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

For shallow burial jacked pipes, the jacking load will control the cross-sectional design of the pipe, and the soil pressure may be insignificant.. Basic theoretical principles The desi

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

re-moved from the face of the pipe jacking

shield or MTBM and transferred to the

sur-face for disposal while the shield or MTBM

and the product pipes to be installed are

dri-ven through the ground using the force

de-veloped 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,

se-wage, communication and electricity

pipe-lines, 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 pres-sure models in Japan Microtunnelling Asso-ciation (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 mod-ified 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, hy-drostatic pressure, etc.:

,

) 0 )(

0 ( ) 0 )(

0 (

H

y

x  

 (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 nega-tive

Application of the principle of super-position can simulate a full voltage in an massif soil of soil in a neighborhood

devel-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

con-tour 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

defor-mation 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 dis-placements 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 exam-ple, 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:

0 )

0 )(

1 ( ) 0 )(

0 ( ) 0 )(

1 ( ) 0 (     

Here, the shear stresses are not consi-dered due to the axial symmetry of the prob-lem Then, for the additional stress on con-tour unsupported produce the following rela-tion:

H

r 

( 1 )( 0 )

Further, considering the case in which the development of the lining is installed, it should be noted that it prevents the free

de-formation 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 resis-tance lining takes the form:

 0 , 0

) 0 )(

1 (

H q q

H

r    

where q0 resistance lining

Fig 1 Calculated scheme lining

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

re-gion 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

ex-pression for the additional radial stresses in

the ring S1 in the contact line L0 with an

massif soil:

0 ) 1 )(

1 (

q

r 

In the case where the lining is

mounted directly to the face output, the

solu-tion of the problem can be obtained using a

known solution of the problem of Lame

[21]: the plane strain thick-walled pipe,

si-mulating lining, the condition that the radial

displacement at the line of contact between

the lining and the massif soil due to the

ac-tion of addiac-tional stresses (5), (6), we obtain

the equation with respect to the value of

re-sistance to q0 Taking into account the

direc-tion of stresses, and by putting in the

formu-la Lame outer tube radius r0 = ∞, the

exter-nal pressure p0 = 0, we write the expression

for the movement of an infinite medium

(massif soil) on the contour L0:

 ,

0

G

R

where the notation: "−" sign in the

expres-sion (7) indicates that if the condition

q0 ≤ γH point massif soil, located on the

contour L0, shift into development

 0

0 0

1

2 

 E

G  mechanical characte-rization of soil, called the shear modulus (8) Equation (7) can be represented in the

form q0 = f(u0), that is,



























0

0

H

G R

u H

where

0 0 2 tg

R

G





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 cer-tain amount of movement of the circuit sec-tion 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:

2

2 1 2 0 1 2

1 2 0 0 1

0

R R

q G

R



The sign in the expression (10) is se-lected 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:

, tg 0

0 u 

where the notation:

1 2 0 1

2 1 2 0 0

1

2 1

2 tg

R R

R R R

G











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

equili-brium states backed by generation, line 2

diagram of equilibrium states lining

Ob-viously, 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

parame-ters 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):













tg

tg

1

1

q

1 2  .

1

1

2 0

2 1 1

0 2 0

2 1

2 0

2 1









































R

R G

G R

R

R

R

Additional stress in the lining (which

are at the same time complete, because no

initial stresses) are determined by the

formu-las:

- On the outer contour of the lining L0:

0 ) 1 (

q

r 

1

1

0 2 0

2 1

2 0

2 1 )

(

q R R R

R

ex









- Lining on the inner loop L1:

1

2 0 2 0

2 1

) (

q R R

in







The internal forces and bending mo-ments in the lining of the radial sections are calculated from structural mechanics [18]:

, 12

; 2

2 ) ( ) (

) ( ) (

































b M

b N

ex in

ex in

(16)





















0

1 0 1

R

R R R

R  the

thick-ness of the lining, b = 1 m

Considering expressions (14)(15) of the formula (16) take the form:

1

12

; 1

3 2

2

0 1 2

0 0

0 1

2 0

2 1 0

0



















































R

R b R q M

R R R

R b R q N

(17)

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

resis-tance R b Conditions strength bolting written

in the form [18]:

,

NS

where N  the calculated normal force,

which is determined from the first equation

(17), NS  limit bearing capacity of the

radi-al section of the lining, which is determined

by the relation 

















b kR

which k 1,

N

M

e0   the eccentricity of the application of the longitudinal force

Using expressions (17), we write





















b kR













































2 0

2 1

2 0

2 1

0

1 0

3 3

2 4 1

R R R R R

R R

Then the condition of the strength of

the lining of sections (18) takes the form

2 2 0

2 1

2 0

2 1 2

0

2 1 0

3

2 1

3 8















































R R R

R R

R b

kR q

where: P u 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

ordi-nate q0 = P u This means that the strength of the lining will be provided if the condition:

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  equili-brium states supported by the diagram

gen-eration, 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

equili-brium Offset massif soil u(l0), is imple-mented to the construction of the lining in the process of promoting the slaughter at a

distance l0, characterized by the segment

OO*

q

0

u

H



0

P

A 1

2 P

u(l )0 0

B

F

E D





0*

u( ) 8

Fig 4 Determination of the equilibrium state of geomechanical system "lining-massif soil" in the

construc-tion of the lining at a distance from the bottom l0

If development is unsupported for a

long time (the lining is installed at a

consi-derable 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

devel-opment of unsupported, that is,

u(∞) = γHR0/2G0

From Fig 4 that the construction of

the lining of the backlog of slaughter

gen-eration leads to a reduction of pressure on

the lining, ie the condition P ≤ P* The

me-chanics of underground structures [3] to

ac-count 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:















OF

OO OF OB

A O BE

AD

P

*

*

   

  0 1    0 1  0 ,

l f u

l u u

l u

u

















where

        ,

2 0

0

0 0

0











 







G

H R

l u u

l

u

l

0

0

2G

H R

the bias circuit output, results from the

deci-sion of the respective plane problem for

un-supported holes

To determine the value of u(l0) should

be considered three-dimensional picture

sur-face deformations develop near the

well-bore

Research related to finding the

dis-placement 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

numer-ical methods such as finite element method,

each of the authors offered their own

formu-la 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 corre-lation analysis between the values of the

ra-tio α* and the relative distance l0/R0 to slaughter generate suggested the use of the exponential dependence of [17]

64

, 0

0

75 , 1















l

Due to the linear nature of the prob-lem, 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 formu-las:

*

) 0 )(

0 ( ) 0 )(

0 (   

x y H , (xy0)(0)0 (25)

3 Conclusion

From the obtained ratio can be impor-tant from a practical standpoint conclusions: For example, from formula (16) that with decreasing thickness of the lining























0

1 0 1

R

R R R

R pressure on it is reduced, and at R1R0 the pressure is

ab-sent, 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

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“Gornye nauki i tehnologii”/ “Mining science and technology”, 2018, No 4, pp 34-40

взаимодействия «футеровка-массив грунта»

строитель-ства тоннелей для прокладки коммуникаций В таких больших городах, как Ханой, Хошимин, до сих пор остаются без решения проблемы про-кладки технических трубопроводов, силовых кабелей, водопровода, кана-лизации Статья описывает метод расчета прокладки коммуникационных тоннелей, учитывающий состав грунта и ограниченные условия строитель-ства для каждой конкретной области, с помощью небольшой туннельной бурильной машины Использование данного метода обеспечивает надеж-ность и экономическую целесообразнадеж-ность проекта строительства

Ключевые слова: масса грунта, прокладка тоннеля, напряжение, расчет, теория упругости,

микротоннелирование