HKIE Transactions, 2014
Vol. 21, No. 1, 35–49, http://dx.doi.org/10.1080/1023697X.2014.884968
Effects of stiffness nonlinearity on E standard penetration test N correlations for analysing
wall deflections in Hong Kong excavations
C.W.W. Nga , A.K. Leunga∗ , S.S.K. Kwokb and F.H.T. Yipb
a Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Hong Kong, People’s
Republic of China; b Housing Department, The Government of the Hong Kong Special Administrative Region, Hong Kong, People’s
Republic of China
(Received 31 October 2012; accepted 8 March 2013 )
Soil stiffness is one of the vital soil parameters governing lateral wall movements of an excavation. For the design of
excavation and lateral support (ELS) works in Hong Kong (HK), it is a common practice to idealise soil as an elastic
material, whose stiffness is characterised by a constant called Young’s modulus (E ), that is then empirically correlated
to uncorrected standard penetration test (SPT) N values through a correlation factor, f . Although soil stiffness is well
recognised to decrease with an increase in strain nonlinearly, most existing E – SPT N correlations do not consider
stiffness nonlinearity explicitly. In order to account for the influence of strain non-linearity on soil stiffness, 2 new sites
were instrumented and monitored, and 12 other relevant case histories in HK were interpreted and back-analysed by using
FREW and Plaxis 2D. It is revealed and verified that reduction of soil stiffness with an increase in strain can be correlated
with an increase in final excavation depth (Hf ). This is because an increase in Hf mobilises larger soil strains to result in a
decrease in soil stiffness. For practical purposes, some moderately conservative Hf – dependent E – SPT N correlations
are established for fill and completely decomposed granite and they are verified with independent field measurements.
Keywords: soil stiffness; nonlinearity; excavation; wall deformation; E – SPT N correlation; decomposed granites
Background
In urban areas of major cities like Hong Kong (HK) where
the costs of land are relatively high, multi-propped excavations for underground facilities are often in demand.
Figure 1 shows a typical multi-propped excavation in HK
and typical profiles of wall and ground deformations. The
definitions of some key parameters are shown, including
(i) final excavation depth, Hf ; (ii) intermediate excavation
depth, Hi ; (iii) average prop spacing, h; (iv) maximum
lateral wall displacement, δhm and (v) maximum ground
surface settlement behind the wall, δvm . Lateral deformation of retaining wall associated with excavation is always
one of the major concerns for practitioners to design
against serviceability limit state. It has been identified that
lateral wall movement is generally governed by six major
factors, namely (i) soil type and its properties such as stiffness; (ii) depth and geometry of excavation; (iii) types and
stiffness of lateral support systems; (iv) construction methods like top-down or bottom-up; (v) construction practice
such as workmanship and (vi) groundwater conditions like
elevation of groundwater table.[1–3]
It is well known that soil stiffness is not constant
but it is affected by many factors such as stress level,
strain level, stress history and stress path.[4,5] Figure 2
∗ Corresponding author. Email: a.leung@dundee.ac.uk
© 2014 Taylor & Francis
shows laboratory-measured relationships between normalised secant shear stiffness (Gsec /p , where p is mean
effective stress) and shear strain for saturated fill and
completely decomposed granite (CDG) specimens that
were sampled from Kwai Shing circuit (KSC) and
Kowloon Bay [6] in HK. Shear strain is defined as twothird of the difference between axial and radial strain
under triaxial loading condition. At very small strains
(<0.001% [7]), the shear modulus is assumed to be elastic, Gmax . For an isotropic elastic material, the relationship
between effective Young’s modulus (E ) and Gmax can be
expressed as:
Gmax =
E
,
2(1 + v )
(1)
where v is the Poisson ratio. As shown in Figure 2,
Gsec /p values of both fill and CDG reduce from their
maximum values (i.e. Gmax /p ) at 0.001% of shear strain to
low values nonlinearly. The range of strain, where Gsec /p
reduces significantly, lies within the typical strain range
for excavations in medium and dense soils like CDG.[8,9]
Similar stiffness reduction curves of other HK soils including completely decomposed tuff and rhyolite are also
observed.[5,10]
36
C.W.W. Ng et al.
where f is a constant correlation factor. Based on backanalyses of measured wall deflections, f -values reported
in the three local documents range from 0.8 to 2. Chan
[12] carried out back-analyses for seven selected deep
excavations in HK (Hf ranging from 12 to 34 m) and
recommended that f -values for fill, alluvium and marine
deposit (MD) are 1.5, while that for CDG is 2.0.
Although many f -values have been stated in the literature, they were back-analysed mainly from case histories
having deep Hf . It is expected that an excavation having deeper Hf would have caused greater stress relief and
hence larger shearing of soil behind a retaining wall. Since
larger induced shear strain would lead to greater mobilisation of E (refer to Figure 2), a lower f -value would
be resulted. Obviously, the use of low f -values in design
would be expected to over-predict wall deflections for
shallow excavations substantially. This is because lower
degree of soil strains and hence higher E can be mobilised
in relatively shallow depths. The use of a single constant
f -value in existing correlations is thus unable to capture
different degrees of mobilisation of E for excavations
having different Hf .
The objective of this paper is to propose some
new E – SPT N correlations which take into account
the stiffness nonlinearity explicitly. Two new excavation sites in HK are selected for instrumentation
and monitoring wall deflections during constructions.
Back-analyses are conducted for the two instrumented
sites and some other relevant case histories using
two softwares, FREW [13] and Plaxis 2D, which are
both pre-accepted by the Buildings Department (BD).
By investigating any correlations between excavation
d
dvm
Hi
h1
Hf
h2
h3
dhm
Average prop spacing
N
h=
 hi
i=1
N
Figure 1. Typical profiles of wall and ground deformations for
multi-propped excavation and definition of parameters used in
this study (modified from Clough and O’Rourke [17]).
Despite the complex soil-structure interaction involved
in an excavation and highly nonlinear behaviour of soil,
it is a common practice to idealise soil as an elastic material, whose stiffness is characterised by a constant E and
empirically correlated it to uncorrected standard penetration test (SPT) N values in HK for the design of excavation
and lateral support (ELS) works. Three local documents,
GCO,[1] GEO,[2] and GEO,[11] summarise some empirical E – SPT N correlations, which are generally expressed
as follows:
E = f · N (MPa),
(2)
3500
Gmax/p'
Fill-B-F3 (p' = 27 kPa)
CDG-KS34-1 (p' = 30 kPa)
3000
Upper bound (Ng et al. 2000)
Lower bound (Ng et al. 2000)
Lab test on fill and CDG
from Kwai Shing Circuit
Lab test on CDG
from Kowloon Bay
Gsec/p'
2500
Typical strain range for retaining walls
Mair (1993); Ng and Lings (1995)
2000
1500
1000
Very small
strain range
Large strain
range
Small strain range
500
0
0.0001
0.001
0.01
0.1
1
10
Shear strain, eq(%)
Figure 2. Laboratory-measured stiffness reduction curves for saturated fill and CDG sampled from KSC and Kowloon Bay [6] in HK.
Notes: Gsec denotes secant shear modulus; shear strain εq is defined as two-third of the difference between axial strain εa and radial
strain εr (i.e. 2(εa − εr )/3) under triaxial loading condition.
HKIE Transactions
(a)
(b)
0
0
5
(c)
SPT N value
SPT N value
25 50 75 100 0
(d)
SPT N value
(f)
SPT N value
(g)
SPT N value
25 50 75 100 0 25 50 75 1000 10 20 30 40 50 0 10 20 30 40 50 0 20 40 60 80100 0
Fill
CDG
(e)
SPT N value
Fill
25 50 75 100
Fill
Fill
MDG
Depth (m)
SPT N value
Fill
Fill
10
CDG
37
CDV
MD
Fill
15
MDG
CDG
20
MDG
AL
MDV/SDV
MDG
25
Measured SPT N value
Linear regression
N95L profile
Figure 3. Geological profiles and SPT N profiles of the two newly instrumented HA sites (a) KSC; (b) SUK and five past HA sites;
(c) HHE; (d) SCR; (e) TTE; (f) CWR and (g) ECW.
depth and E values that were back-analysed, new
E – SPT N correlations are established for fill and CDG
and they are then verified by field measurements. It is
recognised that the use of E – SPT N correlations to analyse wall deflection greatly simplifies the complexity of
soil-structure interaction involved in ELS works. However, it is unrealistic and not the intention to address all
complex soil-structure interaction problems in this paper
since simplicity is intended to be preserved as much as
possible for practical designs in HK.
Categorisation of collected case histories
In order to carry out detailed analyses and to develop new
E – SPT N correlations, two new sites in Kwai Chung
and Sham Shui Po from Hong Kong Housing Authority
(HA), namely KSC, and So Uk site Estate (SUK), were
instrumented for monitoring both lateral wall displacement profiles and ground surface settlements. In addition,
five past HA’s sites in Hung Hom, Chai Wan, Sham Shui
Po, Wong Tai Sin and Kowloon Bay, namely Hung Hom
Estate (HHE), Ex-Chai Wan Estate (ECW), Sai Chuen
Road (SCR), Tung Tau Estate (TTE) and Choi Wan Road
(CWR), were collected. However, only ground settlement
data and SPT N profile are available in these five cases.
Figure 3 shows the ground profiles for the seven HA’s
cases. Similar mixed geological conditions were identified
in all cases (except TTE), comprising successive layers of
fill, MD, and/or alluvium (AL), and/or decomposed granites or volcanic. The Hf of the seven HA’s cases range from
4 to 7.5 m. In all seven cases, relatively soft walls such as
sheet-pile wall (i.e. flexural stiffness of ∼104 kNm2 /m)
were adopted and the bottom-up construction method
was employed. In all seven HA’s sites, no grouting and
hydraulic cut-off were used to control seepage. Other
details of each HA’s case are summarised in Table 1.
Leung and Ng [3] and Chan [12] have collected 15 nonHA’s deep excavation case histories in HK. Among the 15
collected cases, eight of them (i.e. cases CS, DC-I4, DCI6, HS-QR, HS-DV, EH, FW and LWH; refer to Table 1)
documented relevant information including geological
and groundwater conditions, SPT N profile, construction
method and sequence, the ELS system adopted and field
measurement on lateral wall displacement at Hf . Similar to
the seven HA’s cases, typical mixed geological conditions
were identified in all the 15 non-HA’s cases. Except EH,
the 14 non-HA’s cases have Hf deeper than 16 m. In these
14 case histories, stiff walls such as diaphragm wall were
adopted and the top-down construction method was used.
The flexural wall stiffness is about two orders of magnitude higher than that in HA’s cases. For case EH, the Hf is
12 m and a softer sheet-pile wall was used. The bottom-up
construction method was employed. Other details of the
15 non-HA’s cases are summarised in Table 1.
A categorisation method was proposed by Leung and
Ng [3] to divide HK case histories into two groups based
on SPT N values at half of Hf : N ≤ 30 (Group A) and
N > 30 (Group B). According to GEO,[14] coarse materials with N values less than and more than 30 are classified
as loose and dense, respectively. The N value of 30 was
thus used to differentiate wall deformation characteristic of excavations in loose and dense grounds. Based on
this categorisation method, there are 17 and five cases
belonging to Groups A and B, respectively (see Table 1).
In order to take the effects of Hf , wall stiffness and construction method into consideration, it may be logical and
reasonable to further divide case histories in each Group
into two sub-groups. For Hf shallower than 16 m, using
wall types with stiffness softer than 104 kN/m2 /m and the
bottom-up method, they are categorised as “softer” subgroup. On the contrary, cases belong to “stiffer” sub-group
when Hf are deeper than 16 m, used wall types stiffer
than 106 kN/m2 /m and adopted the top-down method.
38
Table 1.
Some detailed information of the 22 collected non-HA’s and HA’s excavation case histories in HK.
Construction
method
Excavation
depth, Hf (m)
Groundwater
table (m depth)
Wall type
Wall stiffness,
Ew I (kNm2 /m)
Average prop
spacing, h (m)
δhm
(mm)
δvm
(mm)
Reference
6.5
4.1
40
15
24
3
Davies and Henkel [34]
Chu et al. [16]
79
86
50
30
24
N/A
Lui and Yau [19]
Chan [12]
Humpheson et al. [35]
Group A (SPT N ≤ 30 at Hf /2)
“Stiffer” sub-group
Chater Station (CS)
Cheung Sha Wan
(CSW)
Dragon Centre (DC)-I4
Dragon Centre (DC)-I6
Hong Kong Station
(HKS)
HSBC Headquarters
Queen’s Road
(HS-QR)
HSBC Headquarters
Des Voeus Road
(HS-DV)
Sheung Wan Crossover
(SWC)
Site Q
Top-down
Diaphragm wall
4.6 × 106
26
14
2.5
1.5
27
27
23
1.5
1.5
4
9.0 × 106
5
5
4.6
16
2
2.7 × 106
5.3
30
10
18
3
5.3
42
20
32
1
2.9
20
N/A
Fraser [37]
18.6
3
4.6
N/A
16
Chan et al. [38]
27.5
N/A
N/A
1
Walsh and Fung [36]
Data from HA
4.6 × 106
“Softer” sub-group
Evergreen hotel (EH)
Hung Hom Estate
(HHE)
Sai Chuen Road (SCR)
Tung Tau Estate (TTE)
Ex-Chai Wan Estate
(ECW)
Choi Wan Road
(CWR)
Kwai Shing Circuit
(KSC)
So Uk (SUK)
Bottom-up
Argyle Station (AS)
Festival walk (FW)
Luen Wo Hui (LWH)
Site P
Wong Tai Sin Station
(WTS)
Top-down
Sheet-pile wall
3.4 × 104
2
2.5
0.65a
2.73a
2.3
Solider pile
7.7 × 104
1.7 × 104
9 × 104
1.7
(Single prop)
(Cantilever)
3
3
5
4.9
2.4a
Sheet-pile wall
1.75 × 104
1.1
2
4
1a
Pipe pile wall
9 × 103
1.5
7.3
1
5
6
(Single anchor)
15
1
25
32
17
13.6
18.7
Ground surface
11
4
2
Ground surface
3.6
4.6
4.2
3.4
4.7
43
45.5
24
N/A
24
N/A
8
6
2
N/A
12
7.5
2
2.5
6.2
4.2
4.5
a Piezometer installed was at least 30 m away from the excavation area.
1.46 × 104
Group B (SPT N > 30 at Hf /2)
“Stiffer” sub-group
Secant pile wall
Diaphragm wall
3.5 × 106
4.6 × 106
2.1 × 106
Morton et al. [39]
Wang [18]
Leung [40]
Chan et al. [38]
Morton et al. [39]
C.W.W. Ng et al.
Site
HKIE Transactions
Nevertheless, it is identified that mobilisation of shear
strain, and hence stiffness, of soil may not be influenced
by the flexural stiffness of braced wall (ranging within
four orders of magnitude between sheet-pile and concrete
diaphragm walls) based on 110 case histories documented
worldwide.[15] Among the 17 case histories in Group A,
eight of them (all the seven HA’s cases and case EH)
are classified as “softer” sub-group, while in Group B,
all cases are classified as “stiffer” sub-group. Since there
are limited case histories in Group B (i.e. 5) and only two
of them (i.e. FW and LWH) have relevant information for
conducting detailed analyses, any E – SPT N correlation
is not derived for Group B in this paper.
Observed deformation characteristics of HK
excavations
Figure 4(a) correlates Hf with measured δvm values for 14
out of 17 cases in Group A. Correlations for the three cases
HKS, SWC and EH are not shown because δvm values are
not available. For the seven non-HA cases belonging to the
“stiffer” sub-group, δvm increases with an increase in Hf
generally. For case CSW, a small δvm of 3 mm was recorded
Maximum ground displacement, dvm (mm)
(a)
50
40
CS
CSW
DC-I4
"Stiffer" sub-group
DC-I6
(non-HA project)
HS-QR
HS-DV
Site Q
Lower and upper bounds-non HA
Average-non HA
HHE
ECW
SCR
"Softer" sub-group
TTE
(HA project)
CWR
KSC
SUK
Lower and upper bounds-HA
Average-HA
Clough and O'Rourke (1990) (Sand)
30
20
10
(Grout-treated ground)
0
0
5
10
15
20
25
30
35
40
45
50
Two newly instrumented sites
(b)
Final excavation depth Hf (m)
Figure 4. Correlations between (a) Hf and δvm and (b) δvm and
δhm for some case histories in Group A.
39
due to increased ground stiffness by grout treatment.[16]
Excluding this unusual case, the mean δvm /Hf for nonHA cases is 0.12%. The peak δvm /Hf in HK excavation
(i.e. 0.15%) is one half of that observed in similar excavations in sandy materials worldwide (i.e. 0.3% [17]). For
the seven HA’s cases belonging to the “softer” sub-group,
δvm /Hf values vary widely from 0.01% to 0.11% with
a mean value of 0.06%. The mean δvm /Hf of 0.06% is
unusually small since it is only one-fifth of that observed
from similar excavations in sandy materials worldwide
(i.e. 0.3%).
Figure 4(b) correlates δhm with δvm for eight cases
including CS, CSW, DC-I4, DC-I6, HS-QR, HS-VR, KSC
and SUK in Group A. Correlations of δhm − δvm for the
other nine cases are not shown since δhm and/or δvm is/are
not reported. Excluding case CSW, the mean δhm /δvm of
the five non-HA cases, which belong to the “stiffer” subgroup, is found to be 2.53. On the contrary, relatively
large δhm /δvm values of 7.5 and 15 are found for the two
newly instrumented HA sites KSC and SUK (“softer” subgroup), respectively. When compared with the overseas
measured mean δhm /δvm derived from up to 30 excavations
using similar construction methods in sandy materials
retained by sheet-pile walls worldwide (i.e. 1.33 [17]),
local measured δhm /δvm values are considerably higher.
This appears to be physically impossible to have unusually small settlement but to have large wall movements. It
should be pointed out that it is not uncommon to observe
settlement markers installed on road pavements in some
excavation sites in HK. Thus, observed small δvm values
in Figure 4(a) and large δhm /δvm values in Figure 4(b) are
not surprising in HK excavations.
Numerical analyses for developing new E -SPT N
correlations
Analysis plan and procedures
In order to develop new E – SPT N correlations, four
series of numerical analyses were conducted by using
FREW and Plaxis 2D. In FREW, a plane-strain ELS
system is analogous to a classical “beam on elastic foundation” but in the vertical plane. A retaining wall is modelled
as an elastic vertical beam joined by a series of nodes,
and soil on each side of the wall is connected to these
nodes. Only horizontal force can be transmitted between
the soil and wall. At each stage of excavation, three stiffness matrices are assembled; one represents the wall for
bending, while the other two represent soil on each side
of the wall. Soil mass is modelled as an “elastic block”
and the behaviour of each “elastic block” is represented
by a flexibility matrix that is pre-calculated from finite
element (FE) calculations.[13] Each “elastic block” is discretised into 101 elements in height, while the length of
each “elastic block” is divided into a series of unequal
elements, which increase in length away from the vertical
40
C.W.W. Ng et al.
Table 2.
A summary of the analysis plan.
δhm
(mm)
23a
14a
13a
19a
15a
31a
19a
17a
25a
20a
1
HHE
ECW
TTE
SCR
CWR
To back-analyse
f -values based
on deduced δvm
through overseas
correlations [17]
7.5
4.5
4.2
6.2
4.9
KSC
SUK
DC-I6
To back-analyse
f -values based
on measured wall
deflections
4
5
6.5
15.5
1
To explore any major
difference in backanalysed f -values
using FREW and
Plaxis
DC-I6 To correlate mobilised
shear strain and
shear modulus with
excavation depth
7.5
27
23
30
27
0.5 m depth
(measured)
Refer to Lui and Yau [19] and Wang [18] Plaxis 2D
DC-I6 To verify newly
proposed E – SPT
N correlations
12
At surface
(assumed)
FREW
3
4
HHE
DC-I4
GWT
δvm
(mm)
Case
2
Objective
Excavation
depth (m)
Series
At surface
(assumed)
Software
FREW
7.3
15
Refer to Wang [18]
31
79
Plaxis 2D
21
aδ
vm and δhm for the five HA’s projects are deduced by using overseas δvm /Hf of 0.3% and δhm /δvm of 1.33.[17]
wall. A unit horizontal force would apply to each element
attaching to the wall. The horizontal displacements at all
nodes due to this unit load would then be calculated and
stored as flexibility coefficients in the flexibility matrix.
By the principle of superposition, the total horizontal displacements at all nodes due to any load combination would
be estimated. The stiffness of soil is then determined by
inverting this flexibility matrix. More detailed descriptions
of the theoretical background and method of analysis of
FREW are given in Pappin et al.[13]
Series 1 aims to back-analyse f -values for the two
newly instrumented HA’s cases, the five past HA’s cases
and case DC-I6 using FREW. Since wall deflections for
the five past HA’s cases (i.e. HHE, SCR, TTE, ECW and
CWR) are not available for back-analysis, overseas correlations derived by Clough and O’Rourke [17] were used
to deduce δhm . By using overseas δvm /Hf of 0.3% and
δhm /δvm of 1.33, the deduced δhm values for cases HHE,
SCR, TTE, ECW and CWR are 31, 25, 17, 19 and 20 mm,
respectively. Since lateral wall displacements deduced by
overseas correlations are higher than those by local correlation, more conservative (i.e. lower) soil stiffness would
thus be back-analysed. For the two new HA’s cases, KSC
and SUK, measured wall deflections were back-analysed.
For case DC-I6, field-measured wall deflections at two
Hi s, 6.5 and 15.5 m (documented in Wang [18]), were
selected for back-analyses. Wall movements at other Hi s
were reserved for verifying new E – SPT N correlations
in Series 4. In each case, an appropriate f -value is obtained
by matching measured/deduced δhm with predicted one at
final snapshot at Hf as close as possible. Other details of
the analysis plan are summarised in Table 2.
In Series 2, back-analyses of two selected cases HHE
and DC-I4, which belong to “softer” and “stiffer” subgroups, respectively, were repeated using another BDapproved software, Plaxis 2D. This aims to explore any
major difference of f -values that were back-analysed
between FREW and Plaxis 2D. The analysis procedures
of each case were identical to those in Series 1.
In Series 3, a plane-strain FE analysis was performed
to explore any correlation between excavation depth
and mobilised shear strain for soils behind a retaining
wall using Plaxis 2D. Case DC-I6, which is a typical
multi-propped deep excavation, was selected for analysis
because it has a comprehensive set of relevant information and field data including SPT N profile, groundwater
table (GWT) and wall deflections.[18,19] It should be
noted that wall deflections for cases DC-I4 and DC-I6
were measured at the same site of Dragon Centre but
from two different inclinometers, I4 and I6.[19] By using
an advanced soil model (i.e. Hardening Soil model with
small-strain stiffness (HSS)), which can capture nonlinear
HKIE Transactions
strain-dependent stiffness observed in laboratory tests
(Figure 2), mobilised shear strain at each intermediate
excavation stage was computed and then correlated with
excavation depth. The analysis procedures were identical
to those described by Wang.[18]
In Series 4, four analyses were conducted to verify new
E – SPT N correlations developed later. Field-measured
wall deflections at two other Hi s, 12 and 21 m (documented in Wang [18]), were selected for evaluating new
correlations for “softer” and “stiffer” sub-groups, respectively. Other details of the analysis plan are summarised
in Table 2.
Ground and groundwater conditions, SPT N profile
and FE mesh
For cases KSC, SUK and HHE (Figure 3(a)–(c)), similar ground conditions are found, consisting of successive
strata of fill, CDG and moderately decomposed granite
(MDG). Based on limited SPT N data, a mean N profile is
determined using the ordinary least squares method. For
case KSC, the mean N value increases from 5 near the
ground surface to 50 at the surface of MDG stratum generally. For cases SUK and HHE, the mean N profiles are
uniform in fill. A linear increase of N value is observed
in CDG. Readings from piezometers show that GWTs for
cases KSC, SUK and HHE were located at 1, 6 and 2.5 m
depths, respectively. It should be noted that the piezometer in case KSC was installed at about 30 m away from
excavation.
For case SCR (Figure 3(d)), relatively thick layers of
soft materials including fill, MD and AL were encountered. Although mean N values are considerably scattered,
they appear to be constant in the top 15 m of the ground.
There is a slight increase of mean N values in the AL layer
up to 20 m depth. A piezometer located at least 30 m away
from excavation recorded that GWT was at 0.65 m depth.
As shown in Figure 3(e), a thick layer of fill was identified up to a depth of 25 m in case TTE. A uniform mean
SPT N profile is observed in the top 15 m generally but
there is a linear increase of N values below 15 m depth.
A piezometer located at least 30 m away from excavation
recorded that GWT was at 2.73 m depth. For case CWR
(Figure 3(f)), an 11 m-thick fill stratum overlies an MDG
stratum. Based on limited N data, a uniform distribution of
mean N value is approximated. According to a piezometer located at least 50 m away from excavation, GWT was
identified at 2.4 m depth. For case ECW (Figure 3(g)),
the ground conditions are different from other HA’s cases
where layers of decomposed volcanic, instead of granite,
were underlain by a 4 m-thick fill stratum. The mean N
profile increases from 10 at the ground surface to about
100 at 10 m depth in the CDV stratum. Based on readings
obtained from a piezometer installed at about 5 m away
from excavation, GWT was identified at 2.3 m depth. It
41
should be noted that there are exiting pile foundations at
20 m (i.e. 2.67 Hf ), 27 m (i.e. 6.0 Hf ), 18 m (i.e. 2.90 Hf ),
28 m (i.e. 6.67 Hf ) and 60 m (i.e. 12.2 Hf ) behind retaining
walls in cases HHE, ECW, SCR, TTE and CWR, respectively. Since these distances are well beyond the influence
zone of HK excavations that were identified by Leung and
Ng [3] (i.e. d > 2.5 Hf ), any stiffening effect of pile groups
on ground mass behind each retaining system can thus be
neglected.
Obviously, different choices of SPT N profiles from
a set of N data would lead to different E back-analysed.
In order to derive moderately conservative E – SPT N
correlation(s), a lower bound of 95% confidence interval
of mean N value (N95L ) is determined for each case history
using the statistical method. N95L profile means that for a
given set of SPT N data, there is 95% of probability for
N data to be higher than N95L . The approach adopted is
consistent with that suggested in Eurocode (EC) 7 [20]
and CIRIA report 185.[21] Since actual GWTs adjacent
to retaining walls in four of the seven HA’s cases are not
known (i.e. KSC, TTE, SCR and CWR), it would be on
the conservative side to assume that GWTs were located
at the ground surface in back-analyses of all the seven
cases in Series 1 and 2. Since vertical distributions of porewater pressure along depth during excavation in all seven
HA’s cases are not available, the hydrostatic pore-water
pressure distribution was assumed in the designs of all
seven HA’s cases and also in each analysis in Series 1
and 2.
For analysis in Series 3, the FE mesh adopted in case
DC-I6 are shown in Figure 5. By taking the advantage of
plane of symmetry, only one half of the excavation was
simulated. As shown in the inset of the figure, the ground
consists of a layer of fill, MD, CDG and a thick MDG stratum. The mean N values are distributed quite uniformly in
the top 15 m and then increase to about 200 before reaching the bedrock. For retaining a 27 m-deep excavation, the
top-down method was adopted and a 1.2 m-thick concrete
diaphragm wall was constructed in conjunction with five
levels of concrete basements. According to piezometers
installed adjacent to the wall, the main GWT at 1.5 m
depth was specified before excavation at both retained
and excavated sides. Since toe grouting was carried out
at the concrete diaphragm wall to control seepage during
construction,[19] the hydrostatic pore-water pressure distributions were assumed both inside and outside of the
excavation at each construction stage.
Input parameters for soil, wall and prop/tie-back
When conducting analyses using FREW in Series 1 and 4,
effective cohesion c (i.e. shear strength attributed to bonding), effective friction angle φ , Poisson ratio v and E for
each soil type are needed. In both series of analyses, all
soil types were assumed to reach a critical state. Mobilised
42
C.W.W. Ng et al.
Plane of symmetry
Diaphragm wall
0
B/F
A
B1/F
SPT N value
100 150 200
0
Fill
Fill
5
MD
B2/F
50
MD
10
15
B4/F
B
CDG
Formation level
Depth (m)
B3/F
20
CDG
25
30
35
40
Bedrock
45
50
Measured SPT N value
MDG
Linear regression
N95L profile
Figure 5. FE mesh and SPT N profile adopted for analysing case DC-I6 (Series 3).
Note: Two soil elements A and B are taken to evaluate mobilised shear strain and shear modulus in Figure 6.
Figure 6. Correlations of mobilised shear strain and
normalised Gsec /p with excavation depth.
friction angle at the critical state φcs
for each soil type was
taken from HA design reports, while effective cohesion
was specified as a small value of 0.1 kPa to prevent any
numerical instability. The profile of E value was deduced
by multiplying f -values to mean N or N95L profile. For all
analyses in Series 1 and simulation using new correlation
in Series 4, the N95L profile was used. When the existing
correlation (Equation (2)) was used in Series 4, the mean N
profile was adopted. As revealed from test results reported
by Wang and Ng,[22] v value of CDG was estimated to
be 0.17. For simplicity, v of all other materials in each
case was assumed to be the same. Table 3 summarises the
input parameters.
For each soil type, the coefficient of earth pressure at
.[23] It is recognised
rest (K0 ) is estimated by 1 − sin φcs
that K0 of residual soil can be affected by various factors such as soil type, overconsolidation ratio, wall type,
wall installation methods [24,25] and also the degrees of
weathering process which lead to decreases in unit weight,
strength and stiffness.[26] Since there is a lack of reliable
in situ meaurement of K0 values and initial stress (prior
to excavation) in the ground, the Jaky equation, which
is commonly used for conservative estimation of K0 of
residual soils and saprolites in HK practical designs,[1]
was adopted for back-analysis purpose. For coefficients
of active (Ka ) and passive (Kp ) pressure, they were estimated using the Coulomb’s theory, which considers the
effect of soil–wall interface friction δ. The estimated Ko ,
Ka and Kp are summarised in Table 3.
When Plaxis 2D was used in Series 2, a linear elasticperfectly plastic model with Mohr-Coulomb failure criterion (MC) was adopted for fill, MD and CDG in both
HHE and DC-I4. When stress states were within the yield
surface of MC, the soil behaves elastically and it obeys
Hooke’s law for the isotropic linear elasticity, which is
characterised by two material properties, E and ν . Since
soil is modelled to be an elastic-perfectly plastic material
in MC when yield stress is reached, yield surface is thus
fixed and it is not affected by plastic straining. At plastic
state, the yield surface of soil is characterised by shear
strength parameters, c and φ , while dilation angle ψ is
HKIE Transactions
Table 3.
Soil type
Fill
MD
AL
CDG
A summary of input parameters adopted for analyses in Series 1, 2 and 4.
c (kPa)
(◦ )
φcs
Unit weight (kN/m3 )
v
K0
Ka
Kp
0.1
35
30
32
35
19
0.17
0.43
0.5
0.47
0.43
0.24
0.30
0.28
0.24
7.36
4.98
5.77
7.36
ref (MPa)
Gmax
pref (kPa)
v
c (kPa)
(◦ )
φcs
105
27
0.17
98
30
0.1
0.1
0.1
32
32
35
Table 4.
A summary of input parameters adopted for case DC-I6 in Series 3.
Soil type
Model
Fill
MD
CDG
MDG
HSS
MC
HSS
Elastic
ref (MPa)
γsat (kN/m3 ) E (MPa) E50
19
19
19
22
43
–
13
–
15,000
m
γ0.7 (%)
25
0.5
40
0.5
1.2 × 10−3
–
1.6 × 10−3
–
0.2
–
Notes: Models MC, HSS and Elastic refer to Mohr-Coulomb, Hardening Soil Small and Elastic models, respectively; γsat denotes
ref denotes the secant stiffness at 50% strength at a reference confining pressure pref and m is the fitting
the saturated unit weight; E50
parameter.
used to control plastic volumetric strain increment. For
comparing any difference of f -values that were backanalysed between Series 1 and 2, all parameters inputted
were identical. Since dilatancy was not considered in
FREW, the dilation angle in Plaxis 2D was taken to be
zero for all soil types. On the other hand, MDG was modelled as an elastic material. A constant E and v of 15 GPa
and 0.2 [27] were specified, respectively.
For simulations in Series 3, the HSS model was
adopted for fill and CDG. The HSS model was developed
on the basis of the Hardening Soil Model (HS), which is
an elasto-plastic model in Plaxis 2D allowing yield surface to be expanded upon plastic straining. The HS model
characterises compression and shear hardenings through
the developments of irreversible plastic strains due to primary compression (under oedometer and isotropic loading
conditions) and deviatoric loadings, respectively. When
subjected to primary deviatoric loading, stiffness of soil is
allowed to decrease hyperbolically and irreversible plastic
strains are developed simultaneously. To consider stiffness
nonlinearity, the following hyperbolic empirical equation
is added in the HS model (i.e. becomes the HSS model) to
allow Gsec to vary with shear strain, γ , nonlinearly [28]:
Gs
Gmax(ref )
=
1
,
1 + a|γ /γ0.7 |
(3)
where Gmax(ref ) is the reference elastic modulus at very
small strains (Figure 6) at a reference effective minor
principle stress σ3(ref
) ; γ0.7 is the shear strain at which
the secant shear modulus Gsec reduces to 72% of G0(ref ) ;
and a is the fitting parameter, which was taken as
0.385.[28] Santos and Correia [28] identified that when
γ was normalised by γ0.7 , an almost unique relationship between normalised shear modulus (i.e. Gs /Gmax )
and normalised shear strain (i.e. γ /γ0.7 ) was obtained.
Based on the measured stiffness reduction curves from
KSC shown in Figure 2, it is found that Gmax(ref ) and
γ0.7 for fill are 105 MPa and 1.2 × 10−3 %, respectively,
whereas Gmax(ref ) is determined to be 98 MPa and γ0.7 is
1.6 × 10−3 % for CDG. The shear strength parameter φcs
of both fill and CDG was taken from Wang,[18] while
c was set to be 0.1 kPa. Due to the lack of experimental
data on stiffness reduction curve for MD, the soil model
MC was adopted for simplicity. By using the existing E – SPT N correlation (Equation (2)), adopting the mean
N profile (Figure 6) and assuming the f -value to be 1.0,
a uniform E profile of 13 MPa was specified in MD.
of MD was taken from Wang [18] and c of 0.1 kPa
φcs
was specified. Similarly, MDG was modelled to behave
elastically. All input soil parameters are summarised in
Table 4.
For structural components of the ELS system, a retaining wall was modelled as an elastic beam in FREW and
as a “Plate” element in Plaxis 2D. Each node of a “Plate”
element in Plaxis 2D has three degrees of freedom, translations in vertical and horizontal directions and in-plane
rotation. When a retaining wall was modelled as an elastic
“Plate” in a plane-strain analysis in Plaxis 2D, the wall
had unit width and it behaved as an elastic beam, which
allowed both axial deformation and in-plane bending. For
prop, it was modelled as an elastic spring in FREW and
as a “Fixed-end anchor” in Plaxis 2D. The flexural or/and
axial stiffness of a retaining wall and prop/anchor were
taken from design reports for the seven HA’s cases and
from Wang [18] for case DC-I6.
44
C.W.W. Ng et al.
Table 5.
A summary of back-analysed f -values of fill and CDG from Series 1 and 2.
Series
1
Case
HHE
ECW
TTE
SCR
CWR
Software
Hi or Hf (m)
Fill
CDG
7.5
2.0
3.5
6.2
2.0
4.2
2.0
4.5
2.0
FREW
4.9
2.0
N/A
Results of back-analysed f -values
Back-analyses from Series 1 show that there is a consistent f -value of 2.0 for fill in all the seven HA’s cases.
The same f -value of 2.0 is found in case DC-I6 at Hi of
6.5 m, but a lower value of 1.0 is back-analysed at Hi of
15.5 m. For CDG, an f -value of 3.5 is found for case HHE.
For the two new HA’s cases, KSC and SUK, which have
comparable Hf , the same f -value of 5.0 is obtained. For
case DC-I6, f -values of 3.0 and 2.0 are back-analysed at
Hi s of 6.5 and 15.5 m, respectively. When compared with
the back-analysed results from the seven non-HA’s cases
reported by Chan [12] (“stiffer” sub-group), the higher
back-analysed f -values for the seven HA’s cases and case
DC-I6 (at Hi s of 6.5 and 15.5 m) (“softer” sub-group) are
expected. This is because the Hf of these cases are much
shallower and there are thus smaller mobilisations of soil
strain and hence soil stiffness, as compared with the seven
cases back-analysed in Chan.[12]
When back-analyses were repeated for HHE and DCI4 using Plaxis 2D (Series 2), the same set of f -values
is obtained for fill and CDG. This is expected because
the same linear elastic-perfectly plastic soil model (i.e.
MC in Plaxis 2D) and same input parameters are used
in FREW and Plaxis 2D, despite their different numerical techniques adopted to compute soil stiffness matrices.
Any E – SPT N correlations derived using FREW and
Plaxis 2D (using soil model MC) are thus considered to
be consistent for analysing wall deflection. Table 5 summarises back-analysed f -values for each case history in
both Series 1 and 2.
Mobilisation of shear strain and shear modulus
during an excavation
Based on the computed results from Series 3, Figure 6
correlates any intermediate excavation depth Hi with
mobilised shear strain for both fill and CDG in case DCI6. At each Hi , computed shear strain of each material was
obtained from a soil element located near the mid-depth of
the corresponding stratum right behind the diaphragm wall
(i.e. elements A for fill and element B for CDG; Figure 5).
As shown in Figure 6, when the excavation reaches Hi of
6.5 m, computed shear strains of fill are higher than that
in CDG because the first stage of excavation took place
mainly at shallow depths in fill. The greater stress relief
2
KSC
SUK
4
2.0
5.0
5
2.0
5.0
DC-I6
HHE
DC-I4
Plaxis
6.5
2.0
3.0
15.5
1.0
2.0
7.5
2.0
3.5
27
1.0
1.5
in fill in front of the diaphragm wall thus causes greater
mobilisations of shear strain. As excavation progresses
downwards from 6.5 to 27 m, the shear strains of both
materials increase significantly by more than an order of
magnitude. The increase of shear strain is attributed to an
increase in shearing upon greater stress relief at deeper
Hi s. When the formation level reaches 27 m depth, the
final shear strains in fill and CDG are 1% and 2%, respectively. Since shear strain of soil is not easy to be determined
accurately both in laboratory and in the field, the observed
consistent correlations for both fill and CDG suggest that
Hi can be used as an indirect parameter to represent the
degree of mobilisation of shear strain induced by an excavation. This is similar to that reported by Stroud [29] who
identified that normalised bearing stress (q/qult , where qult
is the ultimate bearing capacity) is an indirect measure
of shear strain mobilisation when devising E – SPT N
correlations from in situ plate-load tests.
By mapping computed shear strain to normalised stiffness reduction curves as shown in Figure 2, correlations
between Hi and Gsec /p for both fill and CDG are depicted
in Figure 6. As expected, there are consistent reductions
of Gsec /p due to the greater mobilisation of shear strain
at deeper Hi s for both materials. Since mobilised shear
strains in CDG are always smaller than those in fill at any
Hi , Gsec /p of the former material is thus larger. Obviously, shear moduli of both materials are not constant but
they can be mobilised to different degrees at different Hi s.
In other words, the existing empirical E – SPT N correlation (Equation (2)), which can deduce only a constant
soil stiffness, cannot capture the mobilisation of nonlinear
strain-dependent stiffness correctly.
Observed variations between back-analysed f -values
and final excavation depth
Figure 7 correlates Hf with f -values back-analysed from
the 14 case histories in Group A, including (i) the seven
HA’s cases, (ii) case DC-I6 at Hi s of 6.5 and 15.5 m and
(iii) five out of the seven cases reported by Chan [12]
(i.e. EH, HS-QR, HS-DV, CS and DC-I4). Case HKS,
which is one of the seven cases reported by Chan,[12]
was not included in developing a correlation because the
wall movements were most likely stiffened by adjacent pile
foundation.
8
Back-analysed f value
"Softer"
sub-group
HA
cases
7
KSC
5
4
CDG
Fill
Proposed for CDG
Proposed for Fill
SUK
DC-I6
(Hi = 6.5m)
3
2
HHE
EH
DC-I6
(Hi = 15.5 m)
45
for 0 m ≤ Hf < 16 m,
(4a)
For fill,
"Stiffer"
sub-group
E = (−0.06Hf + 2)N
6
HKIE Transactions
HS-QR
HS-DV
E = 1N
for 16 m ≤ Hf ≤ 27 m.
(4b)
If N95L is larger than 30, use N95L equal to 30, unless further
justification can be made.
For CDG,
CS
DC-I4
E = 2.8N
1
0
0
5
10
15
20
Final excavation depth Hf (m)
25
30
Figure 7. Variations of back-analysed f -values with final
excavation depth Hf from 12 case histories.
Among 10 cases in the “softer” sub-group, there are
six cases encountering CDG stratum. It can be seen that
the back-analysed f -values of CDG decrease from 5.0 to
2.0 as Hf increases from 4 to 16 m. For a deeper Hf , there
is a larger mobilisation of soil strains behind a retaining
wall and this hence causes a greater reduction of E (or
f -value; Figure 6). On the other hand, fill was encountered in all the 10 cases. When compared with CDG, lower
back-analysed f -values are found (between 1.0 and 2.0;
Figure 7). This may be because fill in each of the selected
cases was situated in shallow depths and was looser than
that of natural CDG. For Hf shallower than 4 m, f -value
cannot be back-analysed due to the lack of field data.
For the four cases in the “stiffer” sub-group, similar
reductions of back-analysed f -values are found for fill
(from 1.5 to 1.0) and CDG (from 2.0 to 1.5) as Hf increases
(Figure 7). However, the observed reductions of f -values
are evidently smaller than those found in cases in the
“softer” sub-group. This is consistent with the laboratory
measurements shown in Figure 2 that for a given increase
of soil strain, there is a smaller reduction of soil stiffness
at a relatively large strain level when compared with that
at a small-strain range. The back-analysed f -values from
the four cases in the “stiffer” sub-group are similar to the
reported f -values in GCO,[1] GEO [2] and GEO [11] (i.e.
0.8–2.0). This is expected because f -values reported in the
three documents were also back-analysed from some HK
multi-propped excavations, which have relatively deeper
Hf .
Proposed new moderately conservative E -SPT
N correlations
Based on numerical back-analyses of wall deflections at
final snapshot (i.e. at Hf ) from the 14 relevant HA’s and
non-HA’s case histories, the following moderately conservative correlations between E (MPa) and SPT N are
recommended for fill and CDG by (i) assuming GWT at
ground surface and (ii) using the N95L profile for simplicity
and practical purposes:
for 0 m ≤ Hf ≤ 7 m
E = (−0.09Hf + 3.45)N
(5a)
for 7 m < Hf ≤ 27 m.
(5b)
Any correlated E value from Equation (5a) and (5b)
should not be higher than 250 MPa, if no other detailed justifications are made. This upped-bound value of 250 MPa
is deduced from laboratory and in situ tests on CDG that
were reported by Ng and Wang [30] and Wang and Ng.[22]
It should be noted that all N values studied in the case histories in this paper are smaller and equal to 85 when Hf
are shallower than 7 m. Hence, if N values larger than 85
are encountered in excavations deeper than 7 m, cautions
should be taken on the use of new correlations above.
When any correlated E values through Equations (4)
and (5) are to be used for predicting wall deflections, the
Observational Method described in EC 7 [31] and CIRIA
report 185 [21] is recommended. As far as lateral wall displacement is concerned, the Observation Method suggests
to monitor wall deflections continuously during construction and field measurement at each construction stage is
then cross-checked with prediction based on the newly
proposed correlations.[32] For more conservative designs,
some engineers would like to select minimum SPT N values, Nmin . It is interesting to note that for a given δhm
value, a higher f -value is required to devise a higher E profile to match the δhm when using a lower Nmin profile
(comparing the N95L profile) for back-analysis. Since any
f -value back-analysed using a lower Nmin profile should
be well above the two proposed correlations as shown in
Figure 7, the new E – SPT N correlations expressed in
Equations (4) and (5) remain unaffected and they are thus
equally applicable when N95L or Nmin profile is used.
It is well known that the SPT N value can be affected
significantly by many factors such as free-fall energy
of hammer (i.e. method of releasing hammer, types of
anvil and length of rod), effective overburden pressure
and relative density.[33] However, excavations of some
case histories including CS,[34] HS-QR and HS-DV [35]
and EH [36] were constructed before the publications of
Geoguide 2 (1987) and BS1377-7 (1990), when the SPT
was standardised for HK practice. Thus, the measured SPT
N values in all these previous case histories collected could
not be corrected consistently. Even though other excavations after 1987 might have met the requirements of both
Geoguide 2 and BS1377-7, the correction of N value for
46
C.W.W. Ng et al.
(a)
Lateral wall displacement (mm)
0
–20
0
20
40
60
80 100 120
(b)
Lateral wall displacement (mm)
–20
0
0
G/F slab
20
40
60
80 100 120
G/F slab
B1/F slab
B1/F slab
10
10
20
20
30
30
B2/F slab
Depth (m)
Depth (m)
B3/F slab
40
50
40
50
Measured
60
Measured
Computed-existing
60
Computed-new
70
Computed-existing
Computed-new
70
Figure 8. Comparisons between measured and predicted lateral wall displacements at Hi s of (a) 12 and (b) 21 m for case DC-I6
(Series 4).
effective overburden pressure is still difficult and unreliable due to uncertainties of groundwater conditions. For
instance, the period of GWT monitored may not be consistent with that when SPT was conducted. Also, some SPTs
were carried out above GWT (Figure 3) and the effects
of soil suction on N value were not known for sure. For
the ease of practical designs, N values used in the newly
proposed correlations are not corrected.
Verifications of new correlations with field
measurements
In order to verify the new E – SPT N correlations
(Equations (4) and (5)), a series of four analyses were conducted using FREW (i.e. Series 4). For verifying the new
correlations for the “stiffer” sub-group (i.e. Hf > 16 m),
measured wall deflection at Hi of 21 m in case DC-I6
was used. Due to the lack of independent case history
in the “softer” sub-group, a wall deflection profile at Hi
of 12 m of the same case history was used to verify new
correlations for this sub-group (i.e. Hf ≤ 16 m).
For each Hi (12 and 21 m), two numerical runs were
conducted to predict wall deflections using E profiles that
were deduced by existing and new correlations. When the
existing correlation (Equation (2)) was used in the first run,
an f -value of each soil type was taken to be 1.0. The mean
N profile (solid line in Figure 5) was adopted, while the
measured GWT at 1.5 m depth was specified. The simulation was repeated in the second run but a mobilised
E profile was estimated by using the new correlations
(Equations (4) and (5)). For Hi equal to 12 m, f -values
of fill and CDG determined are 1.3 and 2.5, respectively.
For Hi equal to 21 m, f -values of 0.7 and 1.5 were found
for fill and CDG, respectively. To apply the moderately
conservative correlations, the N95L profile (dotted line in
Figure 5) was adopted, while GWT was assumed to be at
the ground surface both inside and outside of the excavation in the analysis. Also the hydrostatic pore-water
pressure distributions are assumed.
Figure 8(a) compares measured and predicted lateral wall displacements when excavation progresses to
Hi equal to 12 m. Clearly, when the existing correlation is used, the peak wall displacement at 15 m depth
is over-predicted by more than 100% significantly. The
substantial over-prediction is because the use of small
f -values in soil stratum (i.e. 1.0) underestimates E . On
the contrary, when larger mobilised E is estimated using
the new correlations, the predicted wall displacement is
much closer to the measured data. It should be noted
that some over-predictions of wall displacement using
the new correlations (Equations (4) and (5)) are not surprising because these correlations were derived based
on conservative assumptions on the N value (i.e. lower
value of N95L ), GWT (i.e. at ground surface) and overseas
correlations.[17] It is evident that a closer prediction of
field observation is obtained when stiffness nonlinearity
is considered in the newly developed correlations. The
peak wall displacement predicted by the new correlations
is three times closer to the field-measured value, when
compared with existing correlations. Comparison between
measured and predicted wall deflection profiles at Hi of
21 m is shown in Figure 8(b). As expected, the predicted
wall displacement using the E deduced by the existing
correlation is significantly larger than the field measurement. This is because the deduced E is significantly
underestimated when a small f -value of 1.0 is used. When
HKIE Transactions
the mobilised E profile is estimated by the new correlations, a closer prediction is obtained. By allowing for
the reduction of E as Hf increases, the closer agreement
between field and predicted wall deflections verifies that
the f -values estimated by using the new correlations are
reasonable.
Summary and conclusions
By carrying out field monitoring on two newly instrumented excavation sites in HK, collecting and categorising
HK case histories and conducting series of numerical
back-analyses using two BD-approved computer softwares FREW and Plaxis 2D, new correlations between
E and SPT N values were investigated and proposed
by considering stiffness nonlinearity explicitly. Based on
the investigation, some conclusions may be drawn as
follows:
(i) 22 case histories in HK (including the two newly
instrumented sites) were collected and reviewed.
They may be categorised into two groups based
on the mean SPT N value – N ≤ 30 (Group A; 17
cases) and N > 30 (Group B; five cases) at half of
final excavation depth (Hf /2). Among the 22 case
histories, only 12 of them documented relevant
information including ground and groundwater
conditions, the SPT N profile and measured lateral
wall displacement at Hf for carrying out detailed
back-analyses.
(ii) In each Group, cases are further divided into
two sub-groups, depending on Hf , wall stiffness
and construction method. For cases having Hf
shallower than 16 m, using wall stiffness softer
than 104 kN/m2 /m and the bottom-up construction method, they were categorised as “softer”
sub-group (eight cases in Group A and none in
Group B). Cases belong to “stiffer” sub-group if
they have Hf deeper than 16 m, used walls stiffer
than 106 kN/m2 /m and the top-down construction
method (nine cases in Group A and five cases in
Group B).
(iii) Based on back-analyses on wall deflections at the
final excavation (i.e. at Hf ) from 12 case histories, it is verified that reduction of soil stiffness
can be correlated with an increase in Hf . This is
because an increase in Hf mobilises larger soil
strains, leading to a decrease in soil stiffness.
(iv) For two selected case histories in “softer” and
“stiffer” sub-groups, the same set of f -values was
back-analysed for both fill and CDG when using
both FREW and Plaxis 2D.
(v) For practical design purposes, new moderately
conservative Hf – dependent E – SPT N correlations are established for fill and CDG. By
47
allowing for the reduction of E as Hf increases,
close agreements between measured and predicted
wall deflections verify that the f -values estimated
by using the new correlations are reasonable.
It should be pointed out that the newly proposed
correlations are based on a limited number of case
histories in HK. The use of any finding from this
study should be treated with caution. If in doubt, the
observational method recommended by EC7 and CIRIA
report 185 may be adopted in conjunction with proposed equations. Further improvements and refinements
of the proposed correlations may be made and extended
to other soils when more relevant and reliable field
data including wall deflection and GWT are obtained in
future.
Acknowledgements
The authors would like to acknowledge the research contract – HAXX07-13N0010/11PG provided by the Hong Kong
Housing Authority for the research work presented in this
paper.
Notes on contributors
Ir. Prof. C.W.W. Ng is Chair Professor of the Department of Civil and
Environmental Engineering at Hong
Kong University of Science and Technology. He was elected as an Overseas
Fellow at Churchill College, Cambridge University in 2005 and Fellow
of the Hong Kong Academy of Engineering Sciences in 2008. His main
interests include soil-structure interaction problems and unsaturated soil behaviour and modelling. Professor Ng has published over 150 SCI journal articles and many conference
papers. He is the main author of two reference books including “Soil-structure engineering of deep foundations, excavations
and tunnels” and “Advanced unsaturated soil mechanics and
engineering”.
Dr. A.K. Leung is a Lecturer in the
Division of Civil Engineering at the
University of Dundee, the UK, after he
obtained a Ph.D. degree in Civil Engineering at the Hong Kong University
of Science and Technology in 2011.
In 2013, he was elected to be the Secretary of the Scottish Universities of
Geotechnical Network (SUGN). His
research interests are unsaturated soil mechanics and its engineering application including slope stability and the design of
unsaturated backfilled material for hot pipeline installation. Dr
Leung is recently investigating the use of plants and energy piles
as sustainable engineering solutions for stabilising infrastructure
slope.
48
C.W.W. Ng et al.
Ir. S.S.K. Kwok is a Chief Geotechnical Engineer of the Housing
Department (HD) of HKSAR Government. After graduating from the
University of Hong Kong in 1980, he
joined the Consultant Company first
and then HD. He became a Chartered Engineer in 1984. His main
interests are site formation construction, foundation works and related
research work.
Ir. F.H.T. Yip is a Geotechnical Engineer of the Housing Department of
HKSAR Government. He graduated
from the Hong Kong Polytechnic University with a BEng (Hons) degree
in Civil Engineering. He has over
18 years working experience in the
geotechnical engineering industry. Ir
Yip is a Registered Professional Engineer in Hong Kong.
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