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Performance of Strut-Free Retaining Walls for 30 M Deep
Excavations in Soft Clay
Bashir Osman
1*
, Abdelrahman Abuserriya
2
Department of Civil Engineering, Engineering College, Sinnar University, Sinnar, Sudan
*Corresponding Author
DOI:
https://doi.org/10.51583/IJLTEMAS.2026.150100056
Received: 16 January 2026; Accepted: 26 January 2026; Published: 06 February 2026
ABSTRACT
Strut-free retaining wall systems offer important advantages for deep excavations, including improved
construction efficiency, safety, and workspace availability. However, their application in excavations deeper
than 20 m in soft clay remains limited. This study investigates the deformation behavior and optimal design
parameters of a strut-free retaining wall system for a 30 m deep excavation in soft clay using three-dimensional
finite element analysis. The retaining system consists of diaphragm walls, buttress walls, cross walls, and rib
walls. A total of sixty-one numerical simulations were conducted to evaluate the influence of the number,
thickness, and height of buttress and cross walls on wall deflection and ground settlement. The Hardening Soil
model was adopted to represent the nonlinear behavior of soft clay, while structural components were modeled
as elastic plate elements. The results indicate that increasing the number of buttress walls in the long
excavation direction significantly reduces maximum wall deflection and surface settlement, whereas the effect
in the short direction is relatively small. Among the investigated layouts, the configuration with two rib walls
in the long direction and one in the short direction provided the most effective deformation control.
Keywords: Strut-free retaining wall; Deep excavation; Soft clay; Buttress wall; Ground settlement; Finite
element analysis
INTRODUCTION
A strut-free retaining wall system is new system to support the deep excavation and it was studied in different
occasion [1-10]. The design of retaining wall supports excavation has to be aware of many things: firstly, the
vertical movement and safety of machines and workers. Secondly, the dimensions of excavation. Thirdly,
water and soil condition and fourthly, the force and load acting on the retaining wall. The advantages of a strut-
free retaining wall system include a wide construction space, enhanced excavation process and reduced time
and cost.
Zheng, et al. [11] presented A new strut-free retaining wall system, referred to as an inclined-vertical framed
retaining wall (IVFRW) for excavation in clay. They designed and established the previous system in China.
The excavation dimension is 80 m wide, 110 m long and 4.9 m deep. The diaphragm wall is 0.6 m thick and 12
m long. The inclined pile is 0.6 m thick, 12 m long and the inclination angle 20 degrees and the capping beam
is 0.423 m thick and 1 m wide. They used PLAXIS 3D to simulate IVFRW system and the hardening soil
model and Mohr-Coulomb to model the soil stress distribution and interface between soil and system structure
respectively. The soil strength reduction is equal to 0.67. The maximum wall deflection is 0.56% H, which is
less than 0.8% as reported in previous studies [12-14]. They made a parametric study to understand the
mechanism and performance of IVFRW. The results show that the wall deflection decreased when the inclined
pile length increased. In contrast, the increasing length of the vertical diaphragm wall changed the computed
vertical wall deflections and surface ground settlements.
Zheng, et al. [15] presented A new strut-free retaining wall system, referred to as an outward inclined-vertical
framed retaining wall (OIVFRW) for excavation in clay. They designed and established the previous system in
China. The excavation area is 23000
and 5.7 m deep. The diaphragm wall is 0.5 m thick and 11 m long.
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The inclined pile is 0.5 m thick, 10 m long and the inclination angle 18 degrees and the capping beam is 0.423
m thick and 1 m wide. They used PLAXIS 3D to simulate the OIVFRW system and the Hardening soil model
and Mohr-Coulomb to model the soil stress distribution and interface between soil and system structure,
respectively. The soil strength reduction is equal 0.67. The maximum wall deflection is 0.41% H, which is less
than 0.8%. They made a parametric study to understand the mechanism and performance of OIVFRW. The
results show that the wall deflection and surface ground settlement decreased when the inclined pile length
increased. In the past, most of excavation systems deep were between 5 m to 20 m and around 8 cases or 10
cases over 20 m [16]. Today, Tan, et al. [17] presented a statistical analysis of 592 deep excavation cases
history in Shanghai from 1995 to 2018 and they found 14% of cases over 20 m in Shanghai only. The required
for new system for deep excavation over 20 m is essential and vital to continue progress in deep excavation
system technology. This paper aims to find the effective range of dimension of buttress walls, rib walls and
cross walls and select the optimum design between three different designs in terms of minimizing the
maximum wall deflection and ground settlement for a strut-free retaining wall system which has 30 m deep in
soft clay.
METHODOLOGY
Model geometry, mesh, and boundary condition
The geometry of the excavation was assumed to be 150 m long, 75 m wide and 30 m deep. The model was
divided in two parts because it is symmetrical in two axes (x and y axes) and to minimize the time of program
analysis. The final excavation depth (H) was 30 m, and the height of the diaphragm wall was assumed to be 50
m. The cross walls and rib wall are located directly under the excavation level. The distance between the
diaphragm walls and the outer boundary of the mesh was larger six times the final excavation depth [18, 19],
which is 195 m to minimize the boundary effect and the depth of the model is 70 m. So, the model geometry is
465 m long, 285 m wide and 70 m deep.
The thickness of a diaphragm wall can be assumed to be 5% H in the preliminary design, where H is the final
excavation depth [20], so the diaphragm wall thickness is 1 m instead of 1.5 m because of excessive
movements were deliberately designed for this study. The mesh of the model is very fine as shown in Figure 1.
Figure 1: Typical geometry and finite element mesh used for analysis
Estimation of soil parameters
A 10-node tetrahedral element simulated the soil volume, and the suitable soil model for soft clay is the
hardening soil (HS) model [21] to simulate the settlement and deformation of soil.
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The hardening soil model simulates the soft clay soil around the retaining system. The hardening soil model
needs 11 parameters, which are unsaturated unit weight which equals 20 kPa, effective cohesion (
) which
equals 0 , effective angle of internal friction (
) which equals 30 [22], angle of dilatancy (
) which equals 0
[23], secant referential stiffness (
) which equals 9488 kPa [22], tangent referential stiffness for primary
oedometer loading (
) which equals 6642 kPa [22], unloading/reloading referential stiffness (
) which
equals 28470 kPa [24], power for stress-level dependency of stiffness (m) which equals 1, Poisson’s ratio for
unloading–reloading (
) which equals 0.2, reference stress for stiffness (
) which equals 100 kPa, value
for normal consolidation (
) which equals 0.5, failure ratio
which equals 0.9 [21, 25]. The input
parameters of the soil were typical values for Taipei silty clay (CL) and were obtained from Lim, et al. [26].
These parameters are calibrated and validated through two case histories [27].
Estimation of structural element parameters
A 6-noded isotropic-elastic-plate element was applied to model the retaining wall system structural members,
such as diaphragm walls, cross walls, rib-walls and buttress walls as elastic behavior. Also, the same element
was applied as to model the elastoplastic behavior and the elastic-plate element is used to simulate the concrete
in the retaining system. The elastic model of the plate needs eight parameters which are thickness (d), unit
weight
which equals 25 kN/m
3
, Young's modulus in first axial direction
which equals 19,717,606 kPa
[28], Young's modulus in second axial direction
, in-plane shear modulus
which equals 8,215,670
kPa [29], Out-of-plane shear modulus related to shear deformation over first direction
, Out-of-plane
shear modulus related to shear deformation over second direction
and Poisson's ratio
which equals
0.2 [29]. As the material is Isotropic so,
and
. The compressive strength of concrete
is assumed to be 27.45 MPa and According to the American Concrete Institute ACI 318-19 [28] code, the
nominal value of Young’s modulus for concrete can be estimated by using equation
. The
stiffness of the structural element was reduced by 20% from its nominal value because of the probability of the
occurrence of cracks in concrete resulting from the large bending moment of the diaphragm [30].
The interface element described the soil-structure interaction. If the relationship between structure and soil is
frictional so, the strength reduction factor
is equal to 1. Also, if the soil-structure interaction is
frictionless or weak frictional, then the strength reduction factor
is less than 1. In this research will
used
equal 1.
Select the height of stage excavation
The retaining wall system is constructed and excavated in many stages: the first stage is the installation of
retaining wall system structural members and the second stage is excavation of the entire soil. The soil was
excavated sequentially, and the groundwater level was assumed to be under the final excavation surface
ground so it would not affect the retaining system. Also, the excavation scenario is conducted at several
excavation heights and different mesh coarseness, and Table 1 shows the maximum wall deflection for every
trial in both directions for different excavation heights and mesh coarseness.
Table 1: Maximum wall deflection for every trial in both directions for different excavation heights and
mesh coarseness
Direction
Long direction
Short direction
Mesh coarseness
Mesh coarseness
Excavation height
(m)
Very
coarse
(m)
Medium
coarse
(m)
Very fine
(m)
Very
coarse
(m)
Medium coarse (m)
Very fine
(m)
3
8.34
7.857
8.736
1.545
1.591
1.56
4
7.12
6.565
8.32
1.39
1.269
1.49
6
6.183
7.183
8.369
1.15
1.106
1.55
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According to Table 1, the excavation height of 6 m is chosen with very fine mesh because it is similar to the 3
m excavation height and very fine mesh to minimize the calculation time.
The retaining wall system design
The retaining wall system comprises four main parts: diaphragm walls, rib walls, cross walls, and buttress
walls
as described in previous study [26]. The schematic diagram of the plan view of the Rigid and Fixed Diaphragm
(RFD) wall retaining system in Figure 2 and Figure 3 shows the schematic diagram of part of plan view and
cross section of the RFD system wall.
Figure 2: The schematic diagram of plan view of the RFD system wall
(a) (b) (c)
Figure 3: The schematic diagram of the RFD system wall: a) part of plan view, b) cross section A-A, c)
cross section B-B
Parametric study.
Four series of simulations were conducted to understand the performance and mechanism of the integrated
retaining system as listed in Table 2. For each series, the thickness of diaphragm walls is constant at 1 m. The
first series was conducted as the basic analysis for finding the optimum number of buttress and cross wall to
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minimize the wall deflection and surface ground settlement. The buttress walls arrangement was uniformly
distributed along both sides of the diaphragm wall. Also, the second and third series of scenarios are conducted
to find the optimum thickness and height of buttress wall. The fourth series is investigated to find the optimum
height of the cross wall and rib wall. Three designs were used to find the optimum design in series 1. The first
is one rib wall before every cross wall, as shown in Figure 4(a) in both directions, the second is two rib walls
before every cross wall as shown in Figure 4(b) in both directions and the third is two rib walls before every
cross wall in long direction and one rib wall before every cross wall in short direction as shown in Figure 4(c).
In total, 61 numerical runs were conducted to investigate to select the optimum design (series 1). As mentioned
before, there are 45 runs for the first type of design (type 1), eight runs for the second type of design (type 2)
and eight runs for the third type of design (type 3).
Table 2: List of simulation programs for design consideration of buttress walls
Series
Number of
buttress wall
(
)
Direction
Number of cross
wall (
)
Thickness of
buttress wall and
cross wall (
(m)
Hight of
buttress wall
(
(m)
Hight of
cross wall
(
(m)
Existence
of rib wall
1-type
1
5, 9, 13, 17, 21,
25, 29, 33, 37
Long
2, 4, 6, 8, 10,
12, 14, 16, 18
1
30
3 m
Yes
3, 5, 7, 9, 11
Short
1, 2, 3, 4, 5
1-type
2
8, 14, 20, 26
Long
2, 4, 6, 8
5, 8
Short
1, 2
1-type
3
8, 14, 20, 26
Long
2, 4, 6, 8,
3, 5
Short
1, 2
2
17
Long
8
0.6, 0.8, 1, 1.2, 1.4,
1.6
30
3 m
Yes
5
Short
2
3
17
Long
8
1
5, 10, 15,
20, 25, 30
3 m
Yes
5
Short
2
4
17
Long
8
1
30
3,6,9,12,18
Yes
5
Short
2
(b)
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(c)
Figure 4: Three types of excavation design: (a) One rib walls before every cross wall in both directions
(b) Two rib walls before every cross wall in both directions (c) Two rib walls before every cross wall in
long direction and One rib wall before every cross wall in short direction
Result and analysis
Effect of the number of buttress walls and cross walls on designs
Figure 5 shows the maximum wall deflection in a long direction for different number of buttress walls in both
directions for type 1, 2, and 3. The number of buttress walls in short direction did not influence the deflection
in long direction in all design types.
(a)
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(b)
(c)
Figure 5: The maximum wall deflection in a long direction for different number of buttress walls in both
directions: (a) type 1 (b) type 2 (c) type 3
From Figure 5, when the number of buttress walls is increased in long direction, the maximum wall deflection
in long direction decreased and decreased until the number of buttress walls equals 20, after that, it goes
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constant as well. Figure 6 shows the maximum ground settlement in a long direction for different number of
cross walls in both directions for type 1, 2 and 3.
(a)
(b)
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(c)
Figure 6: The maximum ground settlement in a long direction for different number of buttress walls in
both directions: (a) type 1 (b) type 2 (c) type 3
From Figure 6, when the number of buttress walls in long direction increased, the maximum ground settlement
in the long direction decreased until number of buttress walls equal 20 after that, it goes constant for type 2 and
3. When the number of buttress walls increased, the maximum ground settlement decreased until number of
buttress walls equal 25 in type 1. The optimum number of buttress walls in long direction are between 9 to 17,
14 to 20 and 14 to 20 for type 1, 2, and 3, respectively. Figure 7 shows the maximum wall deflection in short
direction for different number of buttress walls in both directions for type 1.
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Figure 7: The maximum wall deflection in a short direction for different number of cross walls in both
directions (type 2)
It is noted from Figure 11 that when the number of buttress walls in short direction increased, the maximum
wall deflection in short direction decreased slightly and the number of buttress wall in long direction did not
affect the maximum wall deflection in short direction and the effect of number of buttress walls in short
direction is small. Due to that the maximum wall deflection in long direction is the control of deformation for
the retaining wall system, so the focus on this paper will be in maximum wall deflection for the rest of this
paper. According to the effective range of buttress wall in long direction, the number of cross walls between 4
to 8 and 4 to 6 for type 1 and type 2 respectively. In the same time, the difference of the number of buttress
walls between type 1 and 2 is small. On the other hand, the number of buttress walls in short direction has
small effect on wall deformation. As result, the type 3 will be optimum design to different type in terms of
maximum wall deflection and maximum ground settlement.
Effect of thickness of the cross wall and buttress wall
The excavation model with four cross walls in a long direction and one cross wall in a short direction (type 2)
for the rest of the paper is chosen to investigate the thickness of the cross wall and buttress wall. The thickness
of the buttress wall and the cross wall vary from 0.6 m to 1.6 m with 0.2 m increments, as shown in Table 2.
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Figure 8 shows the maximum wall deflection for different thicknesses for long and short directions
respectively. Figure 9 shows the maximum ground settlement for different thicknesses for long and short
directions respectively.
(a)
Figure 8: The maximum wall deflection on different thickness of cross wall and buttress wall all and
buttress wall (a) long direction (b) short direction
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(a)
b)
Figure 9: The maximum ground settlement on different thickness of cross wall and buttress wall: (a)
long direction (b) short direction
It is noted that when the thickness of the cross wall and buttress wall increased, the maximum wall deflection
and maximum ground settlement decreased in both directions. When the cross wall and buttress wall thickness
changed from 0.6 m to 1.2 m, the maximum wall deflection decreased around 40% and 28% of the maximum
wall deflection in long and short directions respectively. When the cross wall and buttress wall thickness
increased from 0.6 m to 1.2 m, The maximum ground settlement is decreased by 41% and 29% in long and
short directions respectively. The increase in buttress wall and cross wall thickness plays a main role in
minimizing wall deflection and ground settlement. However, it is not a sufficient solution because it is almost
constant when the wall thickness is more than 1.4 m and it is not economic according to ratio of wall
deflection and ground settlement to volume of concrete.
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Effect of height of buttress wall
The height of buttress wall is varied from 5 m to 30 m with 5 m increments as shown in Table 2. Figure 10
shows the maximum wall deflection at different heights of the buttress wall in long and short directions,
respectively. Figure 11 shows the maximum ground settlement on the different heights of the buttress wall in
long and short directions respectively.
(a)
(b)
Figure 10: The maximum wall deflection on different heights of the buttress wall: (a) long direction (b)
short direction
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Figure 11: The maximum ground settlement on different heights of the buttress wall: (a) long direction
(b) short direction
From Figure 10 and Figure 11, it is noted that the maximum wall deflection and ground settlement are constant
when the height of the buttress wall height is from 20 to 30 m in both directions. The decreasing in buttress
wall height from 20 to 5 m is leading to an increase dramatically in maximum wall deflection and ground
settlement and this is clear in the long direction more than the short direction because the number of buttress
walls in long direction.
Effect of the height of the cross wall
Figure 12 shows the maximum wall deflection on different heights of the buttress wall in long and short
directions respectively. Figure 13 shows the maximum ground settlement on different heights of the buttress
wall in long and short directions respectively.
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(a)
(b)
Figure 12: The maximum wall deflection on different heights of the cross wall: (a) long direction (b)
short direction
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Figure 13: The maximum ground settlement on different heights of the cross wall: (a) long direction (b)
short direction
It is noted that the maximum wall deflection and the maximum ground settlement are decreased when the
height of the cross wall is increased until it is equal to 6 m. After that, it goes constant as shown in Figure 12
and Figure 13. Also, the maximum wall deflection of 6 m cross wall high is decreased by about 37 % and 32%
of the maximum wall deflection of 3 m cross wall high in long and short directions respectively. The
maximum ground settlement of 6 m cross wall high is decreased about 37 % and 9% of maximum ground
settlement of 3 m cross wall high.
The profile of the diaphragm wall and ground settlement
The location of maximum wall deflection and maximum ground settlement in the short direction is in the
middle of the short direction and the location of maximum wall deflection and maximum ground settlement in
the long direction is in the middle of the long direction. Also, all the wall deformation is cantilever shape with
a small transition at the toe of the diaphragm wall for both directions. The ground settlement deformation is
spandrel type and the shape of wall deformation and ground settlement is expected to occur [1] for all series in
Table 2.
CONCLUSIONS
This paper presents a series of three-dimensional finite element analyses to optimum design for strut-free
retaining wall system and effective range the number of buttress walls and cross walls, the effect of thickness
of the cross wall, height of buttress wall and height of the cross wall to understand deformation control
mechanisms of excavation. The following conclusions can be presented:
1- The optimum number of buttress walls in long direction are between 9 to 17, 14 to 20 and 14 to 20 for type
1, 2, and 3, respectively.
2- The effect of the number of buttress walls plays a significant role in controlling the deformation
characteristic of the excavation system in the long but not in the short direction. This requires the use of
additional procedures to control in the short direction.
3- the type 3 will be optimum design to different type in terms of maximum wall deflection and maximum
ground settlement.
4- The decrease in the number of cross walls and buttress walls decreased the stiffness of the excavation
project and did not affect the deformation characteristic of the excavation system [31, 32].
5- Effect of thickness of the cross wall and buttress wall is between 0.6 m and 1 m.
6- When the height of the buttress walls is from 20 to 30 m, the retaining system characteristics are constant.
The decreasing in buttress wall height from 20 to 5 m is leading to an increase dramatically in maximum
wall deflection and ground settlement.
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7- When the height of the cross walls is from 6 to 9 m, the retaining system characteristics are constant. The
decreasing in cross wall height from 6 to 3 m is leading to an increase in maximum wall deflection and
ground settlement.
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