A case study on an open hillside landslide impacting on a flexible rockfall barrier at Jordan Valley, Hong Kong

Abstract

A case study on an open hillside landslide impacting on a flexible rockfall barrier at Jordan Valley, Hong Kong is presented in this paper. The landslide occurred sometime in June 2008. This is so far the only case history of landslide debris having been intercepted by a flexible rockfall barrier in Hong Kong. The landslide scar is 10 m wide and 7 m long, and the landslide volume is about 110 m³. The landslide debris was largely retained by the barrier but two of the barrier posts were severely damaged and failed. Debris mobility analysis and structural analysis of this case history have been undertaken with a view to obtaining a better understanding of the possible landslide dynamics and behaviour of flexible barrier upon debris impact. The analyses appear to have reproduced some of the salient field observations. The probable key contributory factors to the failure are highlighted and discussed. Through the study, the possible range of equivalent pseudo-static impact pressure exerted on the flexible barrier by the landslide debris is assessed. The site observations and results of the analyses provide insights pertaining to the importance of robustness in the design and detailing of flexible debris-resisting barriers.

Appendixes

Annex A—Properties and dimensions of the structural components of the barrier adopted in setting up the structural model

Ring net

• 1. Diameter of ring: 350 mm

• 2. Diameter of ring wire: 3 mm (7 spirals)

• 3. Six rings connection

Hollow steel post

• 1. Height: 5 m

• 2. Size: 140 mm × 140 mm

• 3. Thickness: 4 mm

• 4. Radius of gyration: 55.2 mm

• 5. Cross section area = 2.14 × 10³ mm²

• 6. Moment of inertia = 6.52 × 10⁶ mm⁴

• 7. Section modulus = 93.1 × 10³ mm³

• 8. Yield stress = 235 MPa

• 9. Elastic modulus = 200 GPa

• 10. Founded on shallow concrete footing of dimensions 400 mm × 400 mm × 500 mm depth

Energy dissipating device

The energy dissipating devices attached to the uphill cables were not activated as observed during the site inspections. Energy dissipating device is therefore not included in the structural model.

Extension rope cables

• 1. Diameter of top rope cable is 20 mm (6 threads of 19 wires)

• 2. Diameter of bottom rope cable is 20 mm (6 threads of 19 wires)

• 3. Tensile failure load is 270 kN

Annex B—Estimation of energy dissipation by plastic deformations of barrier posts and failure of post foundations

B.1 Energy dissipation by plastic deformations of barrier posts

Energy dissipation by plastic deformations of barrier posts could be estimated based on plastic moment of the posts and the angle of rotation:

$$ E={M}_p\theta $$

(B1)

where

M _p :

plastic moment of the structural member

θ :

angle of rotation

M _p is the multiple of the sectional modulus (Z) and yield stress (σ _p ) which equal to 22 kNm. Z and σ _p of the steel posts are 93.1 × 10³ mm³ and 235 MPa respectively. However, M _p is reduced to 14 kNm due to buckling failure (see M _x for post P1 shown in Table 1). Site inspections indicated that the angle of rotation of posts P1 and P15 was about 90°, i.e. θ is taken as π/2. It follows that energy dissipation due to bucking of the two posts is 44 kJ for two failed posts (i.e. P1 and P15).

B.2 Energy dissipation by failure of post foundations

The energy dissipation due to foundation failure of posts relates to the sliding resistance (R _T ) acting on the post foundation and the displacement of the foundation. A simplified approached is adopted in this calculation. It is assumed that R _T , which comprises the resistance acting on the base of the foundation (R _S ) and the passive resistance (R _P ), is constant throughout displacement process (see Fig. 18).

Calculation of R _P :

$$ {R}_P=0.5{k}_p\gamma {H}^2w $$

(B2)

where

k _p :

is passive pressure coefficient = 3.7 (using Rankin theory with friction angle at the interface of the foundation and ground = 35° assumed)

γ :

is unit weight of soil, assumed to be 18 kN/m²

H :

is depth of foundation = 0.5 m

w :

is width of foundation = 0.4 m

Hence, R _p  = 6.7 kN (say 7 kN)

Calculation of R _S :

$$ {R}_S=N \tan \phi $$

(B3)

where

N :

is normal force acting on the base of foundation (=68 kN), which is the calculated axial compression force when UDP = 50 kPa (see Table 1), with self-weight and side friction neglected

ϕ :

is friction angle at the interface of the foundation and ground = 35° assumed

Hence, R _S  = 48 kN

Fig. 18

Calculation of the sliding resisting acting of the post foundation

Total sliding resistance, R _T  = R _S  + R _P  = 55 kN

Energy dissipation is approximated by the multiple of R _T and displacement of foundations. The displacements of posts P1 and P15 are 2.2 and 1 m, respectively, as observed on site. It follows that the energy dissipation due to failure of post foundation is 176 kJ.