situ stress state,

and this represents a long-term condition.

Most real soil materials are neither perfectly

drained nor perfectly undrained, but rather

behave somewhere in between, in a partially

drained state. However, depending on the

problem being analysed, employing an

assumption of drained or undrained

behaviour may be more or less valid. For

example, relatively impermeable clay is

likely to behave undrained in short-term

situations, where the stress conditions are

changed, such as basement excavations, but

the same clay may behave drained when

considering the slope stability of a 150-year-

old railway embankment.

The third assumption that needs to be

considered is the choice of constitutive

model and the appropriate stiffness

parameters for the soil within that model.

For example, the Mohr-Coulomb model,

which assumes a linear elastic relationship

up to a linear plastic failure criterion, is one

of the simplest material models available

and is controlled by a single Young’s

modulus which governs the soil stiffness.

This model does not consider the

nonlinearity of the soil material and the

reduction in soil stiffness as the strain level

increases. More advanced models, such as

the small strain hardening soil model, are

available, which capture three soil

behaviour regimes. Initially, an elastic, very

stiff soil response is observed in the small

strain region followed by a nonlinear

elasto-plastic response of the material in

the larger strain zone, and, finally, a fully

plastic response at soil failure. Most soils

exhibit some degree of stiffness anisotropy

between vertical and horizontal stiffness.

Therefore, the possible influence of

stiffness values in different directions

within a soil mass should also be

considered prior to deciding what

geotechnical investigation testing will be

carried out and what numerical analysis

will be completed.

Installation of flood defence works on the river bank Installation of masonry stone wall lining the flood relief channel

70 • DEEP FOUNDATIONS • JAN/FEB 2017 DEEP FOUNDATIONS • JAN/FEB 2017 • 71

A.

B.

C.

(A.) Initial failure points close to shaft wall toe, (B.) development of slip circle into the gravel aquifer and (C.) full base failure through heave of the soil over-lying the gravel aquifer

To achieve confidence in the accuracy of

the predictions of soil stresses and the

resulting soil movements that are

generated, it is critically important to

calibrate the soil model employed in any

numerical analysis. This calibration exercise

typically involves simulating a number of

laboratory and, possibly, field tests within

the FEM environment to determine a

synthetic soil response curve that can be

compared to the real experimental results.

The parameters are typically varied until a

reasonable match is achieved between the

laboratory and simulated soil test results.

This is an iterative process as the same

parameters are then used to simulate

additional laboratory experiments tested

under different conditions. The soil

material parameters are adjusted until a

reasonable match is seen with the full suite

of laboratory tests. This calibration exercise

can lead to improved understanding of the

advantages and disadvantages of different

constitutive models. Typically, as the

constitutive model becomes more complex,

the calibration time required to determine

each of the required parameters becomes

longer. A balance should always be struck

between introducing complexity to a FE

model and the accuracy of the output

required. This balance should be informed

by considering what the FE results will be

used for. For example, a nonlinear soil

model may be required to satisfy tight

movement criteria while underpinning a

structure that is sensitive to deformation,

whereas a linear soil model may suffice for

other applications where movement criteria

are less critical.

Case Study - Deep Access Shaft for Tunnel ConstructionGavin & Doherty Geosolutions (GDG) was

commissioned with the analysis of a series

of deep access shafts used to construct a set

of tunnels for a new sewer network under a

major North American city. The soil

stratigraphy consisted of interbedded

glacial till layers of silty clay with a range of

plasticity values. The clay layers were

underlain by an open gravel deposit, which

was also a high-pressure aquifer with

artesian conditions, and, therefore, base

heave blow-out at the bottom of the shaft

was a serious concern during construction.

The shafts, which ranged from 25 to 38 m

(82 to 125 ft) in depth, were constructed

using a secant piled starter wall over the

upper 18 m (59 ft) and a structural shotcrete

wall over the lower reaches of the shaft. In

the permanent condition, the base heave

would be resisted by a permanent concrete

however, three general assumptions

common to every soil-structure numerical

model are considered below.

One of the first steps in any soil-structure

interaction problem is to quantify the in-situ

stress regime, i.e., to determine what the

stresses are in the ground prior to con-

struction-induced changes to the stress

regime due to loading (e.g., foundations) or

unloading (e.g., basement excavation). The

in-situ stresses include the vertical and

horizontal stresses, as well as the pore pres-

sures. The vertical stresses can be derived

from the stratigraphy of the site and the

density of the various materials present;

however, the lateral effective stress is a much

more complicated parameter to quantify

accurately. The lateral effective stress is

influenced by the stress history and past

geological events, such as glaciation. A K0

parameter, which is the ratio of the vertical to

horizontal in-situ stress, is often used as an

input in numerical modelling software, and

this parameter can have a dramatic impact

on the results of FEM analyses. Laboratory

tests and correlations from field tests have

been developed to quantify this parameter

and these can be used to select an appro-

priate K0 value for input in the soil-structure

interaction analysis. Further consideration

should be given to the variability of the value

of K0 within a stratum as it may be

influenced by local properties, such as soil

fabric, particularly in cohesionless material.

One of the next steps in the modelling

process is to determine whether the material

is likely to behave as undrained or drained.

This is a critical question as soil material may

behave very differently depending on the

assumption adopted. Undrained behaviour

does not allow for volume changes or the

dissipation of excess pore pressures, and,

therefore, this typically represents a short-

term response to loading/unloading. By

contrast, drained behaviour represents the

fully-equalised conditions where the pore

pressures remain at their in-situ stress state,

and this represents a long-term condition.

Most real soil materials are neither perfectly

drained nor perfectly undrained, but rather

behave somewhere in between, in a partially

drained state. However, depending on the

problem being analysed, employing an

assumption of drained or undrained

behaviour may be more or less valid. For

example, relatively impermeable clay is

likely to behave undrained in short-term

situations, where the stress conditions are

changed, such as basement excavations, but

the same clay may behave drained when

considering the slope stability of a 150-year-

old railway embankment.

The third assumption that needs to be

considered is the choice of constitutive

model and the appropriate stiffness

parameters for the soil within that model.

For example, the Mohr-Coulomb model,

which assumes a linear elastic relationship

up to a linear plastic failure criterion, is one

of the simplest material models available

and is controlled by a single Young’s

modulus which governs the soil stiffness.

This model does not consider the

nonlinearity of the soil material and the

reduction in soil stiffness as the strain level

increases. More advanced models, such as

the small strain hardening soil model, are

available, which capture three soil

behaviour regimes. Initially, an elastic, very

stiff soil response is observed in the small

strain region followed by a nonlinear

elasto-plastic response of the material in

the larger strain zone, and, finally, a fully

plastic response at soil failure. Most soils

exhibit some degree of stiffness anisotropy

between vertical and horizontal stiffness.

Therefore, the possible influence of

stiffness values in different directions

within a soil mass should also be

considered prior to deciding what

geotechnical investigation testing will be

carried out and what numerical analysis

will be completed.

Installation of flood defence works on the river bank Installation of masonry stone wall lining the flood relief channel

Paul Doherty BE, Ph.D., C.Eng., is the managing

director of GDG, a specialist geotechnical engineering

consultancy in Dublin, Ireland, providing innovative

geotechnical solutions across a broad range of civil

engineering sectors. John O’Donovan Ph.D., C.Eng.,

MICE, a senior engineer leads the urban construction

sector at GDG specialising in the design of founda-

tions and basement structures and in the assessment

of ground movement on existing buildings.

plug at the bottom of the shaft, which was

also toed into the side walls using a shear

key type construction. While this concrete

plug provides resistance in the long term,

base heave was a significant concern

immediately after excavating to the final

depth, before the plug could be constructed

and the concrete achieve its maximum

compressive strength.

A 2D numerical model of the shaft was

developed that considered the soil layer

response and the stiffness of the structural

elements forming the shaft walls. The

model was calibrated using oedometer

tests, triaxial results and falling head

permeability experiments. Three separate

analyses were considered: (i) an undrained

type soil response, (ii) a drained soil

response and (iii) staged construction

considering all of the consolidation phases.

In the first analysis, which was relevant

to the short-term condition, the soil was

considered to behave undrained. This

analysis showed that immediately after

excavating to the base of the shaft, the

unloading of the soil created negative pore

pressures below the base. These negative

pore pressures can also be thought of as “soil

suctions,” and provide added stability to the

soil below the shaft, which ensured the shaft

was stable immediately after the excavation.

The second analysis considered the soil

to act as fully drained, and, therefore,

represented the soil condition following

dissipation of the excess negative pore

pressures. This analysis showed the shaft to

be completely unstable with the soil plug

heaving upwards and the shaft collapsing

as the failure surface intersected the gravel

aquifer, resulting in a catastrophic failure.

The final analysis, which was much

more complex, considered the time taken to

build the shaft and modelled the partially

drained consolidation during the construc-

tion process. Once the final dig was com-

plete, the analysis then considered the time

dependent change in the pore pressure

regime in the soil as the material transitioned

from undrained to drained conditions. This

analysis predicted the factor of safety as a

function of time following excavation to the

target base elevation. The development of

the failure mechanism was apparent and the

time to failure was shown to be in the order

of four months. This type of analysis allowed

a pragmatic construction programme to be

developed that relied on a relatively quick

construction of the base plug. A suite of

monitoring points was also established on

the shaft walls and base to allow the heave to

be assessed and compared with the predic-

tions to provide confidence in the residual

safety of the shaft at any moment in time.

Case Study - Flood Defence EmbankmentsThe Office of Public Works is responsible

for identifying urban areas in Ireland that

are at risk of periodic flooding, and, in one

such location, the local town and county

councils had developed a flood defence

scheme to protect life and property from

both severe high tides and river flooding

due to extreme rainfall events. GDG was

commissioned to complete the design of

the flood defences along a 500 m (1,640 ft)

long cul-de-sac to the north of a tidal stretch

of river and adjacent to a golf course that

has been identified for future development.

The defences that were required in this area

were a combination of flood walls to

contain the river and a flood relief channel

to relieve flood waters that may threaten a

nearby low-lying residential area.

The proposed design required a

reinforced concrete gravity retaining wall to

complete the flood defences. A detailed

hydrogeological analysis and numerical

seepage study was undertaken. GDG also

provided the designs for the relief channel

to alleviate flooding, for a road access to the

golf course, for the relocation of services and

for a pedestrian access from the nearby road

to an underpass at the adjacent rail line.

ConclusionsDespite the advancement of computing

power and the improved efficiency of

numerical modelling software, we must

remain diligent in our search for robust,

reliable and efficient engineering solutions.

These solutions are not driven by increased

computing power or user-friendly software

interfaces — they are provided by engineers

with relevant experience and a will to

dedicate time to critically think about

challenging problems. Real value is

provided when these traditional engi-

neering ideals are combined with the most

up-to-date numerical modelling capa-

bilities. A tradesman relies on their tools to

complete a job to a high standard and so

does a geotechnical engineer; however, the

final finish is driven by the engineer and not

the tools available to them. While numerical

model l ing sof tware has improved

dramatically, the final solution adopted for

construction should be one that recognises

(a) the underlying limitations of the

software, (b) the level of calibration, (c)

simplifications in the soil behaviour and

geometry that are modelled, and (d) the

experience of the user in analysing the

problem at hand. Engineering should always

be done by engineers and not computers!

Seepage analysis of the proposed flood defence system

72 • DEEP FOUNDATIONS • JAN/FEB 2017