International Conference on Civil Engineering

Architecture & Urban Sustainable Development

18 &19 December 2013, Tabriz , Iran

EVALUATION OF JOINTS INFLUENCE ON

SEGMENTAL TUNNEL LINING BEHAVIOR

Peyman Mahyar1*, Shahram Vahdani2

1. M.Sc. Student, School of Civil Engineering, University of Tehran, Payman.mahyar@ut.ac.ir

2. School of Civil Engineering, College of engineering, University of Tehran, Svahdan@ut.ac.ir

Abstract
The use of TBM for excavation and construction of tunnels such as subways, roads, and
railroads in urban areas are rapidly increasing. Yet, design of segmental tunnel linings are
based on empirical methods. These methods ignore the influence of type of segmental
joints and variations of stress distributions in cross-sectional areas of the segmental
linings, while the behavior of tunnel lining is significantly affected by the segmental
joints type and hence, they cannot predict realistic structural behavior of the lining
systems. This paper deals with two-dimensional finite element analyses of the segmental
tunnel lining for three conditions; segmental lining models without joints; segmental
lining models with pin joints; and with real behavior of joints. Numerical modeling
includes linear-elastic springs to model the surrounded ground and rotational springs at
joint of the segments. The final results of the analyses illustrated that different joint types
have little effect on the radial deformation of ring, therefore using extracted moment-
rotational behavior of joints causes realistic bending moment distribution, between the
hinged and fix cases of segmental joints.

Key words: mechanized tunnel, segmental lining, lining joints, ring performance, finite element
method.

1. Introduction
Shield tunneling has become a well-established tunnel construction method in various ground
conditions. The shield tunnel is lined by reinforced concrete segments through the use of
connecting bolts and with out of bolts [1]. The contact plane between each two adjacent
circumferential segments, in a single ring is indicated as a segmental joint. Due to the radial
and tangential deformation of the segmental lining, employing flexible joint is strongly
recommended. To prevent the concrete and gasket damage, the load in segmental joint must
be small [2]. The segmental joint controls the greater part of ring and the global lining
behavior. Proper understanding of the joint behavior helps to an improved understanding of
 International Conference on Civil Engineering
Architecture & Urban Sustainable Development
18 &19 December 2013, Tabriz , Iran

the realistic tunnel lining behavior which is essential for tunnel engineers to design a tunnel
structure in a more accurate and safe approach.
Most of the previous numerical modeling dealing with this type of problem has been based on
two-dimensional models which lead to problems of reduced complexity [3], [4]. For example
Muir Wood [5] investigated the segmental lining behavior as a homogeneous ring, Mansour
[6], Abu-Krisha [7] and Ding et al.[8] studied the influence of different parameters such as
face pressure, grouting pressure, material characteristics of the soil and depth of cover of the
tunnel, Hefny et al.[9] considered the behavior of jointed tunnel lining and
Teachavorasinskun[10] studied the effect of joint on moment distribution of lining. Also
Zhang & Koizumi [1] investigated the load bearing capacity of key-segment based on
experimental test results. Former researchers seldom dealt with the 3D modeling of segmental
lining like Klappers et al [11], Chen & Mo[12], [13]. Different theoretical models were
developed to describe the joint behavior with the aim of getting realistic analytical and
numerical lining models. For example, a simple theoretical model for describing the moment-
rotational behavior of the segmental joints was developed by Gladwell and later by Janssen
[2]. The moment-rotational behavior in the segmental joint derived by Janssen takes into
account only linear-elastic material behavior [14]. Using this idea the segmental joint will
collapse after having reached the maximum linear-elastic capacity [2]. The existence of joints
in a tunnel ring will influence the behavior and the actual stress pattern in the lining and hence
segmental joints can be used for lining behavior evaluation. The segmental joint will have a
behavioral mode somewhere between a total fixation and a hinge [15]. Therefore the inclusion
of joint is necessary. Yet, in most cases, design of segmental tunnel linings is based on
conventional methods. However, the conventional methods ignore the influences of segmental
joints and type of joint material and in most cases these joints are considered as a hinge. In
reality, these parameters cause to develop three-dimensional stress distribution in concrete
segments with corresponding undesired deformations. Furthermore, the non-uniform stress
distribution, with stress peaks and totally the unexpected stress paths in the segments are the
reason for the appearance of damages and cracks, which lead to a decrease in structural
durability and an increase in maintenance costs, and thereby a higher risk profile [16]. By
employing real moment-rotational behavior of these joints and assigning this behavior to joint
springs in 2D beam-spring numerical modeling it is possible to evaluate the influences of the
segmental joint type with various geometry and mechanical features on lining behavior.

2. Studied tunnel linings

Based on existing information available in design and implementation of mechanized tunnels,
all segmental joints common in domestic tunneling industry are classified. These joints
include segmental joints used in line 3, 4 and 7 of tehran subway, line 1 and 2 of tabriz
subway, line 2 of mashhad subway and third part of isfahan subway. All these tunnels are
circular with different excavated cross-sectional areas. These tunnels have been supported
 International Conference on Civil Engineering
Architecture & Urban Sustainable Development
18 &19 December 2013, Tabriz , Iran

with reinforced concrete segmental lining with a length of approximately 1.5m. These tunnels
have different inner and outer diameters and different segment numbers, thus in order to make
equal condition for comparison, inner and outer diameters are considered 8m and 8.5m,
respectively, and eight segments are considered in each ring. Studying these different
segmental joints shows that they can classified in four groups: rectangular joints, trapezoidal
joints, rectangular joints with straight bolt and rectangular joints with diagonal bolt (figure 1).

Figure 1: schematic picture of joints classification

3- Numerical model
To analyze the Influence of different joints on segmental tunnel lining behavior, 2-D finite
element model was used. In this model segments have been modeled by using two nodes
beam element and joints have been modeled by using rotational springs. These springs are
modeled for three conditions; segmental lining joints without joints; segmental lining joints
with pin joints; and with assigned treatment of the real behavior of joints spring. Due to the
axial symmetry around the y-axis half ring modeling is used for simplicity (figure 2).
Moment-rotational behavior of these rotational springs for four group of segmental joints that
was earlier mentioned, is extracted from mahyar’s work in 2013 [17].
 International Conference on Civil Engineering
Architecture & Urban Sustainable Development
18 &19 December 2013, Tabriz , Iran

Figure 2: beam-spring model for ring

The surrounding ground is represented by radial linear-elastic springs. The springs can be
placed in the radial and tangential directions. The tangential springs offer little value in the
analysis and an unnecessary complication to the model. The stiffness of the spring element is
related to Young’s modulus E (MPa) and Poisson’s ratio ν of the surrounding soil [18]. The
numerical value of the spring constant at each support is calculated from the modulus of
subgrade reaction of the surrounding ground multiplied by the tributary length of lining on
each side of the spring. Many ground condition can be encountered within the length of the
tunnel. Parametric studies that vary the ground conditions and the spring constants should be
performed to determine the worst case scenario for the lining [19]. Figure 3 shows spring
elements surrounding the lining which are placed in the radial direction. The stiffness of the
spring elements can be calculated as follows:
Ae Er
(1) K
R(1  r )
Where R is the radius of the tunnel (m), Er, ν are Young’s modulus (Mpa) and Poisson’s ratio
of the surrounding ground respectively, and Ae is specific subarea of the tunnel wall related to
the respective spring (m2). Giving specific subarea as:
(2) Ae  R b

Where θ is the radial angle of spring influence (rad.) and b is the length of the influence of
each spring in tunnel axis direction (m). The prescribed loads are applied to the model and the
corresponding resulted displacement at each joint is checked. For joint that moves away from
the center of the tunnel into the ground, the spring is left active. When the joint displacement
is toward the center of the tunnel, the spring is removed or made inactive. This process is
repeated until all displacements match the spring condition (active or inactive) at that joint
[18].

The earth pressure is proposed to act in radial direction towards the tunnel center as shown in
figure 4. The initial normal earth pressure acting on the tunnel lining σn0 can be defined as:
(3)  n   v 0 cos2    h 0 sin 2 
Where; σv0 is the overburden pressure σh0 is the horizontal earth pressure at rest which can be
defined as  h 0  kh 0 v 0 and θ is the angles measured counter clockwise from the tunnel
 International Conference on Civil Engineering
Architecture & Urban Sustainable Development
18 &19 December 2013, Tabriz , Iran

bottom, and Kh0 is the coefficient of horizontal earth pressure at rest [20]. Thus, based on
tunnel alignment, the maximum depth of studied tunnels is changing in range of 14m to 50m
and design is based on this overburden pressure [17]. Ground, lining and spring properties
that used in the numerical modeling are represented in table 1.
As shown in Figure 5, the loading overhead exerted on tunnel lining can be divided into
uniform and oval compressive loads. The uniform load is the average of minimum and
maximum loading on the tunnel lining and the oval load is half of the difference between
these loads which has a cos2θ distribution on tunnel lining, where θ is the angle measured
from the vertical direction around the tunnel. The uniform load causes uniform radial
deflection and stress distribution in the ring and the oval load leads to non-uniform radial
bending deflection and stress concentration.

Figure 3: Spring elements surrounded the circular lining Figure 4: Loads on shield tunnel lining [20]

Table 1: Properties of ground, tunnel and lining [17]

 International Conference on Civil Engineering
Architecture & Urban Sustainable Development
18 &19 December 2013, Tabriz , Iran

Properties Value
Tunnel inner Radios 4.00 m
Tunnel outerRadios 4.50 m
segmental lining thickness 0.25 m
length of ring or width of segmen 1.50 m
No. of segmens per ring 8
No. of segmental joints per ring 8
Young's modulus of concrete 30 Gpa
Poisson's ratio of concrete 0.2
unit weight of concrete 24.00 kN/m3
Uniaxial compressive strngth of concrete 35.00 Mpa
Young modulus of Soil 114.00 Mpa
Poisson's ratio of Soil 0.28
Coefficient of earth pressure at rest 0.5
Soil spring stiffness 3.886 MN/m

Figure 5: Loading subdivided into a uniform load σ0 and an ovalising load σ1

As previously emphasized, segmental joints determine the greater part the behavior of the
global lining. A good understanding of the joint behavior leads to an improved understanding
of test results and a more realistic analytical and numerical modeling. The behavior of
segment joints is significantly affected by the normal force present in the joint, caused by a
uniform radial pressure on the lining [2]. The uniform radial load is directly related to the
depth of the tunnel alignment, so due to placement of the tunnels at different depths, the
uniform radial pressure and the normal force in the segmental joints must be classified
according to the depth of the tunnel. ITA recommends four below critical sections for design
calculations: section with deepest overburden, section with the shallowest overburden, section
with highest groundwater table and section with the lowest groundwater table (figure 6) [21].
 International Conference on Civil Engineering
Architecture & Urban Sustainable Development
18 &19 December 2013, Tabriz , Iran

Figure 6: Critical sections to be checked [21]

4- Description of results
The results of the numerical models analyzed in this paper are briefly given in this section.
Figure 7 illustrates radius deflection of the ring as subjected to the prescribed loads that was
previously mentioned. It is obvious that different segmental joint types have a little effect on
radius deflection of the ring. Only in maximum bending moments (positive and negative)
deflection of different joint types lied between no joint and pin jointed rings and stiffer joint
types cause to approaching the treatment of rings to behavior of rings with no joint.

The numerical results of the circumferential bending moments are presented in figure 8. As
shown in figure 8, circumferential bending moment distribution of different joint types lied
between no joint and pin jointed rings and stiffer joint types cause to approaching the
treatment of rings to behavior of rings without joint.

case (1) case (2)

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Architecture & Urban Sustainable Development
18 &19 December 2013, Tabriz , Iran

case (3) case (4)

Figure 7: Representation of the circumferential radius deflection

case (1) case (2)

case (3) case (4)

 International Conference on Civil Engineering
Architecture & Urban Sustainable Development
18 &19 December 2013, Tabriz , Iran

Figure 8: Circumferential bending moment distribution in ring

As a consequence, the increase of uniform load (changing tunnel alignment depth) that causes
the higher normal force in the joints implies the production of higher bending moment acting
on tunnel lining and more deflection in lining as shown in figure 9&10.

Figure 9: Circumferential bending moment in different cases Figure 10: Radius displacement in different cases

The circumferential bending moment distribution represents stress distribution in lining,

accordingly in case of pin jointed and lining without joint stress concentration is obvious
while in similar cases with moment-rotational behavior of real joint assigned to the joint
spring stress concentration is obviously lower.

5- Conclusions
Six types of segmental joints, under effect of four loading types have been analyzed:

1- Using the realistic join behavior does not affect the deflection of the ring significantly.

2- True bending moment distribution lies between the hinged and the fix joints, closer to fix
joint.

3- the most efficient numerical model consist of; the beam element to represent the segment,
rotational spring to the joint behavior and compressive springs to represent the surrounding
media.

References
 International Conference on Civil Engineering
Architecture & Urban Sustainable Development
18 &19 December 2013, Tabriz , Iran

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Architecture & Urban Sustainable Development
18 &19 December 2013, Tabriz , Iran

[20] JSCE, 1996, Japanese standard for shield tunneling, 3rd Ed., Japan Society of Civil Engineers,
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