Load transfer mechanism of geotextile-reinforced sand layer over semirigid column-improved soft soil

Abstract

Many design guidelines have been proposed for piled embankments, most of which consider piles or columns as rigid inclusions. In this study, a small-scale physical model test was performed to investigate the load transfer mechanism of a geotextile-reinforced sand layer over a soft subsoil improved by semirigid columns. A multi-stage load was applied at the top of the sand layer until the columns started to yield. When the columns yielded, a reverse load transfer was observed. Vertical stresses were measured and analyzed in terms of efficacy and stress reduction ratio (SRR) with a comparison of existing design guidelines for assessing soil arching. Among the reviewed guidelines, the approach recommended by the Dutch guidelines provided the closest results to the experimental data, whereas the one adopted by the American guidelines predicted well the change in efficacy and SRR under different surcharge loads. However, the load transfer mechanism after the yielding of columns is beyond the scope of the existing design guidelines. In addition, it was found through regression analysis that the increment of vertical stresses on columns and surrounding soil followed an inclined line under partially undrained conditions during loading stages and a curve during consolidation.

Full text

RESEARCH PAPER
Load transfer mechanism of geotextile-reinforced sand layer
over semirigid column-improved soft soil
Pei-Chen Wu
1
•Wen-Bo Chen
2
•Wei-Qiang Feng
3
•Jian-Hua Yin
1
•Tsz-On Ho
4
•Shu-Ran Huang
1
Received: 4 December 2022 / Accepted: 25 December 2023
ÓThe Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024
Abstract
Many design guidelines have been proposed for piled embankments, most of which consider piles or columns as rigid
inclusions. In this study, a small-scale physical model test was performed to investigate the load transfer mechanism of a
geotextile-reinforced sand layer over a soft subsoil improved by semirigid columns. A multi-stage load was applied at the
top of the sand layer until the columns started to yield. When the columns yielded, a reverse load transfer was observed.
Vertical stresses were measured and analyzed in terms of efficacy and stress reduction ratio (SRR) with a comparison of
existing design guidelines for assessing soil arching. Among the reviewed guidelines, the approach recommended by the
Dutch guidelines provided the closest results to the experimental data, whereas the one adopted by the American guidelines
predicted well the change in efficacy and SRR under different surcharge loads. However, the load transfer mechanism after
the yielding of columns is beyond the scope of the existing design guidelines. In addition, it was found through regression
analysis that the increment of vertical stresses on columns and surrounding soil followed an inclined line under partially
undrained conditions during loading stages and a curve during consolidation.
Keywords Geotextile Load transfer mechanism Physical model test Soft soil Semirigid columns
1 Introduction
Recently, deep cement mixing (DCM) has been widely
applied as a ground improvement technique in Hong Kong.
In the third runway system project of Hong Kong Inter-
national Airport, a layer of geosynthetic-reinforced (GR)
load transfer platform (LTP) was designed over the soft
soil treated using DCM columns before reclamation work
[1,47]. Similar to geosynthetic-reinforced column-sup-
ported (GRCS) embankments, the load transfer mechanism
plays a significant role in reducing settlements, improving
the bearing capacity of soft ground, and shortening the
construction period.
The load transfer mechanism usually functions with the
soil arching phenomenon in pile- or column-supported
embankments with or without geosynthetic reinforcements
[11,26,33,39]. A family of friction models was estab-
lished based on Terzaghi’s soil arching theory [27,29].
Then, the method of load–displacement compatibility
(LDC) analysis was proposed by Filz et al. [8] to consider
the relationship between settlement and soil arching in
GRCS embankments. Another approach to investigate soil
&Wen-Bo Chen
geocwb@gmail.com
Pei-Chen Wu
peichen.wu@connect.polyu.hk
Wei-Qiang Feng
fengwq@sustech.edu.cn
Jian-Hua Yin
cejhyin@polyu.edu.hk
Tsz-On Ho
tsz.on.ho@connect.polyu.hk; Ryan-TO.Ho@arup.com
Shu-Ran Huang
shu-ran.huang@polyu.edu.hk
1
Department of Civil and Environmental Engineering, The
Hong Kong Polytechnic University, Hong Kong, China
2
College of Civil and Transportation Engineering, Shenzhen
University, Shenzhen, China
3
Department of Ocean Science and Engineering, Southern
University of Science and Technology, Shenzhen, China
4
Ove Arup & Partners Hong Kong Ltd (a Former Postdoctoral
Fellow in Department of Civil and Environmental
Engineering, The Hong Kong Polytechnic University),
Hong Kong, China
123
Acta Geotechnica
https://doi.org/10.1007/s11440-023-02213-8(0123456789().,-volV)(0123456789().,-volV)

arching is to conduct three-dimensional physical model
tests. These tests take into account factors such as the
consolidation of subsoils and the potential membrane effect
of geosynthetic reinforcements (GRs). In these tests, sub-
soils are either real soils [59] or simulated using other
materials, such as foams [24,29,34,35] and water bags
[42,43]. In recent decades, full-scale and field tests have
been conducted to explore the development of soil arching
and the influence of cyclic loadings on the development of
soil arching [42,43,60].
In the majority of experiments, piles are modeled by
small concrete piles or rigid blocks. However, it is worth
noting that the conclusions drawn from these experiments
may not be directly applicable to semirigid or flexible
columns, such as columns made of cement-treated soft soil,
stones, or sand. Significant lateral deformations of stone
columns and sand piles can have a substantial impact on
the load transfer mechanism and the development of soil
arching, particularly when the surrounding soil cannot
provide sufficient confining pressure. The lateral defor-
mations of semirigid columns, such as DCM columns, are
relatively smaller than those of stone columns and sand
piles. Many studies have focused on the bearing capacity
and consolidation behavior of DCM column-treated soft
soil under embankment loadings [12,25,48,50,55,56].
Finite element methods were adopted to study the perfor-
mance of GR embankments supported by DCM columns
[22,23,41,47,50,52]. However, the structuration and
bonding formed within the cement-treated soil may break
under significant loading levels, which can lead to failure
or strain-softening behavior of cement-treated soils
[16,52]. Current design guidelines for GRCS embank-
ments fail to capture the progressive failure and strain
softening of DCM columns, which were reported and
simulated by Yapage et al. [50,51]. In addition, only a
limited number of studies have focused on the load transfer
mechanism in semirigid columns, geosynthetics, and soils.
In this study, a small-scale physical model test for a
geotextile-reinforced (GR) sand layer over a soft subsoil
improved using cement-treated soil columns was con-
ducted to investigate the load transfer mechanism of
semirigid column-supported embankments. A multi-stage
surcharge load was applied until the columns yielded,
which was identified by a sudden drop in vertical stress on
the columns and a sudden increase in settlement.
2 Experiment setup and testing program
The physical model test was conducted in a steel tank with
dimensions of 1000 mm (length) 9600 mm (width) 9
800 mm (depth), as shown in Fig. 1. Six cement-treated
soil columns were installed in the subsoil of Hong Kong
marine deposits (HKMD) overlaid by a GR sand layer.
Similar setups were adopted by Zaeske [59] and van
Eekelen et al. [34], in which the repeatability has been
proved by dozens of tests. A multi-stage surcharge load
was applied using a self-designed loading system equipped
with a reaction frame and six pneumatic cylinders with a
maximum output vertical stress of 200 kPa. The materials
and transducers used in the model test are described in the
following sections.
2.1 Materials
The subsoil in the physical model test was made through
the reconstitution of the HKMD originally excavated from
the coastal area of Lantau Island in Hong Kong [46].
HKMD is a type of dark gray soft soil with high com-
pressibility and notable plasticity, whose basic properties
are listed in Table 1. It should be noted that the effective
cohesion of HKMD is nearly zero [6,53]. The properties of
the sand used in this study are listed in Table 1.
A piece of woven geotextile with a size of 1000
mm 9600 mm was prepared and framed with a pair of
rectangular stainless-steel casing trims with an outer size of
950 mm 9550 mm and an inner size of 900 9500 mm, as
shown in Fig. 2. Considering the focus of this study is on
the vertical deformation and the load transfer mechanism
of vertical stresses acting on the columns, geotextile, and
surrounding soils, it is imperative to control the movement
of the geotextile in the horizontal direction in order to
eliminate any potential impact on the strain within the
geotextile and the load distribution. The casing trims were
used to restrict the horizontal sliding/displacement of the
geotextile but allow free vertical movement with the set-
tlement of the underlying soil during the loading tests.
The tensile properties of the woven geotextile were
determined using the wide-width strip method (ASTM
D4595) [2]. The secant tensile modulus (J
s
) of the geo-
textile is 680 kN/m in the longitudinal direction and 150
kN/m in the transversal direction. The tensile strength of
the geotextile is 69 kN/m in the longitudinal direction and
17.3 kN/m in the transversal direction. Geotextiles with
similar tensile moduli were used in small-scale physical
model tests conducted by other researchers [24,34,35].
The semirigid columns adopted in this physical model
were cement-treated soil columns with a diameter of 100
mm and a length of 400 mm. To ensure consistency of
quality, the cement-treated soil columns with a cement
content of 20% in terms of the dry mass of cement to the
dry mass of HKMD were prefabricated individually, in a
similar manner to cast concrete specimens. Reconstituted
HKMD with an initial water content of 100% was thor-
oughly mixed with ordinary Portland cement (OPC) by a
concrete mixer for 10 min. Cement–soil mixtures were
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subsequently cast into a PVC mold with an inner diameter
of 100 mm by five layers. Immediately after filling each
layer, the PVC mold containing the cement–soil mixtures
was put on a vibration table and subjected to vibration for
at least 60 s to avoid large voids in the mixture. The
cement–soil mixture transformed into solid columns after
24 h. After being demolded from the PVC mold and
wrapped with plastic sheet, the columns were stored in a
chamber with a temperature of 20 °C and relative humidity
of 90% for curing of 28 days. Similar approaches of fab-
ricating cement-treated soil columns were adopted by Yin
and Fang [55] and Ho et al. [12], owing to the advantage of
producing columns of uniform quality for physical model
tests. The columns were installed in the physical model
after 28 d of curing. Unconfined compression (UC) tests
with a strain rate of 1 mm/min were conducted on cement-
treated HKMD specimens with a diameter of 100 mm and a
length of 200 mm after 28-day curing to obtain an average
UC strength q
u
= 0.53 MPa and a secant Young’s modulus
E
50
= 70 MPa. E
50
was determined by the stress at 50% of
the UC strength to the axial strain corresponding to this
stress [13,20,31,32].
Fig. 1 Test setup and the layout of transducers (unit in mm)—alongitudinal cross section and bfour horizontal cross sections
Table 1 Basic properties of Hong Kong marine deposits (HKMD) and sand
HKMD G
s
Atterberg limits PI (%) w
0
(%) pH Loss of ignition (%) u’(
Æ
)C
e
/V C
c
/V C
ae
/V
LL (%) PL (%)
2.65 43.2 22.6 20.6 100 6.44 4.46 24 0.03 0.24 0.002
Sand G
s
q
d
(Mg/m
3
)w
opt
(%) d
10
(mm) d
30
(mm) d
60
(mm) u’(
Æ
)
max min
2.56 1.742 1.536 16.5 0.17 0.27 0.59 34.6
Gsis the specific gravity, LL is the liquid limit, PL is the plastic limit, PI is the plasticity index, w0is the initial water content, C
e
/V is the slope of
unloading/reloading line, C
c
/V is the slope of normal consolidation line of the reconstituted HKMD, C
ae
/V is the creep coefficient, q
d
is the dry
density, and wopt is the optimum water content.
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2.2 Transducers
Earth pressure cells (EPCs) with capacities of 0.2 MPa and
2 MPa were used to measure the vertical stresses at dif-
ferent locations. Two pore pressure transducers (PPTs)
were placed at different locations in the subsoil. Linear
variable differential transformers (LVDTs) were used to
measure the settlements at the top surface of the sand layer.
Load cells were used to record the loading output of the
loading system. An NI PXIe 4331 datalogger was used to
record the voltage signals from EPCs, PPTs, LVDTs, and
load cells.
2.3 Model preparation and setup
Lubricant was applied to the side walls of the physical
model tank to minimize the effect of the side friction
between the walls and soils. Intact HKMD was thoroughly
mixed with additional water to form a slurry with a water
content of 100% and was subsequently carefully poured
into the tank to minimize the air trapped inside the soil. The
consolidation of the slurry under a uniform load of 5.35
kPa was then conducted. Prefabricated vertical drain bands
(PVDs) were employed to speed up the consolidation
process. PVDs were removed after consolidation. Metal
pipes with an inner diameter of 100 mm were inserted
vertically into the subsoil guided by a wooden plate with
circular holes. Level rulers were used to check the verti-
cality of the pipes. Soil inside the metal pipes was extracted
along with these pipes forming holes in the subsoil for the
installation of prefabricated cement-treated soil columns.
After carefully inserting the columns into the holes, cement
slurry with a cement content of 20% was poured into the
holes to fill the gap between the columns and the sur-
rounding soil. It is worth mentioning that the method of
installing cement-treated soil columns used in this study is
different from the real practice of constructing DCM col-
umns. The effect of in situ mixing procedures on the
properties of the columns and surrounding soils is not
considered in this study. Eight EPCs were placed at the top
of the HKMD subsoil improved by cement-treated soil
columns, as shown in Fig. 1.
To simulate the load transfer platform used in the third
runway system project of Hong Kong International Airport,
a sand blank with a thickness of 50 mm was placed on top
of the subsoil before installing the geotextile and the EPCs
for measuring the vertical stress over the geotextile. The
total thickness of the sand layer reached 350 mm after
filling another six layers of sand (each with a thickness of
50 mm). The construction of the sand layer took approxi-
mately 15 d. The total weight and volume of the sand were
controlled to obtain a sand fill with a relative density of
Fig. 2 Illustration of casing trims for fixing geotextile (unit in mm)
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80%, and a rigid porous plate was placed on the top of the
sand to serve as a loading plate and a platform for setting
the LVDTs.
2.4 Geometrics and scale effects
A certain height of embankments is required by the current
design guidelines so that soil arching can be fully devel-
oped. The GR sand layer in this study was 0.35 m, which
was higher than the minimum height recommended by BS
8006 [3], Dutch design guidelines [37], and the Federal
Highway Administration (FHWA) of the United States [28]
under the geometrical configuration of the physical model
test, namely 0.15, 0.22, and 0.33 m, respectively.
Without scaling, stress and time in this physical model
test were the same as those in the geotechnical prototype,
which requires other variables to be scaled down accord-
ingly [4,45], as shown in Table 2. The same approach was
also adopted by van Eekelen et al. [34] to avoid consid-
ering stress-dependent behavior of filling materials. They
also clarified that it is not necessary to apply scaling rules
when comparing the measured results with the results
calculated by analytical models. The scale of the physical
model test was approximately 1:6 for the diameter and
spacing of the columns in an embankment reported by
Jamsawang et al. [15].
3 Experiment results
3.1 Settlement and excess pore pressure
A multi-stage loading test was started five days after the
construction of the sand layer using the self-designed
loading system following a loading sequence of 10, 20, 40,
and 80 kPa. Surface settlements were measured during the
loading tests. Each loading test was conducted until the
excess pore pressure was nearly fully dissipated. Figure 3a
shows the actual load applied at the top of the sand layer
and the surface settlement, measured using load cells and
LVDTs, respectively. The surface settlement was below 20
mm under the applied load of 10, 20, and 40 kPa, showing
the effectiveness of cement-treated soil columns in con-
trolling settlement. A significant increase in surface set-
tlement was observed when the applied load reached 80
kPa. Figure 3b plots the final settlement under each load
stage. The shape of the settlement–log(load) curve is
similar to typical e-log(r) curves obtained from oedometer
tests covering both over-consolidated and normally con-
solidated states. The composite ground of HKMD
improved by cement-treated soil columns under the geo-
textile-reinforced sand fill exhibited a low compressibility
Table 2 Scaling of variables
Parameter Scaling Dimension
Time 1 [T]
Stress 1 [M/LT
-2
]
Length 1:x [L]
Stiffness of geotextile 1:x [MT
-2
]
Tensile strength of geotextile 1:x [MT
-2
]
Area 1:x
2
[L
2
]
Force 1:x
2
[MLT
-2
]
Strength of soil and columns 1 [M/LT
-2
]
Fig. 3 aMeasured surface settlement and applied load with time and
bSurface settlement versus applied load (log scale)
Fig. 4 Measured excess pore pressures with time at different
locations in HKMD
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when the applied load was lower than 40 kPa; however, it
showed a high compressibility when the applied load
reached 80 kPa. The significant difference could be
attributed to the yielding of the cement-treated soil col-
umns, which is discussed in the next section.
Figure 4presents the excess pore pressures in the
HKMD measured over time using PPT1 and PPT2. When
the applied load was smaller than 80 kPa, no significant
difference in the measured excess pore pressures was
observed between the bottom level (PPT1) and middle
level (PPT2) of the HKMD. Rapid dissipation of excess
pore pressure at both levels was observed at the beginning
of each loading stage. As the applied load approached 80
kPa, it was observed that the excess pore pressure mea-
sured at the bottom of the HKMD was greater than that
measured at the middle level. In addition, the excess pore
pressure at the middle level dissipated faster than that at the
bottom. The observed responses of the excess pore pressure
were probably attributed to the different drainage paths for
the soils at different locations and yielding of the columns
that changed the stress state and drainage situations for the
PPTs at different locations. It should be noted that the
yielded columns might have lateral expansion toward the
surrounding soil, resulting in an increase in lateral stress
and pore water pressure inside the surrounding soil [6,56].
3.2 Vertical stress
Vertical stresses measured using EPCs at different loca-
tions are presented in Fig. 5. Figure 5a, b shows the ver-
tical stresses above the GR. There was no significant
difference observed between the vertical stress measured
by EPC12 and that measured by EPC15. A notable differ-
ence between the vertical stress measured by EPC13 and
that measured by EPC14 was observed after 80 d when the
cement-treated soil columns yielded. Figure 5c, d presents
the vertical stresses (beneath the GR) at the top of the
columns and the HKMD subsoil, respectively. Before the
yielding of the columns, the vertical stress measured by
EPCs on each column did not exhibit significant differ-
ences. However, when the columns started to yield, there
was a non-negligible difference in the vertical stresses
among different columns. This difference could be attrib-
uted to the eccentric loading after the yielding of the col-
umns and different boundary effects. It should also be
noted that the vertical stresses presented here were based
0
5
10
15
20
25
30
35
40
0 20 40 60 80 100 120
Vertical stress (kPa)
Time (day)
EPC1
EPC2
EPC3
0
10
20
30
40
50
60
0 20406080100120
Vertical stress (kPa)
Time (day)
EPC6
EPC7
EPC8
0
50
100
150
200
250
020406080100120
Vertical stress (kPa)
Time (day)
EPC14
EPC13
EPC16
0
200
400
600
800
0 20 40 60 80 100 120
Vertical stress (kPa)
Time (day)
EPC4
EPC5
EPC9
EPC10
(a) (b)
(c)
(d)
(e)
0
100
200
300
400
500
600
0 20 40 60 80 100 120
Vertical stress (kPa)
Time (d ay)
EPC12
EPC15
Above GR
Beneath GR
At the bottom of subsoil
EPC12
EPC15 EPC13 EPC14
EPC16
EPC4 EPC5
EPC9 EPC10
EPC1
EPC2
EPC3
Beneath GR
Above GR
EPC11
EPC6 EPC7 EPC8
EPC11
Fig. 5 Measured vertical stresses at the locations of aEPCs 12, 15; bEPCs 13, 14, and 16; cEPCs 4, 5, 9, and 10; dEPCs 6, 7, 8, and 11; and
eEPCs 1–3
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on local measurements. The limitations of the local mea-
surements are discussed in Sect. 5. Figure 5e shows that
the vertical stresses at the bottom of the HKMD subsoil
were smaller than those at the top. This could be attributed
to the skin friction between the columns and the sur-
rounding soil. Comparing the excess pore pressure with the
vertical total stress at the bottom of the HKMD subsoil, it
can be observed that the excess pore pressure was higher
than the vertical total stress at the beginning of the loading
test. This could be attributed to additional lateral stress
caused by the yielded columns and Mandel–Cryer effect
[9] or creep effect of the HKMD [57].
To better address the mechanism of load transfer, the
model test is divided into three zones: column, strip, and
square zones, as shown in Fig. 6a. The column zone covers
the cement-treated soil columns and the portion of the sand
layer above the columns, the strip zone is the area between
two adjacent column zones, and the square zone is the area
enclosed by four strip zones. Strip and square zones are
similar to those adopted by van Eekelen et al. [37]. It
should be noted that the difference between vertical stres-
ses above and beneath the geotextile in the column zone
may be significant, depending on the development of the
membrane effect of the geotextile. The circular cross sec-
tion of columns can be converted into a square with an
equivalent size of a. The area influenced by each column is
illustrated using a column-soil unit, as shown in Fig. 6b.
Figure 7a shows the average vertical stress in the col-
umn zones. For the first two loadings, the vertical stresses
above and beneath the geotextile show no discernible dif-
ference, indicating that the membrane effect of the geo-
textile was not fully mobilized. As the development of the
membrane effect depends on the deflection of the geotex-
tile related to the differential settlements between the
columns and surrounding soft soil, it can be deduced that
the differential settlements during the first two loading
stages were not remarkable. When the load increased to 40
kPa, a significant difference was observed between the
vertical stresses above and beneath the geotextile, indi-
cating that a certain settlement occurred, which induced a
noticeable tension that caused the development of the
membrane effect in the geotextile. Owing to the membrane
effect, the load taken by the geotextile was transferred to
adjacent columns, thereby increasing the vertical stress
beneath the geotextile in the column zones. When the
applied load was increased to 80 kPa, the vertical stresses
above and beneath the geotextile in the column zones
reached their peak values, indicating the yielding of col-
umns. The yielding of columns induced a dramatic settle-
ment on the surface of the sand layer, as shown in Fig. 3.
After the test was completed, the column beneath EPC10
was retrieved from the physical model. This column had a
typical shear failure, as shown in Fig. 7. After the test was
completed, the column beneath EPC10 was retrieved from
the physical model. This column had a typical shear failure,
as shown in Fig. 7a. It is important to mention that the
main focus of this study was on the load transfer before and
after the yielding of cement-treated soil columns. The
physical model test did not specifically delve into the
failure modes of the soft ground improved by cement-
treated soil columns, or the failure modes of each column
installed in this test. Despite the yielding of the columns,
the geotextile can continue to transfer the load to the col-
umns. This load transfer could be due to the large differ-
ential settlements between the columns and surrounding
soil as more loads could be transferred back to the sur-
rounding soil. Considering the progressive failure of
cement-treated soil columns, the membrane effect of the
da
Fig. 6 Illustration of acolumn, square, and strip zones and bcolumn-soil unit
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geotextile may accelerate the yielding of columns. In
addition, the yielding stress of the columns in the physical
model test was lower than the UC strength (0.53 MPa),
which is uncommon as the strength of cement-treated soil
columns under a confining pressure is normally higher than
the unconfined compressive strength. Possible reasons
could be: (1) The length-to-diameter ratio of the columns
was 4:1, which was higher than that of the specimens for
the UC tests (2:1), (2) the clamping effect inherent in UC
tests, and (3) the local measurement of the vertical stress,
which is discussed in Sect. 5.
Figure 7b shows the average vertical stresses above and
beneath the geotextile in the strip and square zones, where
the vertical stresses above the geotextile were greater than
those beneath the geotextile. It is interesting to note that the
vertical stress above the geotextile in the strip zone
exceeded the applied load immediately after the load was
applied. However, the increase in the vertical stress above
the geotextile in the square zone did not exceed the applied
surcharge load. At the beginning of each loading stage, the
geotextile strips supported by two adjacent columns
worked together with the columns, forming an ‘‘equivalent
bridge’’ to participate in the transfer of load. In addition,
given the partially undrained condition of the surrounding
soil at that moment, the vertical stress above the geotextile
in the strip zone was compatible with that above the geo-
textile in the column zone before the yielding of columns.
However, as the excess pore water pressure dissipated, the
soil in between the columns started to settle. This soil
settlement initiated a load transfer process, wherein the
load was transferred from the square zone of the geotextile
to the strip zone and subsequently to the columns, resulting
in a decrease in the vertical stresses above the geotextile in
both the square and strip zones. As mentioned earlier, the
yielding of the columns resulted in a reverse load transfer
from columns to the geotextile when the surcharge load
increased to 80 kPa. Thus, the reverse load transfer sig-
nificantly increased the load above the geotextile in the
strip zone. However, the increase in vertical stress after the
yielding of columns could also be attributed to the geom-
etry change of the load distribution in the strip zones,
which probably affected the local measurement of the
vertical stress.
3.3 Load distribution
3.3.1 Load parts A, B, and C
According to van Eekelen [34,35], the load transfer in
embankments can be divided into load parts A, B, and C,
which are the portions of the load acting on columns,
transferred to GR, and supported by the subsoil, respec-
tively, as illustrated in Fig. 8. In this study, the vertical
stresses above and beneath the geotextile in the column
zone were used to calculate load parts Aand A?B,
respectively, whereas those beneath the geotextile in the
0
50
100
150
200
0 20 40 60 80 100 120
0
100
200
300
400
500
0 20 40 60 80 100 120
Fig. 7 Vertical stresses above and beneath the geotextile in acolumn zones and bstrip and square zones
Fig. 8 Illustration of load parts A,B, and C
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strip and square zones were used to determine load part C.
The equations for determining load parts A,B, and Care
provided as follows.
A¼ra
cAcð1Þ
B¼rb
cra
c

Acð2Þ
C¼rb
stripAstrip þrb
squareAsquare ð3Þ
where ra
cand rb
care the vertical stresses above and beneath
the geotextile in the column zone, respectively, rb
strip rep-
resents the vertical stress beneath the geotextile in the strip
zone, rb
square is the vertical stress beneath the geotextile in
the square zones, and Ac,Astrip , and Asquare are the areas of
the column, strip, and square zones within each column-
soil unit, respectively. ra
strip and ra
square are the vertical
stresses above the geotextile in the strip and square zones,
respectively. ra
strip and ra
square are not included in the above
equations but are used in the following discussion. ra
c,rb
c,
rb
strip,rb
square,ra
strip,ra
square,Ac,Astrip , and Asquare are illus-
trated in Fig. 6.
Figure 9shows load parts A,B, and C(per column-soil
unit) calculated using the vertical stresses measured at
different locations and time points. In the first loading
stage, there was no significant difference between load
parts Aand C, and load part B was nearly zero, indicating a
slight effect of the geotextile. As the surcharge load
increased, load part Abecame the largest portion among
the three load parts. A significant reduction occurred in the
load taken by the HKMD subsoil. The increase in load part
Bindicated that the geotextile started to contribute to the
load redistribution. However, load part Adecreased when
the columns started to yield. After the yielding of columns,
load part Cbecame the dominant portion.
The sum of load parts A?B?Cand the total applied
load per soil-column unit are shown in Fig. 9. When the
applied load was 10 and 20 kPa, the sum of the load parts
A?B?Cagreed well with the applied load per soil-
column unit. When the load was 40 kPa, the sum of the
load parts A?B?Cwas smaller than the applied load
per soil-column unit. This was mainly due to the local
measurement of the vertical stress using EPCs, which is
discussed in Sect. 5. When the applied load reached
80 kPa, there was a significant difference between the sum
of the load parts A?B?Cand the applied load per soil-
column unit. This could be attributed to the yielding of the
columns, which might change the area of the column
zones.
3.3.2 Load transfer mechanism
To investigate the load transfer mechanism of the GR sand
layer over the semirigid column-improved soft soil under
surcharge loads, the vertical stresses in the column, strip,
and square zones have been analyzed at different stages.
Figure 10a shows the relationships between the vertical
stresses in the column and square zones (above the geo-
textile) in different stages. In each loading stage, the ver-
tical stresses in both the column and square zones increased
until the subsoil started to consolidate. The ratio of the
increment of ra
cto the increment of ra
square was nearly
identical in each loading stage. Linear regressions were
conducted on ra
cand ra
square in the loading stages, as indi-
cated by the dotted lines in Fig. 10a. The slope is similar to
the stress concentration ratio, which is an important index
representing the load distribution on the soft soil improved
by columns [11,54]. The average slope of the dotted lines
in the four loading stages is 2.44. As the surcharge
increased in a short period of time, the subsoil was con-
sidered to be in a partially undrained condition during the
loading stages. A linear envelope line with a slope of 6.16
can be drawn by fitting the relationship between ra
cand
ra
square before consolidation at each loading stage (imme-
diately after load application). Soil arching in the overlaid
GR sand layer started to develop when the consolidation
settlement of the subsoil increased, causing an unloading
process to occur in the square zone. When the consolida-
tion was completed, the load transfer paused, resulting in a
stable state, which can be enveloped by a line with a slope
of 13.73. In this physical model test, the slope of the
envelope line after the consolidation of the subsoil was
approximately doubled compared to that before consoli-
dation. The two envelop lines before and after the con-
solidation of the subsoil formed a region where the vertical
stress increments caused by the different surcharge loads
followed a path of an inclined line under the partially
undrained condition during loading stages and a curve
during consolidation. However, the path crossed the lower
boundary of the region (the envelope line describing the
0
1
2
3
4
5
6
7
8
0 2040608010012
0
Fig. 9 Load distribution in a column-soil unit regarding load parts A,
B, and C
Acta Geotechnica
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state immediately after the application of load) as the
columns started to yield.
Figure 10b shows the relationships between the vertical
stresses in the column and strip zones (above the geotex-
tile) at different stages. Linear functions can be used to fit
the relationship between ra
cand ra
strip during the loading
stages, as shown by the dotted lines in Fig. 10b. The dotted
lines are nearly parallel with an average slope of 0.66,
indicating that the vertical stress increment in the strip zone
was larger than that in the column zone owing to the par-
tially undrained condition during the loading stages. Two
envelope lines with slopes of 1.85 and 11.76 representing
the stages before and after the consolidation, respectively,
are plotted. The slope of the envelope line after consoli-
dation is approximately six times greater than that before
consolidation, indicating that the consolidation of the
subsoil largely affected the load transfer between the col-
umn and strip zones above the geotextile. An inclined line
under the partially undrained condition during loading
stages followed by a curve during consolidation was also
observed in the region formed by the two envelope lines
before and after consolidation. After the columns yielded,
the path shifted outside of the defined region.
Figure 10c shows the relationships between the vertical
stresses in the column and square zones (beneath the
geotextile) at different stages. Similarly, linear functions
can be used to fit the relationship between rb
cand rb
square
during the loading stages, as indicated by the dotted lines in
Fig. 10c. These dotted lines are nearly parallel and have an
average slope of 7.21, which represents the stress con-
centration ratio of the vertical stress in the column zone to
that in the square zone. The value agrees with the typical
stress concentration ratio of GRCS embankments with
semirigid columns, which ranges from 5 to 10 [11]. Two
envelope lines with slopes of 20.23 and 47.25 representing
the stages before and after the consolidation, respectively,
are plotted. The ratio between the slopes of the envelop
lines before and after consolidation is approximately 2,
0
50
100
150
200
250
300
350
400
0 50 100 150 200 250 300
0
50
100
150
200
250
300
350
400
0 1020304050607080
0
100
200
300
400
500
600
0 1020304050
0
100
200
300
400
500
600
0 5 10 15 20 25 30 35 40
Fig. 10 Relationship between vertical stresses in acolumn zone versus square zone (above the geotextile), bcolumn zone versus strip zone
(above the geotextile), ccolumn zone versus square zone (beneath the geotextile), and dcolumn zone versus strip zone (beneath the geotextile)
Acta Geotechnica
123

which is similar to the ratio obtained from Fig. 10a. In
addition, a similar path of an inclined line under the par-
tially undrained condition during the loading stages fol-
lowed by a curve during consolidation can be also
observed. The relationship between the vertical stresses in
the column and square zones after the yielding of the
columns is similar to that in the loading stages before
yielding.
The relationships between the vertical stresses in the
column and strip zones beneath the geotextile at different
stages are fitted by dotted lines with an average slope of
5.07, as shown in Fig. 10d. Two envelope lines with slopes
of 11.41 and 22.67, representing the stages before and after
the consolidation, respectively, are plotted. The slope of
the envelope line after consolidation is approximately 1.7
times greater than that before consolidation. A similar path
of an inclined line under the partially undrained condition
in the loading stages followed by a curve during consoli-
dation can be also observed. The relationship between the
vertical stresses in the column and square zones after the
yielding of the columns is similar to those in the loading
stages before yielding.
4 Assessment of arching effect
Many scholars have started to consider the strain-softening
and progressive failure of column-supported embankments
[51,58,61]. However, only the elastic behavior of col-
umns/piles is considered in the current design methods for
determining arching effect. Therefore, it is worth investi-
gating the load transfer mechanism after the yielding of the
columns with the comparison to the results provided by the
current design methods in order to improve the design
methods not only for guiding the design but also for ana-
lyzing and explaining the reasons behind failures and
geohazards.
4.1 Assessment of arching effect using current
design methods
According to Hewlett and Randolph method, pile (or col-
umn) efficacy Eis the proportion of the load taken by
columns. In this study, the efficacy of the cement-treated
soil columns is calculated as follows:
EA¼A
cHþpðÞs2ð4Þ
EAþB¼AþB
cHþpðÞs2ð5Þ
where EAis the efficacy in which the effect of geotextile is
ignored, EAþBis the efficacy in which the effect of
geotextile is considered, Aand Brepresent load parts Aand
Bdetermined by Eqs. (1) and (2), respectively, pis the
surcharge load at the top of the GR sand layer, sis the size
of the column-soil unit influenced by the column, cis the
unit weight of the embankment fill, and His the height of
the embankment.
SRR is an index used to assess the development of
arching. SRR ¼1 indicates that no arching effect occurs in
the filling materials. A smaller SRR value indicates a more
significant arching effect. In this study, SRR can be cal-
culated as:
SRR ¼C
cHþpðÞs2a2
ðÞ ð6Þ
where Cindicates load part Cdetermined by Eq. (3).
Additionally, four commonly used methods from the
current design guidelines for GRCS embankments are
adopted to predict the efficacy Eand stress reduction ratio
SRR.
4.1.1 Hewlett and Randolph’s method
A semi-spherical arching model was proposed to analyze
the load transfer in GRCS embankments and adopted in the
French guidelines and BS 8006 as an additional method.
The critical location is assumed to be at the crown of
semicircular arches or pile caps. Equations (4)–(9) are the
equations for determining the efficacy and stress reduction
ratio.
Critical location at the crown of arches:
Ecrown ¼11a
s

2

a1a1a2þa3
ðÞð7Þ
SRRcrown ¼a1a1a2þa3ð8Þ
a1¼1a
s
hi
2Kp1
ðÞ
;a2¼s
ffiffiffi
2
pH
2Kp2
2Kp3

;and a3
¼sa
ffiffiffi
2
pH
2Kp2
2Kp3
 ð9Þ
Critical location at pile caps:
Ecap ¼b
1þbð10Þ
SRRcap ¼1
1þbðÞ1a=sðÞ
2
hi ð11Þ
b¼2Kp
ðKpþ1Þð1þa=sÞð1a=sÞKpð1þKpa=sÞ

ð12Þ
where Kp¼1þsinðu0Þ
1sinðu0Þ,sis the column spacing, cis the unit
weight of the embankment fill, His the height of the
Acta Geotechnica
123

embankment, ais the equivalent size of the column, and u0
is the friction angle of the embankment fill. The surcharge
load is converted into an additional height DH¼p=c[42].
The efficacy and stress reduction ratio used for comparison
are min Ecrown;Ecap

and max SRRcrown;SRRcap

,
respectively.
4.1.2 German EBGEO method
German EBGEO [5] adopted the multi-shell arches theory
of Zaeske [59]. In EBGEO, subsoil support is considered
only when calculating the tensile strain of GR. The efficacy
and SRR are calculated as follows:
E¼cHþprz0
ðÞs2þrz0a2
cHþpðÞs2ð13Þ
SRR ¼rz0
cHþpðÞ ð14Þ
rz0¼kv
1ðcþp=HÞHðk1þh2
gk2Þv
n
þhgðk1þh2
gk2=4Þvðk1þh2
gk2Þv
hio
ð15Þ
where hg¼sd=2 for Hsd=2, and hg¼Hfor H\sd=2,
v¼aðKcrit1Þ
k2sd,Kcrit ¼tan245þu0
2

,k1¼ðsdaÞ2
8,
k2¼s2
dþ2asda2
2s2
d
,sdis the center-to-center spacing between
two diagonal columns, and pis the surcharge load.
4.1.3 Adapted Terzaghi method
Sloan et al. [30] extended Terzaghi’s soil arching theory
and proposed an adapted Terzaghi method, which has been
adopted in FHWA design guidelines [28]. The pile efficacy
determined by the adapted Terzaghi method can be
expressed as follows:
E¼1SRR 1 a2
s2
 ð16Þ
SRR ¼
c
a1eaH
ðÞþpeaH
cHþpðÞ ð17Þ
where a¼pcKTtan u0=s2a2
ðÞand pcis the column
perimeter. KT¼0:75 is suggested by Filz and Smith [7].
4.1.4 Concentric Arches (CA) model
The CA model is a three-dimensional (3D) soil arching
model adopted in the Dutch design guidelines [37]. In the
CA model, 3D concentric hemispherical arches are devel-
oped in square zones, whereas two-dimensional (2D)
concentric semicircle arches are developed in strip zones.
The pile efficacy is expressed as follows:
E¼cHþpðÞs2FGRsquare FGRstrip
cHþpðÞs2ð18Þ
and the stress reduction ratio is:
SRR ¼FGRstrip þFGRsquare
cHþpðÞs2a2
ðÞ ð19Þ
where FGRsquare and FGRstrip are the loads acting on the
square and strip zones, respectively. van Eekelen et al. [36]
presented in detail a method for determining FGRsquare and
FGRstrip.
4.2 Pile efficacy
Figure 11a shows the changes in efficacy with surcharge
load. When the surcharge was smaller than 40 kPa, the GR
did not substantially increase the efficacy of the columns.
As the surcharge increased, a significant difference
between the efficacies with and without considering the
membrane effect of the GR can be observed, indicating that
the GR started to function. It was found that both the
efficacies with and without considering the effect of the GR
show a decrease during the process of increasing the sur-
charge load. This was due to the partially undrained con-
dition of the subsoil, which delayed the load transfer. The
differential settlements between the columns and sur-
rounding soil increased with the consolidation of the sub-
soil, resulting in an increase in the deflection of the GR,
and thus increasing the efficacy. The efficacy of the col-
umns at the end of the consolidation slightly increased with
an increase in surcharge load. This finding agreed with the
results of a finite simulation conducted by van der Peet and
van Eekelen [40]. A further increase in the surcharge load
resulted in the yielding of the cement-treated soil columns.
Linear correlation relationships can be found between
the efficacies with and without considering the membrane
effect of the GR under different surcharge loads, as shown
in Fig. 12. The ratios of the efficacies with and without
considering the effect of GR are 1.16, 1.09, 1.19, and 1.28,
under the surcharge loads of 10, 20, 40, and 80 kPa,
respectively. The values generally agree with the range
(1.15–1.3) reported by Low et al. [24] obtained from a
series of 2D physical model tests. The development of the
membrane effect of GR is related to its deflection and the
differential settlement between the columns and sur-
rounding soil. However, no direct measurement has been
carried out on the deflection of GR, which is one of the
limitations of this physical model test, as discussed in
Sect. 5.
Among the four design guidelines, the result of the
adapted Terzaghi method agreed well with the trend of the
efficacy calculated using the measured data considering the
GR effect (after consolidation) before the yielding of the
Acta Geotechnica
123

cement-treated soil columns. However, it should be noted
that the results calculated by the adapted Terzaghi method
are highly dependent on the value of KT. Higher KTvalues
result in higher efficacies. Therefore, this method must be
used with caution. Despite its failure to capture the
changing trend of efficacy considering the GR effect, the
CA model gave results similar to those calculated using the
measured data. The results of the German EBGEO [5]
method agreed well with the efficacy calculated using the
measured data disregarding the effect of the geotextile.
4.3 SRR
Figure 11b shows the SRR calculated using the measured
data and the current design methods. The SRR calculated
using the measured data tended to decrease with increasing
surcharge load, indicating that more significant arching
occurred under a larger surcharge load. However, the SRR
increased during the loading stages, which could be
explained by the partially undrained condition within the
short period of the loading stages. As the subsoil consoli-
dated, the differential settlements between the columns and
surrounding soil increased, resulting in an increase in the
deflection of the geotextile, and thus reducing the SRR.
The adapted Terzaghi method captured the general
decreasing trend of the SRR calculated using measured
data. When the surcharge load was small (below 40 kPa in
this study), both the CA model and Hewlett and Ran-
dolph’s method provided SRR values similar to those
calculated using the measured data. However, the German
EBGEO method gave an overestimated SRR compared
with the other methods. van Eekelen et al. [4] reported
similar results and explained that the German EBGEO
0
0.2
0.4
0.6
0.8
1
10 20 30 40 50 60 70 80
0
0.2
0.4
0.6
0.8
1
10 20 30 40 50 60 70 80
Fig. 11 aEfficacies and bstress reduction ratios calculated by measured data and estimated by different methods under different surcharge loads
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.1 0.2 0.3 0.4 0.5 0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.3 0.4 0.5 0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.3 0.4 0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.3 0.4 0.5
Fig. 12 Relationship between efficacies with and without the effect of GR under the surcharge loads of a10 kPa, b20 kPa, c40 kPa, and d80
kPa
Acta Geotechnica
123

method does not take into account the increase in arching
caused by consolidation.
4.4 Discussion
Hewlett and Randolph’s method provided overestimated
values in terms of the efficacy of semirigid columns.
However, the vertical stress acting on the columns calcu-
lated by Hewlett and Randolph’s method was generally
smaller than those calculated by the German EBGEO [5]
method and the CA model [40]. Thus, this method should
provide lower efficacies. Under no surcharge load, Hewlett
and Randolph’s method resulted in an efficacy of 0.48,
which was smaller than the efficacy calculated using the
CA model. The overestimated results of Hewlett and
Randolph’s method were due to the height of the sand layer
used in the calculation, which was increased by the addi-
tional height converted from the surcharge loads. There-
fore, Hewlett and Randolph’s method might not be
suitable for embankments supported by semirigid columns
subjected to large surcharge loads.
The efficacies and SRRs calculated by the CA model,
German EBGEO method, and Hewlett and Randolph
method remained constant under the different surcharge
loads. This was because these methods are based on limit
state equilibrium, which can only determine a constant
arching stress value. The amount of deformation required
to achieve the arching state assumed by these methods
remains unclear [18]. The actual deformations that occur in
GRCS embankments are incompatible with the required
deformations, which leads to different results for various
arching models. In addition, the decrease in efficacy and
the increase in SRR due to the yielding of columns are
beyond the scope of the current design guidelines.
In addition, it should be pointed out that the consistency
or contradiction between the testing results and prediction
by the design guidelines in this study should not be simply
applied to other cases without performing additional
investigations to take into account scale and boundary
effects. However, the comparisons presented here may
serve as a valuable reference for future endeavors, such as
conducting full-scale experiments and numerical analysis
on the load transfer mechanism of geotextile-reinforced
sand layer over soft soil improved by semirigid columns.
5 Limitations of the physical model test
For small-scale physical model tests, one inevitable limi-
tation is the scale effect. However, conducting small-scale
tests is an economical way to address specific engineering
issues and provide references for numerical modeling that
bridges small-scale tests to real projects. Further
experimental and numerical studies should be conducted to
investigate the influence of different factors, such as col-
umn configurations, material properties, and loading con-
ditions on the load transfer mechanism. Two technical
limitations are addressed in detail, as follows.
5.1 Local measurement of vertical stress
The distribution of vertical stress at the top of columns/
piles is usually non-uniform. The vertical stress tends to be
greater near the periphery of columns/piles [10]. As the
size of the EPCs used in this study was smaller than the
diameter of the cement-treated soil columns, the measured
vertical stress only represented the local vertical stress at
the center of each column instead of the overall average
stress over each column. Therefore, the local measurement
using small-sized EPCs probably underestimated the load
taken by the cement-treated soil columns, indicating that
the actual efficacies of the columns could be higher than
those calculated using measured vertical stresses.
5.2 Deflection of GR
The development of soil arching in GRCS embankments is
related to the deflection of the GR or the differential set-
tlement between the columns and surrounding soil [14,17].
Therefore, it is important to measure the deflection of GRs.
However, no direct measurement was performed on the
deflection of the GR in this small-scale physical model test.
In full-scale experiments or field tests, settlement plates
can be installed above the GR or in the subsoil to monitor
the deflection of the GR or settlement of the subsoil.
However, settlement plates were not applicable in this
study with the current setup. Nevertheless, the maximum
sag of the GR in the square zones can be estimated by the
following equation proposed by King et al. [19]:
ds;max ¼0:558 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ra
squareðsaÞ4
J
3
sð20Þ
where ds;max is the maximum sag of the GR in the square
zones. The calculated maximum sags under the surcharge
loads of 10, 20, 40, and 80 kPa are 2.79, 5.13, 7.87, and
18.08 mm, respectively. Comparing the maximum sags
with the ratios of efficacies with and without considering
the effect of GR, it can be roughly revealed that the
membrane effect of the GR on efficacy increases with the
deflection of the GR.
Although the tensile modulus of geotextiles/geogrids
was reported to have little effect on the efficacy of columns
[21,34,35], it could affect the soil arching by influencing
the deflection of GR, as indicated by Eq. (20). Considering
that the current design methods reviewed in Sect. 4follow
Acta Geotechnica
123

the two-step design approach which assumes that arching
actions are independent of the subsoil deformation and
deflection of GR, the analysis on the load transfer mech-
anism in this study does not consider the influence of the
tensile modulus of GR.
6 Findings and conclusions
A small-scale physical model test was conducted to
investigate the load transfer mechanism of a GR sand layer
over a soft subsoil improved by semirigid columns. A
multi-stage surcharge load was applied to the sand layer
until the yielding of columns was observed. The arching
effect was assessed and compared with the current design
methods for GRCS embankments. The main findings and
conclusions are as follows:
(a) Significant surface settlement was observed when the
columns started to yield. The geotextile facilitated
the load transfer between the columns and the
subsoil.
(b) When the columns yielded, the reverse load transfer
from the column zone to the strip zone was
significant.
(c) Vertical stresses before and after the consolidation of
the subsoil were enveloped with two lines, creating a
region where the increments of the vertical stresses
followed an inclined line under the partially
undrained condition during loading stages, and a
curve during consolidation.
(d) Among the current design guidelines reviewed, the
CA model of the Dutch guidelines provided efficacy
and SRR that were closest to those obtained from the
local measurement of vertical stress. The adapted
Terzaghi method can predict well the change in
efficacy and SRR under different surcharge loads.
However, the decrease in efficacy and the increase in
SRR due to the yielding of the columns are beyond
the scope of the current design guidelines.
Acknowledgements The work in this paper is supported by a
Research Impact Fund (RIF) project (R5037-18) and three General
Research Fund (GRF) projects (PolyU 15210020; PolyU 15210322;
PolyU 15226722) from Research Grants Council (RGC) of Hong
Kong Special Administrative Region Government of China. The
authors also acknowledge the financial support from Research Insti-
tute for Land and Space of The Hong Kong Polytechnic University
and three grants (CD82, CD7A) from The Hong Kong Polytechnic
University.
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