Table 3 The general law of similarity of the model test.

From: Model experimental investigation on staggered segmental tunnel linings considering the surrounding soil pressure

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Parameters

Geometric dimensions

Lining outer diameter

D

Cls=Dp/Dm

Segments thickness

t

Cls=tp/tm

Lining inner diameter

r

Cls=rp/rm

Bolt diameter

d

Cl=dp/dm

Lining width

B

Cls=bp/bm

Bolt length

l

Cl=lp/lm

Deformation parameter

Segment stress

σs

Cσs=CEs

Segment strain

εs

Cεs

Segment ring deflection

δs

Cδs=Cls

Segment ring angle

θs

Cθs

Material properties

Elastic modulus of segments

Es

CEs

Elastic modulus of bolts

Eb

CEb

Poisson ratio of segments

µs

Cµs

Poisson ratio of bolts

µb

Cµb

Mechanical properties of materials

Bending stiffness of segments

EsLs

CEsIs=CEsCls4

Bending stiffness of bolts

EbIb

CEbIb=CEbCl4

Shear stiffness of segments

GsAs

CGsAs=CEsCls2

Shear stiffness of bolts

GbAb

CGbAb=CGbCl2

Tension stiffness of segments

EsAs

CEsAs=CEsCls2

Tension stiffness of bolts

EbAb

CEbAb=CEbCl2

External loads

Concentrated load

F

CF=CEsCls2

Uniform load

q

Cq=CEs

Bending moment

M

CMs=CEsCls3

Similarity constants

Cls

15.5

Cl

15

CEs

12.41

CEb

5.92

Cµs

1

Cµb

1

Cεs

1

Cθs

1