Research design lining for utilities tunnel in the city based on state of lining massif soil

DOI: 10.17073/2500-0632-2018-4-34-40
Nguyen Duyen Phong (Hanoi University of Mining and Geology, Hanoi, Vietnam)
Dang Trung Thanh (Hanoi University of Mining and Geology, Hanoi, Vietnam)
Tran Tuan Minh (Hanoi University of Mining and Geology, Hanoi, Vietnam)
Nguyen Van Thinh (Hanoi University of Mining and Geology, Hanoi, Vietnam)
Research design lining for utilities tunnel in the city
based on state of "lining-massif soil"
Nowaday, in order to resolve the problem of utilities tunnel in large cities is very necessary. The technical
pipelines, power cables, plumbing, drainage, ... in the large cities such as Hanoi, Ho Chi Minh is still a
problem with no explanation. Within the paper, the method to calculate the anti-tunnel structure of small
tunnel by small tunneling machine. In fact, due to the condition of the soil is not good and the limited
construction conditions, it is necessary to calculate the composition of the tunnel for the tunnel. For each
area to ensure stability, aesthetics, economics, ... for the project.
Keywords: soil mass, tunnel lining, stress, calculation, elasticity theory, microtunneling, determination

1. Introduction
Microtunnelling is a special case of
pipe jacking [5], where remote control of an
automated microtunnel boring machine
(MTBM) is employed. Excavated soil is removed from the face of the pipe jacking
shield or MTBM and transferred to the surface for disposal while the shield or MTBM
and the product pipes to be installed are driven through the ground using the force developed by a jacking frame installed
in a fixed shaft.
Pipe Jacking has been widely used for
new pipeline installations [7]. Application
areas involve oil & gas, water supply, sewage, communication and electricity pipelines, and pipe-roof projects [9]. Usually
jacked pipes are glass Fibre Rein-forced
plastic Mortar Pipes (FRMP), concrete
pipes, clay pipes, cast ductile iron pipes, and
steel pipes.
For shallow burial jacked pipes, the

jacking load will control the cross-sectional
design of the pipe, and the soil pressure may
be insignificant. However, for deep burial
projects, high soil pressure may lead to the
buckling of pipes [15], then the soil pressure
becomes a crucial factor. Soil pressure on
jacked pipes was also invoked to estimate
the jacking force [11].

In current practices, the soil pressure
on jacked pipes is estimated upon soil pressure models in Japan Microtunnelling Association (JMA), German standard ATV A
161 (ATV A 161), UK ‘Pipe Jacking
Association’ (PJA), ASCE 27, and Chinese
standard GB 50332 (GB 50332) [2, 6, 8,
12, 14].
These soil pressure models are modified from one of Terzaghi arching models
(termed Arching model I) [13].
2. Basic theoretical principles
The design of technical tunnels shall
be arranged in areas of weak sediment, weak
soil characteristics, which exist in the initial
stress domain, causing gravity, hydrostatic
pressure, etc. The design of technical tunnels
shall be arranged in areas of weak sediment,
weak soil characteristics, which exist in the
initial stress domain, causing gravity, hydrostatic pressure, etc.:

(x0)(0)  (y0)(0)  H , (xy0)(0)  0,

(1)

where γ  the average volume weight of
soil, H  depth of the development; "" sign
is adopted in accordance with the rule of
elasticity theory, according to which the
compressive stresses are considered negative.
Application of the principle of superposition can simulate a full voltage in an
massif soil of soil in a neighborhood devel-

СТРОИТЕЛЬСТВО ГОРНЫХ ПРЕДПРИЯТИЙ И ОСВОЕНИЕ ГОРНОГО ПРОСТРАНСТВА

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opment as the sum of the initial σ(0)(0) and
additional σ(1)(0) (remove) the stresses caused
by the formation of development. Thus, we
can write:
σ(0)=σ(0)(0)+σ(1)(0),
(2)
where σ denotes all components of the stress
tensor.
The concept of "removable stresses"
was introduced by prof. I.V. Rodin [20] for
simulating the formation of the production
in a prestressed, massive massif of rocks.
Using this concept, it is easy to imagine that
in the formation of a development its contour must be freed from the total normal and
tangential stresses. This can be achieved by
superimposing stresses on the initial field

around the generation of additional stresses
of the same magnitude, but opposite in sign.
Physically, this means that the initial
stresses acting on the contour of the future
development must be "lifted".
After installing the lining, which has a
certain rigidity, depending on the thickness
of the underground structure and the deformation properties of the material from which
it is made, a redistribution of stresses occurs
in the massif soil. In this case, in the case
when the lining is installed directly into the
face immediately after opening the section
of the mine, the removed (additional)
stresses acting on the side of the massif soil
are completely transferred to it as a load
(radial pressure). The lining is included in
the joint work with the massif soil as an

integral element of the unified deformable
system "lining-massif soil". The calculation
scheme for determining the permissible displacements of the massif soil and stresses in
the support is shown in Fig. 1.
Having thus described the problem has
an analytical solution presented, for example, in [16, 17]. Following the provisions set
out in the above-mentioned works, altering
the way to solve this problem. Assuming
that development is not supported, then the
contour L0 massif soil (area S0) boundary
condition for the total stress in the polar
coordinate system, taking into account the

expressions (1), (2) can be written as:
 (r0 )   (r1)(0 )   (r0)(0)   (r1)(0)  H  0. (3)
Here, the shear stresses are not considered due to the axial symmetry of the problem. Then, for the additional stress on contour unsupported produce the following relation:
 (r1)(0)  H .
(4)
Further, considering the case in which
the development of the lining is installed, it
should be noted that it prevents the free deformation contour L0 development, creating
resistance. For convenience, we consider the
interaction of elements of a single system of
"lining-massif soil", as shown in Fig. 2.
Condition (4), taking into account the resistance lining takes the form:
 (r1)(0 )  H  q0  q0  H ,
(5)
where q0  resistance lining.

Fig. 1. Calculated scheme lining
СТРОИТЕЛЬСТВО ГОРНЫХ ПРЕДПРИЯТИЙ И ОСВОЕНИЕ ГОРНОГО ПРОСТРАНСТВА

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Fig. 2. The scheme of loading a single deformable system "lining-massif soil"

In (5) accepted that the normal stresses
acting in the direction to the contour L0 region S0, are compressed, ie negative. The
outer loop support (ring S1) having radial
compressive stress q0, simulating mountain
pressure on underground construction from
the rock mass (the area S0). Neglecting the

initial stresses in the lining, we write the expression for the additional radial stresses in
the ring S1 in the contact line L0 with an
massif soil:
 (r1)(1)   q0 .
(6)
In the case where the lining is
mounted directly to the face output, the solution of the problem can be obtained using a
known solution of the problem of Lame
[21]: the plane strain thick-walled pipe, simulating lining, the condition that the radial
displacement at the line of contact between
the lining and the massif soil due to the action of additional stresses (5), (6), we obtain
the equation with respect to the value of resistance to q0. Taking into account the direction of stresses, and by putting in the formula Lame outer tube radius r0 = ∞, the external pressure p0 = 0, we write the expression
for the movement of an infinite medium
(massif soil) on the contour L0:
R
u0   0 q0  H ,
(7)
2G0
where the notation: "−" sign in the expression (7) indicates that if the condition
q0 ≤ γH point massif soil, located on the
contour L0, shift into development.

G0 

E0
 mechanical characte21   0 

rization of soil, called the shear modulus. (8)
Equation (7) can be represented in the
form q0 = f(u0), that is,

 u 2G0 
  H  u0 tg 
q0  H 1  0
R

H
0


2G0
where tg  
.
R0

(9)

This relation (9) in the mechanics of
underground structures is called the equation
of equilibrium states of soil mass, since it
implies that each value of resistance support
(pressure on the lining) corresponds to a certain amount of movement of the circuit section of development. Further, the problem of
putting in Lame outer tube radius r0 = R0,
the external pressure p0 = q0, the inner radius
r1 = R1, and the internal pressure of p1 = 0,
we arrive to the second problem of plane
deformation lining. We write the expression
for the radial displacements of points of the
outer contour of the lining:
R

q
u0  0 2 0 2 1  21 R02  R12 . . (10)
2G1 R0  R1





The sign in the expression (10) is selected for the same reasons as in the formula
(7), i.e. if q0 > 0 point of the contour L0
moved inside the ring (lining).
Equation (10) may also be present in
the form q0 = f(u0), and is easy to see, this
relationship is linear. We represent it in the
form of:

СТРОИТЕЛЬСТВО ГОРНЫХ ПРЕДПРИЯТИЙ И ОСВОЕНИЕ ГОРНОГО ПРОСТРАНСТВА

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q0  u0 tg ,

(11)

where the notation:

tg  

R02  R12

2G1
. (12)
R0 1  21 R02  R12





Equations (9) and (11) connect the
same parameters q0 and u0. We construct the
corresponding graphic dependences together
in one drawing, as shown in Fig. 3 [1, 10].

Fig. 3. Determination of the equilibrium state of a single deformable system "lining-massif soil"

Fig. 3 line 1 is a diagram of equilibrium states backed by generation, line 2
diagram of equilibrium states lining. Obviously, the point A of intersection of two
charting will correspond to the equilibrium
state of a single deformable "lining-massif
soil". The value of q0 = P corresponds to the
pressure on the lining (lining resist) with
given geometrical and mechanical parameters set directly in the face, and the value of
u0 = U  displacement massif soil in these
geological conditions. The position of point
A is determined by the combined solutions
of equations (9) and (11):
1
q0  H

tg 

1
tg 
R12
R02
 H
. (13)
 R12  G0 
R12 
1  2  
1  2   2 
R0 
 R0  G1 
Additional stress in the lining (which
are at the same time complete, because no
initial stresses) are determined by the formulas:
- On the outer contour of the lining L0:
1

R12
1 2
R0
( ex)
(1)
 r   q0 ;    
q0 ; (14)
R12
1 2
R0
- Lining on the inner loop L1:
2

(in )  
q0 . .
(15)
R12
1 2
R0
The internal forces and bending moments in the lining of the radial sections are
calculated from structural mechanics [18]:
(in )  (ex)
b;
2
(in )  (ex) 2
M  
b ,
12
N 

(16)

 R 
where   R0  R1  R0 1  1   the thick R0 
ness of the lining, b = 1 m.
Considering expressions (14)(15) of
the formula (16) take the form:

R2 
 3  12 
qR
R0 
N   0 0 b

;
R1 
2
1



R0 

2
q0 R02  R1 
M 
b 1   .
12  R0 

СТРОИТЕЛЬСТВО ГОРНЫХ ПРЕДПРИЯТИЙ И ОСВОЕНИЕ ГОРНОГО ПРОСТРАНСТВА

(17)

37


where: Pu  limit pressure that can withstand
considered bolting without loss of bearing
capacity.
Thus, the line 2 in Fig. 3 characterizes
the equilibrium state of the concrete lining,
it should be limited to the point having ordinate q0 = Pu. This means that the strength of
the lining will be provided if the condition:
P ≤ Pu

(21)
Significantly improve the static lining
work is possible if it does not build directly
at the bottom and install with some lag l0
from the bottom. In this case, the diagram
for the determination of the equilibrium state
of the deformed system "lining-massif soil"
is as shown in Fig. 4.
Here, as before, a straight 1  equilibrium states supported by the diagram generation, 2  line diagram of equilibrium
states lining, erected at a distance l0 from the
bottom. A point of intersection of the graph
corresponds to the equilibrium state of a
single deformable system "lining-massif
soil". For comparison, a straight 3 (dotted
line) shows a diagram of equilibrium states
lining being built directly at the bottom and
a point B  appropriate occasion equilibrium. Offset massif soil u(l0), is implemented to the construction of the lining in
the process of promoting the slaughter at a
distance l0, characterized by the segment
OO*.

The expression (17) allows you to test
the strength of the lining.
Suppose, for example, the lining is
made of concrete, which compressive
strength is characterized by calculated resistance Rb. Conditions strength bolting written
in the form [18]:

N  NS ,

(18)

where N  the calculated normal force,
which is determined from the first equation
(17), NS  limit bearing capacity of the radial section of the lining, which is determined
 2e 
by the relation NS  kRb b1  0  , in
 

which k  1 , e0 

M
N

 the eccentricity of

the application of the longitudinal force.
Using expressions (17), we write
 2e 
NS  kRb b1  0  
 



R2 
4 2  12 
R0 
 R 
. (19)
 kRb R0 1  1  

2
R


R
0

 3 3  1 

R02 

Then the condition of the strength of
the lining of sections (18) takes the form
 R12 
R2 
1  2  2  12 
R0 
8kRb  R0 
Pu  q0 
2
3b

R2 
 3  12 
R0 


(20)

q

H

0

1
B
A

P*

P

3

2


F u0

8


0* E D
0
u(l0 )
u( )

Fig. 4. Determination of the equilibrium state of geomechanical system "lining-massif soil" in the construction of the lining at a distance from the bottom l0

СТРОИТЕЛЬСТВО ГОРНЫХ ПРЕДПРИЯТИЙ И ОСВОЕНИЕ ГОРНОГО ПРОСТРАНСТВА

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If development is unsupported for a
long time (the lining is installed at a considerable distance from the bottom when
l0→∞), all the possible displacement of the
massif soil at this time and realized OF
interval corresponds to a shift in the development
of
unsupported,
that
is,
u(∞) = γHR0/2G0.
From Fig. 4 that the construction of
the lining of the backlog of slaughter generation leads to a reduction of pressure on
the lining, ie the condition P ≤ P*. The mechanics of underground structures [3] to account for this effect using the ratio:
P=P*α* or α*=P/P*.
(22)
Considering the similar triangles AEF
and OBF, O*AD and OBE in Fig. 4, can be
written:
P
AD O * A OF  OO *
* 





P * BE
OB
OF
u    u l0 
u l 

 1  0  1  f l0 , (23)
u  
u  
where
u l 
u l0 
R H
f l0   0 
, u    0

2G0
u    R0 H 


 2G0 
the bias circuit output, results from the decision of the respective plane problem for unsupported holes.
To determine the value of u(l0) should
be considered three-dimensional picture surface deformations develop near the wellbore.
Research related to finding the displacement contour generation, depending on
the distance to the bottom, in a large number
of works, among which are the works of
N.A. Davydov [19] and M. Baudendistel [4].
Deciding the proper task of the theory of
elasticity in the volume setting using numerical methods such as finite element method,

each of the authors offered their own formula for determining the value of f(l0).
Using a concrete representation for
f(l0), being the substituted into the expres-

sion (23), arrive at the appropriate formulas
for the calculation of the correction factor
α*. So, based on the results Baudendistela
M., prof. N.S. Bulichev a result of the correlation analysis between the values of the ratio α* and the relative distance l0/R0 to
slaughter generate suggested the use of the
exponential dependence of [17]
 1, 75 0 R0 
.
(24)
*  0,64 e



Due to the linear nature of the problem, in geomechanics accepted accounting
backlog of construction of the lining of the
slaughter carried out by adjusting the initial
stress field (1) intact massif soil. Then the
corresponding components of the initial
field multiplied by the value of α*, hence the
initial stresses are determined by the formulas:
l

(x0)(0)  (y0)(0)  H *, (xy0)(0)  0 . (25)
3. Conclusion
From the obtained ratio can be important from a practical standpoint conclusions:
For example, from formula (16) that with

decreasing thickness of the lining

 R 
  R0  R1  R0 1  1  pressure on it is
 R0 
reduced, and at R1  R0 the pressure is absent, that is, q0→0. In very soft ground,
when the condition G1>>G0 (G1  the shear
modulus of the material lining) and can take
G0/G1→0, the pressure q0 in the lining tends
to the value of the initial stress in the rock
mass in its natural state, e.g. q0→γH.
References
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Huy, Nguyen Duyen Phong, Andrey S. Samal,
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in Trenchless Construction. Reston, Virginia,
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“Gornye nauki i tehnologii”/ “Mining science and technology”, 2018, No. 4, pp. 34-40
Название:
Аннотация:

Ключевые слова:

Метод расчета коммуникационных тоннелей в черте города на основе
взаимодействия «футеровка-массив грунта»
В настоящее время перед мегаполисами остро стоит проблема строительства тоннелей для прокладки коммуникаций. В таких больших городах,
как Ханой, Хошимин, до сих пор остаются без решения проблемы прокладки технических трубопроводов, силовых кабелей, водопровода, канализации. Статья описывает метод расчета прокладки коммуникационных
тоннелей, учитывающий состав грунта и ограниченные условия строительства для каждой конкретной области, с помощью небольшой туннельной
бурильной машины. Использование данного метода обеспечивает надежность и экономическую целесообразность проекта строительства.
масса грунта, прокладка тоннеля, напряжение, расчет, теория упругости,
микротоннелирование

СТРОИТЕЛЬСТВО ГОРНЫХ ПРЕДПРИЯТИЙ И ОСВОЕНИЕ ГОРНОГО ПРОСТРАНСТВА

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