Geotecnical Limit State Australian
Geotecnical Limit State Australian
Geotecnical Limit State Australian
Part II – Foundations
Patrick K. Wong
Coffey Geotechnics Pty Ltd, Sydney, Australia
Robert A. Day
Coffey Geotechnics Pty Ltd, Melbourne, Australia
Harry G. Poulos
Coffey Geotechnics Pty Ltd, Sydney, Australia
ABSTRACT
Part I of this paper provided the background to limit state design and some of the problems and
confusions associated with its use in geotechnical engineering, particularly for retaining structures.
Despite these difficulties, there is definitely a place for limit state design in geotechnical
engineering.
In this paper (Part II), the differences between Working Stress Design and Limit State Design (LSD)
for foundation engineering are briefly described, together with a description of the factored
resistance and factored strength approaches in limit state design. The benefits of limit state design
in foundation engineering are illustrated through a number of examples involving a footing on stiff
clay, a footing on medium strength rock, and a pile group.
The authors conclude that the use of limit state design in Geotechnical Engineering has benefits as
long as the underlying design principles and soil-structure interaction effects are properly
understood and communicated.
1 BACKGROUND
In engineering design, it is essential that a structure has a low probability of collapse under the
worst load combination. It is equally important that deflections are within tolerable limits under
normal operating conditions. Engineers use factors of safety in design to account for uncertainties
and approximations that have to be made on material properties, loads and methods of design
analysis.
Broadly speaking, factors of safety are applied in the following two methods of design:
Pw ≤ Ra (1)
Ra = Rug/FOS (2)
The Working Stress method is still widely used today; for example, a FOS of 3 is commonly used for
design of foundations and a factor of between 1.25 and 1.5 is commonly used for design of slopes
and dams.
Why then is there such a wide range of FOS, with a significantly higher FOS being used in building
foundations compared to slopes? It turns out that the FOS of 3 used in foundations is not really a
factor of safety on the strength of the foundation, but is a factor to limit the settlement based on
experience of most soils for which relatively stiff and linear behaviour will persist if the stress levels
are kept below about 1/3 their ultimate capacities (Atkinson, 2007). Understanding this principle is
important as it will later explain how more cost-effective designs can be achieved when the Limit
State Design approach is used for stiffer geotechnical elements.
Limit State Design (partial factors of safety approach):
The development and principles associated with limit state design have been discussed in Part I of
this paper. In brief, the Limit State Design approach in Geotechnical Engineering comprises two
parts:
The Strength Limit State requires that the following equation be satisfied under ultimate loading
conditions:
Rug* ≥ S* (3)
where: Rug* = design geotechnical strength
S* = design action effect under all ultimate load combinations
However, there are several ways in which the values Rug* and S* may be evaluated as described
below:
(a) Factored Resistance Approach (North American approach, but also used in Australia)
The ultimate capacity, Rug, is calculated without reduction of geotechnical parameters, and
the calculated geotechnical resistance is factored down to the design ultimate, Rug*, so
that:
(b) Factored Strength Approach (European approach, but also used in Australia)
The design ultimate capacity, Rug*, is calculated with partial reduction factors applied to
the geotechnical parameters so that:
In this paper, subscripts have been used for Rug and Rug* to distinguish the difference between the
different evaluation methods because they do not always produce the same results (e.g. where
different partial factors are used in pile shaft friction and end bearing pressure in Method (b)).
Further confusion is caused by the fact that the design action effect, S* may also differ dependent
on the way in which Rug* is calculated. For example, S* is equal to the factored up ultimate load on
a footing or an isolated pile foundation, and remains unchanged so long as S* is less than Rug*
regardless of which way Rug* is evaluated. However, this is not the case when S* is, for example,
the design action effect on a corner pile of a pile group under combined axial, lateral and moment
loading (see Section 3) or the resulting bending moment on a retaining wall (see Section 4).
The Serviceability Limit State requires that under the serviceability loading conditions, the resulting
deflection does not exceed the tolerable limit. The tolerable limit may be for the purpose of
meeting operational, durability, or aesthetic requirements as specified by the owner or designer.
Serviceability loads are generally a combination of unfactored dead load plus a reduced component
of the live load as specified in the Australian Loading Code AS1170.1 (1989). Because of the
possible reduction in the live load component, the design serviceability load is not necessarily the
same as the working load used in traditional working stress design method.
There is general agreement with designers that material parameters should not be reduced when
the serviceability limit state is being considered. However, Pells et al (1998) recommended that
the design elastic modulus for Sydney Sandstone and Shale be reduced by a factor of 0.75. The
authors of this paper are of the opinion that this reduction factor on elastic modulus is not
necessary; as long as a cautious approach has been adopted when selecting the elastic modulus
value based on test results or experience, and that any stress level dependency has been properly
considered (see Section 2.2 for example).
2 SHALLOW FOUNDATION
For this approach, the working load, Pw would be considered to be 600 + 200 = 800kN
The allowable bearing pressure, pa , and the required footing width, B, would be calculated using a
traditional FOS of 3, so that:
pa = (6 x Su + 1.0 x γ)/3.0 = 207kPa (8)
B = √(800/207) = 1.97m (9)
For this approach, the Strength Limit and Serviceability Limit States would be calculated as follows:
(a) Strength Limit State
S* = 1.2 x 600 + 1.5 x 200 = 1020kN (10)
Rug = (6 x Su + 1.0 x γ) x B2 = 620B2 kN (11)
Rug* = 0.65 x Rug = 403B2 kN (12)
B = √(1020/403) = 1.59m (13)
2.1.3 Discussions
It can be seen that for the example of a shallow footing on a stiff clay foundation, both working
stress and limit state design approaches result in a similar footing size of 2m. More importantly, it
can bee seen from Section 2.1.2 that the footing size is governed by the deflection criterion, and
not the strength of the foundation.
For this example, we will consider a pad footing founded on Class III Sandstone (Pells et al, 1998)
with the following parameters
(a) Dead load, DL = 9000kN
(b) Live load, LL = 3000kN
(c) Partial load factor on DL, ψD = 1.2
(d) Partial load factor on LL, ψL = 1.5
(e) Live load reduction factor for serviceability assessment = 0.4
(f) Allowable bearing pressure = 6000kPa
(g) Ultimate bearing pressure = 35MPa
(h) Young’s modulus of rock mass, ER = 1000MPa
(i) Geotechnical strength reduction factor, Φg = 0.75
(j) Find required footing size so that settlement ≤ 10mm
For this approach, the working load, Pw would be considered to be 9,000 + 3,000 = 12,000kN
The required footing size, with the expectation that settlement would be less than 1% of the footing
width (Pells et al, 1998) is:
For this approach, the Strength Limit and Serviceability Limit States would be calculated as follows:
(a) Strength Limit State
S* = 1.2 x 9,000 + 1.5 x 3,000 = 15,300kN (18)
Rug = 35,000 x B2 kN (19)
Rug* = 0.75 x Rug = 26,250 x B2 kN (20)
B = √(15,300/26,250) = 0.763m (21)
2.2.3 Discussions
It can be seen that for the example of a pad footing on a medium strength sandstone foundation,
deflection is also the governing case but this time the footing size assessed using the lmit state
design method is significantly smaller than that assessed using the working stress method (i.e.
0.92m compared with 1.41m). The serviceability bearing pressure of about 12MPa assessed for the
smaller footing is only slightly more than 1/3 of the ultimate bearing pressure of the rock, and
unlike soils, yielding of competent rock is not expected to occur until much closer to the ultimate
bearing pressure. Therefore, the solution found using the limit state method is considered to be
acceptable and results in a more cost-effective design.
3 PILE FOUNDATION
For an isolated single pile foundation, the use of a limit state design approach in recent years has
enabled designers and contractors in Australia to achieve more cost-effective solutions in a similar
way as that discussed in Section 2.2, particularly for continuous auger piles or bored piles socketed
in rock. Ultimate end bearing pressures of greater than 30MPa are nowadays frequently used in
design of piles socketed into low to medium strength shale and sandstone, and with settlements of
less than 15mm.
On the other hand, there is still some confusion, and opinions are divided, amongst geotechnical,
structural engineers, and government authorities regarding the appropriate use of limit state design
approach for pile groups under combined axial, lateral, and moment loading. This is a common
problem for bridge pier foundations and is illustrated using the following example:
(a) Group of 3 x 3 driven precast 400mm square piles at 1.5m grid spacing driven through 15m
of stiff clay and socketed 1m into weathered rock and terminating in low strength rock
(b) The soil and rock properties as summarised in Table 1.
(c) Ultimate axial load = 22.5MN
(d) Ultimate lateral load = 1.0MN
(e) Ultimate moment = 9MNm
(f) Geotechnical strength reduction factor, Φg = 0.7 (assuming sufficient dynamic load tests
with signal matching would be carried out to assess Rug)
Table 1 – Soil and Rock Properties Used in Pile Group Example (Driven Piles)
Elastic Modulus (MPa) Ultimate Ultimate Ultimate
Axial Lateral shaft end lateral yield
Depth Material friction bearing pressure
(m) fs (kPa) pressure fy (kPa)
fb (kPa)
0 to 15 Stiff clay 20 14 50 - 200 to 900(1)
15 to 16 Very low strength rock 100 70 200 - 3,000
16 to 20 Low strength rock 1,500 - - 20,000 -
>20 Medium strength rock 2,500 - - - -
(1) fy varies linearly from 200kPa at top of pile to 900kPa at 2m below top of pile
Analysis of the above pile group example has been carried out using the computer program DEFPIG
developed by the University of Sydney (Poulos, 1980). Two sets of analysis were carried out – (Case
1) without and (Case 2) with the application of geotechnical strength reduction factors to the shaft
friction, end bearing pressure, and the lateral yield pressure. The results of the pile group analyses
are presented in Table 2.
4 CONCLUSIONS
From the examples given in this paper, the authors conclude that the use of Limit State Design in
Geotechnical Engineering has the following benefits as long as the underlying design principles and
soil-structure interaction effects are properly understood and communicated:
(a) Partial factors can be varied to take account the different levels of uncertainties in design.
(b) Strength and deflections criteria are clearly separated and if nothing else, should make the
designer think more carefully about the meaning of factors of safety (i.e. are they for
strength or deflection control?).
(c) Provide the ability to optimise the design of foundations based on satisfying both strength
and serviceability criteria rather than lumping these together as used in the traditional
working stress approach.
(d) For pile groups under combined axial, lateral and moment loading, the combined use of
factored strength and factored resistance methods can be used effectively to optimise the
design and testing of piles.
REFERENCES
Atkinson, J.H. (2007) The Mechanics of Soils and Foundations, 2nd Edition, Taylor and Francis (pub).
AS1170.1-1989 SAA Loading Code - Dead and live loads, Standards Australia International Ltd
AS2159 – 1978 SAA Piling Code, Standards Association of Australia
AS2159 – 1995 Piling - Design and Installation, Standards Australia International Ltd
Pells, P.J.N. Mostyn, G. and Walker, B.F. (1998) Foundations on Sandstone and Shale in the Sydney
Region, Jnl and News of the Australian Geomechanics Society, Vol. 33, Part 3, 17-29.
Poulos, H.G. (1980) User Guide to DEFPIG – Deformation Analysis of Pile Groups, School of Civil
Engineering, University of Sydney.