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CSS design guide of rock shed for soil sliding and rock falling

1. Scope

This section provides requirements for the design of Rock Shed (Shelter Tunnel). A rockfall refers to quantities of rock falling freely from a cliff face. Rockfall is the natural downward motion of a detached block or series of blocks with a small volume involving free falling, bouncing, rolling, and sliding. A slope failure is the mass of soil beneath a natural slope or a slope of an embankment by the formation of a slide due to weakened self-retain ability of the earth under the influence of a rainfall or an earthquake.

The following conditions shall be secured for avoiding the collapse during construction and ensuring the stability of slope.

- A detailed geotechnical survey
- The location of settlement

2. Reference Standards

2.1 ASTM Standard

A761/A761M-16 Specification for Corrugated Steel Structure Plates, Zinc Coated, for Field-Bolted Arches
A796/A796M-17 Practice for the Structural Design of Corrugated Steel Arches for Storm and Sanitary Sewers and Other Buried Applications
D 698 Test Method for Laboratory Compaction Characteristics of Soil Using Standard Effort(600kN∙m/m3)
D2487 Classification of Soil for Engineering Purposes(Unified Soil Classification System)

2.2 CAN/CSA-S6-14, “Canadian Highway Bridge Design Code” Section 7 Structural Analysis

2.3 AASHTO Standard Section 12 Structural Analysis

2.4 KDS 44 60 05 : 2016(Korea Design Standard) Live Load (Rockfall) Calculation

3. Design Flowchart

4. Modeling

As Rock shed is asymmetric structure, the load is transferred from high to low by the unbalanced earth pressure. So the FEA analysis should be performed for accurate axial force of member, Since the constant earth pressure direction is in one direction and it is a structure that resists external forces.(See Figure.1, 2) (The FEA program used MIDAS GTS NX or ABAQUS)

The cover at the top of the shelter tunnel can be flattened to fit the site requirements (Figure 1), and the falling inclination angle of up to 30°(Figure.2) against the case will be designed so that the falling fall will fall to the opposite side at the inclination angle construction costs may be higher than in Figure 1, but there are benefits of minimizing maintenance costs and traffic control.

4.1 Material Condition of 2D Modeling
- CSS : 1D, Beam / Isotropic-Elastic
- Interface : 2D, Plane Strain / Isotropic-Mohr-Coulomb
- Natural soil : 2D, Plane Strain / Isotropic-Mohr-Coulomb
- Structural backfill : 2D, Plane Strain / Hyperbolic(Duncan-Chang)

- General backfill : 2D, Plane Strain / Hyperbolic(Duncan-Chang)

4.2 Material Condition of 3D Modeling
- CSS : 1D, 2D, Beam, Plate / Isotropic-Elastic
- Interface : 3D, Solid / Isotropic-Mohr-Coulomb
- Natural soil : 3D, Solid / Isotropic-Mohr-Coulomb
- Structural backfill : 3D, Solid / Hyperbolic(Duncan-Chang)
- General backfill : 3D, Solid / Hyperbolic(Duncan-Chang)
4.3 Boundary Condition of 2D Modeling
- Side : X-direction Displacement Constraint, Roller,
- Bottom : X, Y-direction Displacement Constraint, Hinge
4.4 Boundary Condition of 3D Modeling
- Side : X, Y-direction Displacement Constraint, Roller,
- Bottom : X, Y, Z-direction Displacement Constraint, Hinge

The design should be applied with expected conditions of the site construction and similar values as shown in Figure.1 & 2 and the results are shown in Table 1.

5. Load Calculation

5.1 Dead Load
- Calculated by the MIDAS GTS NX programMIDAS GTS NX。
5.2 Live Load (Rockfall) (KDS 44 60 05 : 2016)

There are two ways to calculate the impact strength on rock shed.
- When Rockfall is falling directly above the tunnel superstructure
- When Rockfall is falling within 5m from side wall
If rock-fall is falling directly on top of the structure, the impact force is calculated assuming that there is sand cushioning material.
If rock-fall is falling within 5m from side wall, the impact force is calculated using the theory of elastic modulus.

1) If Rockfall is falling directly above the tunnel superstructure

-PS =2.455 x λ2/5 x W2/3 x Hr3/5 x i
-PSV= PS × sinθ
2) If Rockfall is falling within 5m from side wall

- Pb = 3Pbs x2z / π (r2+z2)5/2

- Pbs = 2.455 × λa2/5 × W2/3 × Hr3/5
where,
Ps ,Pbs = Impact force on the soil surface caused by rockfall (kN)

λ = Lame’s constant, 5,000~8,000kN/m2

= Eν / (1+ν)(1-2ν)

λa = 1,000kN/m2
W = Unit weight of rockfall (kN)
Hr = Falling height of rockfall value (m)

i = modified coefficient for soil thickness (if soil thickness is 0.9m, i<1) θ = Gradient of slope, degrees
E =Modulus of elasticity of Sand(3.0MPa)
ν = Poisson’s ratio of soil "Poisson"

Pb = When the center of load point is 0 point, the earth pressure per unit area generated in x, y, z (kN/m2)

x = Horizontal distance from center of load point to wall (m)
y = Horizontal distance parallel from center of load point to wall (m)

z = Vertical distance from center of load point to wall (m)
r = Distance from center of load point to wall (m)

r2=x2+y2

The energy of rockfall is normally dependent on the degree of rock movement, the precise estimated weight of rockfall is required (KDS 44 60 05 : 2016)

The estimated weight of rockfall can be calculated by (m3) × 26.5 kN/m3 using the volume of rockfall.

Volume calculation of rockfall can be calculated by circle and hexahedron.
- R: radius(m), On circle.
- length × width × height, On hexahedron.
However if the weight of rockfall is impossible to calculate on site construction, It can be substituted by the average weight of rockfall, 0.4ton (On design input Condition).

6. Result

6.1 Axial Force

According to the FEA analysis, when you consider member check, Axial force is necessary results of service thrust regarding to Wall Resistance, Seam Resistance, Combined Thrust and Moment, Global Buckling, CSS Reaction.

6.2 Bending Moment

According to the FEA analysis, when you consider members check, bending moment is necessary results of service moment regarding to Combined Thrust and Moment.

7. Member Check (CAN/CSA-S6-14, AASHTO LRFD 2014)

7.1 Thrust

The thrust is calculated by the load factor multiplied by each live load considering dead load and impact coefficient.
The following formula measures compressive force considering the structural feature, backfill and relative stiffness of the structure against ground.

Tf = αDTD + αLTL(1 + DLA) (CAN/CSA-S6-14)

where,
TD = Unfactored thrust per unit length(Dead Load)
TL = Factored thrust per unit length(Dead Load+Live Load)

α = Load factor(αD=1.5, αL=1.75)
DLA = Dynamic load allowance expressed as a fraction of live load

7.2 Wall Resistance (AASHTO LRFD 2014, 12.7.2.3~4 )

Rn = ∅ fyA > Tf
where,
A = Wall Area

fy = Yield strength of Metal
∅ = Resistance factor as specified

7.3 Seam Resistance (AASHTO LRFD 2014, 12.7.2.5)

Rn =∅SR >Tf
∅ = Resistance factor as specified(0.67)
SR = Ultimate seam strength(kN/m)

7.4 Combined Thrust and Moment (CAN/CSA-S6-14 S-7, AASHTO LRFD 2014, 12.8.9.5 )

Since the rock shed structure has high flexural rigidity, the bending moment is inevitable. Therefore, it is necessary to examine the combination of thrust and moment considering the load factor.

(Tf/PPf)2 + Mf/MPf < 1.0
where,
Tf = Total factored Thrust
Mf = Total factored Moment
PPf = ∅Afy, Factor thrust resistance
MPf = ∅Zfy, Factor moment resistance

7.5 Global Buckling (AASHTO LRFD 2014, 12.8.9.6)

Rb = 1.2 ∅bCn(EpIp)1/3(∅sMsKb)2/3Rh
where,
∅b = Resistance factor for general buckling

Cn = Scalar calibration factor to account for some nonlinear effector=0.55

Ep = Modulus of elasticity of pipe wall material
Ip = Moment of inertia of stiffened culvert wall per unit length
∅s = Resistance factor for soil

Ms = Constrained modulus of embedment computed based on the free field vertical stress at a depth halfway between the top and springline of the structured.
Kb = (1-2υ) / (1-υ2 )
υ = Poisson’s ratio of soil "Poisson"

Rh = Correction factor for backfill geometry = 11.4 / (11+S/H)

S = Culvert span
H = Depth of fill over top of culvert

8. CSS Reaction
The foundation structure should be designed for member force and standard stability; over turning, sliding and bearing capacity by assuming that vertical and horizontal forces on the Corrugated Steel Structure Plates affect to the top base load.
Therefore the axial force acting on the Corrugated Steel Structure Plates can be calculated as the upper reaction force divided by the vertical and horizontal forces acting on the Corrugated Steel Structure Plates and the base joint.

9. Displacement

If the design backfill and the compacted density are in agreement with the actual engineered backfill and the compacted density, the displacement phenomenon and the displacement amount can be predicted in advance.

10. Case study

DAEDOTech Co., Ltd @Copyright

DAEDOTech Co., Ltd @Copyright

DAEDOTech Co., Ltd @Copyright

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DAEDO_RockShed_ConstructionProcedure_2019

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DAEDOTech Co., Ltd @Copyright

NOTE: The engineering design the model for Foundation, Head wall and Retaining Wall based on FEA analysis. Any further inquires concerning Design consultant, Please contact DAEDOTech Co., Ltd EngineeringTeam (ceseson@daedotech.co.kr)