Design Standards for Railway Structures and Commentary

(Cut and Cover Tunnel)Ghani

Introduction

Limit state design Allowable stress method

Ultimate limit state Serviceability limit state Fatigue limit state

Safety Factor

Load factor,

Structural analysis factor,

Material factor,

Member factor, Ground investigation coeff.,

Ground resistance coeff., Structure factor,

!

Design of Main Structure

Characteristic value of load, Fk

Design load, Fd = γf . Fk

Section force, S(Fd)

Design section force, Sd = ∑{γa

.S(Fd)}

Load factor, γf

Structural analysis coeff., γa

Section Force

Characteristic value of material strength, fk

Design strength of material, fd = fk / γm

Section capacity, R(fd)

Design section capacity, Rd = R(fd) / γb

Material factor, γm

Member factor, γb

Section Capacity

Verification equation,γi . Sd / Rd < 1.0

Safety from: Bending moment, axial force,

shear force

Safety from: Floating

Must satisfy

γ1 . Us / (WS+WB.2Q2+2QB) < 1.0

Must satisfy

1. Ultimate Limit State Study of safety from section failure and body stability:

Design of Main Structure

2. Serviceability Limit State Study of stress and cracking:

(i) Stress under bending moment and axial force:

Regarding the limits on stress, the bending compressive stress of concrete during action by permanent load is 40% or less of the design compressive strength, and the tensile stress of steelduring action by variable load is equal to or less than the design tensile yield strength.

(ii) Cracking:

Design of Main Structure

3. Fatigue Limit State

In a case where the percentage variable load share of the design section force is large and the number of cycles high, safety from fatigue is studied by confirming that the conditions in equation below are satisfied.

γi . σrd /(frd / γb ) < 1.0

Design of Temporary Work

(Design Standards for Railway Structures and Commentary – Cut

and Cover Tunnel)

Surveying

Planning

Hypothesizing Design

Condition

Design START

Is it sandy soil with high

groundwater level?

Studying boilingYES

Is there artesian water

below the bottom surface

of the cut?

NO

Studying heavingYES

Is it soft clay ground?

NOStudying heaving

by background load

YES

H > 15 m

NO

NOIs it based

on customary

design method?

YES•Computing embedding depth•Studying support work and wall surface

*Customary design method

•Deciding ground constant•Hypothesizing groundwater level•Construction environment

•Setting cutting range •Soil retaining work•Support work•Cutting (excavation) method•Auxiliary work method

Selecting soil retaining wall

YES NO

Can be used as main body

Hypothesizing cutting method and sequence, support work

type and location

Computing load

Computing design embedding length

•Embedment length decided based on:• balance of moments• boiling• creeping• heaving• bearing force

ABC

Section computation of wall body

Studying struts

C

B

A

• Struts• Ground anchor• Reinforcing material

Studying wales and angle braces

Computing deformation of soil

retaining wall

Is displacement of the soil retaining wall within the

allowable value?

NO• Allowed value decided based on tie-ins with main structure• Allowed value decided based on failure of background

NO

NO

Is displacement of surrounding

structures within allowable value?

NO Allowed value based on surrounding environment conditions

ENDYES

Special comment)* This design flow chart was mainly the elastic-plastic method. For the customary designmethod, necessary items are studied as convenient

Calculation (1)Active lateral pressure

Ps = Ks.qs

qs = surcharge load (10 kN/m2)

Ks = Ka

cohesion

For sand: For clay:

Wall friction, δ = ɸ/3

Passive lateral pressure

Pp ＝ Kpr(Σγ ti ・ hi － Pw) ＋ Kpc ・ c ＋ Pw in the case of sand Pp ＝ Kpr(Σγ ti ・ hi) ＋ Kpc ・ c in the case of clay

Σγ ti ・ hi － Pw > 0

Where:Pp: Passive lateral pressure (kN/m 2 ) Kpr: Passive lateral pressure coefficient of dead weight component of soil at the focus point Kpc: Passive lateral pressure coefficient of cohesive component of soil at the focus point c: Cohesion of soil at the focus point Σγ ti ・ hi: All of overburden pressure of soil at the focus point Pw: Pore water pressure at the focus point

𝐾 𝑝𝑟=cos𝜑2/{1−√ sin (𝜑+𝛿 ) .sin 𝜑cos𝛿 }

2

𝐾 𝑝𝑐=2√𝐾 𝑝𝑟

Calculation (2)Equal lateral pressureThe equal lateral pressure used for the beam elasto-plastic spring method is the lateral pressure that acts on the passive side as lateral pressure that does not contribute to deformation of the wall.

Accordingly, the computation is done based on the effective active lateral pressure and the effective passive lateral pressure obtained by subtracting the equal lateral pressure from the active and passive lateral pressures shown in the following Figure.

Boiling

Heaving

Heaving by background load

Embedment Length Design1. Toe stability based on lowest strut 2. Toe stability based on pivot point below excv. base

Designing Strut𝜎 𝑐

𝜎𝑐 𝑎𝑧+

𝜎 𝑏𝑐

𝜎 𝑏𝑎𝑦 ( 1−𝜎𝑐

𝜎 𝑒𝑎𝑦 )≤1

𝜎 𝑐=NA N=

𝑅×𝐵𝑛 +∆𝑁

𝜎 𝑏𝑐=𝑀𝑍 𝑀=

𝑊 0 .𝐿𝑘2

8

𝜎 𝑏𝑎𝑦=[140−2.4 (𝛽−4.5 ) ] 1.5

𝛽=𝐿𝑏

𝜎 𝑒𝑎𝑦=1100000

( 𝐿𝑟 𝑦 )2

Additional CalculationCalculation of Stress for Wale

𝑆𝑡𝑟𝑒𝑠𝑠 ,𝜎𝑏 : 𝑀𝑍 ≤ 𝜎𝑏𝑎

= Allowable bending stress

= Load to wale (kN/m/wale)

= Bending span of wale (m)

𝑊 𝑜=𝑅 . 𝛽 = Strut reaction per unit width

= Effective ratio to wale

= Section modulus (mm3)

𝜎 𝑏𝑎= {140−2.4 ( 𝜆−4.5 ) }1.5