10. Application to stability of rock slope‡：このマークが付してある著作物は、第三者が有する著作物ですので、同著作物の再使用、同著作物の二次的著作物の創作等については、著作権者より直接使用許諾を得る必要があります。

Rock slope
Natural slope
Cut slope for roadway etc.
Bench cut slope in open pit mine

Open pit mine
Coal
Limestone
Aggregate
著作権処理の都合で、この場所に挿入されていたBench cut

写真を省略させて頂きます。

10.1 Outline

Site

Prefecture

Date

Movement

Tenninkyo

Hokkaido

1980, 10/16

Slide

Ofuyumisaki

Hokkaido

1981, 12/19

Souunkyo

Hokkaido

Echizenmisaki

Volume（m3）Inclination

Rock type

20,00080

Welded tuff

Slide240,000

80

Pyroclasticrock

1987, 6/9

Fall

11,00080

Welded tuff

Fukui

1989, 7/16

Toppling

1,00090

Pyroclasticrock

Sarunagi

Nagano1991, 10/18

Fall

3,00080

Slate chert

Katanakake

Hokkaido

1993, 7/12

Slide-fall

2,00080

Pyroclasticrock

No.2 Shiraito

Hokkaido

1993, 7/12

Fall

2,50080

Pyroclastic
rock

Tanihana

Niigata

1995, 4/2

Fall

5,00070

Rhyolite

Toyohama

Furubira

1996, 2/10

Fall

11,00080

Pyroclasticrock

No.2 Shiraito

Shimamaki

1997, 8/25

Slide-toppling

42,00075

Pyroclastic
rock

Slope collapse whose volume was more than 10000 m3 between 1980 and 2001except for mine accidents (Ueno andYamagichi, 2002)

社団法人地盤工学会（1997）、北海道古平町国道
229号岩盤崩落調査委員会報告書、p. 9図2-1

制限資料

10.2 Examples of rock slope collapse

Toyohama (Investigation Committee forRock Slope Collapse at Toyohanma
Tunnel in Furubira, Hokkaido, 1997,
volume is 11,000 m3）

社団法人地盤工学会（1997）、北海道古平町国道
229号岩盤崩落調査委員会報告書、p. 5写真1-1

制限資料

Rock slope collapse at No. 2 Shiraito Tunnel(Investigation Committee for No. 2 Shiraito
Tunnel, 1998, volume is 56,000 m3)

著作権処理の都合で、この場所に挿入されていた『北海道新聞 第二白糸トンネルの岩盤崩壊記事の写真』を省略させて頂きます。

Collapse
Fill to prevent
further collapse

Rock slope cpllapsee at Sunago Coal Mine. A bench is 10 m high, volume
is 13,500 m3

Helicopter investigation around Shakotan
Peninsula in 1998

Investigation in Hiroo Town after Tokachi-oki
Earthquake in 2003Helicopter investigation in Hama Kotanuka
and Churui in 2004

10.3 Geometry of rock slope failure

General classification

著作権処理の都合で、Geometry of rock slope collapse(Goodman, 1980). (a)：Plane slide,(b)：wedge slide, (c)：toppling

この場所に挿入されていた『Goodman (1980), Introduction to RockMechanics, John Wiley and Sons, p. 256, Fig.
8.1』を省略させて頂きます。

制限資料

Toppling failure (Pant and Adhikary, 1999)
Reprinted from Rock Mech. Rock Engng, 1999, Vol. 32, No. 2, p.161, Fig. 3a, Pant, S. R. and Adhikary, D. P., Implicit andExplicit Modeling of Flexural Buckling of Foliated Slopes, pp. 157-164., with permission from CSIRO.

For Shakotan Peninsula（Investigation Committee for Toyohama
Tunnel Accident, 1997）

Detachment-sliding down type
Fracture grows upward
Weathered detachment
plane is vertical or steeply
inclinedSize of falling rock block is1 m to 10 m
Overhang geometry

Sliding down type
Fracture grows upward
Weathered detachment
plane is vertical or steeply
inclinedSize of falling rock blockis several meters to 10 m
Overhang geometry

Toppling type
Fracture grows downward
Weathered detachment
plane is vertical or steeply
inclinedSize of falling rock block isseveral meters to several
ten meters

Slide type
Fractures grow upwardand downward
Weathered detachment
planes are vertical andhorizontal
Falling rock block is
between 1 m andseveral ten meters.

10.4 Causes of rock slope collapse（Investigation Committee for Toyohama
Tunnel Accident, 1997）

Topography
Steep cliff, overhang

Geology, rock type andweathering
Igneous rocks
Hard and strong, but
discontinuous

Pyroclastic rocks
Soft and weakLess fractures, but easily
weathered

WeatherRain
Temperature variation
Freeze-thaw cycle

Ground water
Pore pressure

External forces
Earthquake
Erosion by sea wave

10.5 Criterion for rock slope collapse

Plane slide(Limit equilibrium method)
W sin β = CA + W cos β tan φW

Weight of rock block
1 HHH
⎛1
⎞
=γ⎜ H ⋅−tan β ⎟tan α 2 tan α tan α⎝2⎠

γH 2 ⎛ tan β ⎞=⎜1 −⎟2 tan α ⎝tan α ⎠γ

Unit volume weightCACohesion
Area of shear plane
H=tan α cos βFriction angle

φH

Tensile crackαβ

Shear planeExample
Calculate possible maximum H when cohesion is 10 MPa,friction angle is 30 degree, unit volume weight is 27 kN/m3、
α = 60 (degree) and β = 30 (degree).
Answer: 208 m

TopplingθθxxWeight of the rock isW = γ bhl.
where b, h, l is thickness, width, length ofthe rock, respectively. Ignoring the bending
moment due to deformation of the rockfor convenience, the bending moment at x = l is1
M = γ hbl 2 sin θ2θxＷMRThe reaction in the axial direction isθ

R x = γ hbl cosθ
Taking tensile stress as positive, the axialx

stress due to the reaction isσ R = −γ l cosθ

ＷRyM
Rx

Remember

σM =MyIz

where σ M is stress by bending moment, y is the distance from the neutral axis
and I z is the momentof inertia. Therefore, the stress at x = l becomes
12σ = σ M + σ C = γ hbl 2 sin θ⎛ 3l⎞= γ l ⎜ sin θ − cos θ ⎟⎝h⎠h 12− γ l cosθ
32 bh

Example
Calculate angle at which toppling occur in he case whereunit volume weight is 27 kN/m3, length is 100 m, width is
5 m and tensile strength of rock mass is 5 MPa.
Answer：3 degree10.6 Monitoring of rock slope(Hokkaido Development Bureau, 2004)

Simple measurement
北海道開発局建設部道路建設課、北海道における岩盤斜面対策工マニュアル（案）第6編6-9図6-3-3

北海道開発局建設部道路建設課、北海道における岩盤斜面対策工マニュアル（案）第6編6-9図6-10図6-34

北海道開発局建設部道路建設課、北海道における岩盤斜面対策工マニュアル（案）第6編6-9図6-10図6-35

制限資料
制限資料

Deformation

Fracture opening

制限資料

Relative displacement

Measurements using instruments
北海道開発局建設部道路建設課、北海道における岩盤斜面対策工マ
ニュアル（案）第6編6-9図6-10図6-3-6

北海道開発局建設部道路建設課、北海道における岩盤斜面対策工マニュアル（案）第6編6-9図
6-10図6-3-7

制限資料

制限資料

Strain of rock mass

Tilt of rock mass

Measurements using instruments
北海道開発局建設部道路建設課、北海道における岩盤斜面対策工マニュアル（案）第6編6-9図6-11図6-3-8

制限資料

北海道開発局建設部道路建設課、北海道における岩盤斜面対策工マニュアル（案）第6編6-9図
6-11図6-3-9

制限資料

Laser survey

GPSMeasurement in rock mass by using
instruments
北海道開発局建設部道路建設課、北海道における岩盤斜面対策工マニュアル（案）第6編6-9図6-11図6-3-10
制限資料

Borehole tiltmeter

北海道開発局建設部道路建設課、北海道における岩盤斜面対策工マニュアル（案）第6編6-9図6-11図6-3-11

制限資料

Rock mass deformation

Measurement in rock mass by using
instruments

北海道開発局建設部道路建設課、北海道における岩盤斜面対策工マニュアル（案）第6編6-9図6-12図6-3-12

制限資料

北海道開発局建設部道路建設課、北海道における岩盤斜面対策工マニュアル（案）第6編6-9図
6-12写真6-3-2

制限資料

Pipe type-strainmeter

Water level10.7 Prediction of rock slope collapse

Many dangerous slopes
When does it fall?

An overhang rock at Monami
Park in Sapporo

Prediction using displacement rate
dt/du is the inverse ofdisplacement rate
Collapse times of twocases of landslides anda rock slope collapse
were predicted byusing a similar method
at the error of 6 min., 5hours and 20 min.,respectively.

dt / dutOtF