ANALISIS LERENG BATUAN

Metode kinematika
• "Kinematic" refers to the motion of bodies without
reference to the forces that cause them to move
(Goodman, 1989).
• Untuk mengetahui potensi jenis longsoran yang mungkin
terjadi pada suatu lereng
• Data yang digunakan kombinasi orientasi bidang
diskontinyu, muka lereng bersama sudut gesek dalam
• Analisis dilakukan menggunakan proyeksi stereografis
• Asumsi dasarnya kohesi = 0

(a) (b)
Rock faces formed by persistent discontinuities: (a) plane
failure formed by bedding planes in shale parallel to face
with continuous lengths over the full height of the slope on
Route 19 near Robbinsville, North Carolina; (b) wedge
failure formed by two intersecting planes in sedimentary
formation dipping out of the face on Route 60 near
Phoenix, Arizona. (Image by C. T. Chen.)

Pengukuran struktur batuan
• Kedudukan struktur batuan
(sesar, perlapisan, dan
kekar) dapat ditentukan
dengan menggunakan
kompas geologi.
• Untuk menyatakan
kedudukan struktur batuan,
maka harus dilakukan
pengukuran tentang jurus
(strike), kemiringan (dip), dan
arah kemiringan (dip
direction).
• Kedudukan struktur batuan
dapat dinyatakan dengan
strike/dip atau dip/dip
direction.
Strike
Dip Direction
Dip

Contoh
• Misalkan suatu kekar mempunyai strike
N 60o E dan dip 40o maka penulisan kedudukannya
adalah N60oE/40o.
• Jika suatu kekar mempunyai dip 70o dan dip direction nya
N30oE maka penulisan kedudukannya adalah 70o/030o.
• Penulisan dip direction selalu dalam tiga digit.

Penggambaran bidang diskontinu dan kutub (pole) diskontinu :
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Penggambaran bidang & Kutub
• Perhatikan sebuah bidang
yang mempunyai kemiringan
50o dan arah kemiringan 130o.
• Langkah 1 : Kertas transparan
diletakkan di atas Equatorial
equal-area stereonet,
gambarkan lingkaran jaring
dan beri tanda titik utara dan
pusat jaring. Ukurkan arah
kemiringan 130o searah jarum
jam dari titik utara dan beri
tanda posisi ini pada lingkaran
jaring.

lanjutan
• Langkah 2 : Putar tanda arah
kemiringan ke arah utara sampai
berimpit dengan sumbu W – E.
Ukurkan kemiringan 50o dari lingkaran
luar ke arah pusat jaring. Dan gambar
busur lingkaran besar.
• Untuk menggambarkan kutub bidang,
ukurkan 50o dari pusat jaring ke arah
lingkaran luar jaring dan beri tanda
titik, yang merupakan kutub bidang
tersebut.
• Langkah 3 : Putarkan ke posisi
semula sehingga arah utara yang
ditandai pada langkah 1 berimpit
dengan arah utara jaring. Dengan
demikian, bidang dengan orientasi
kemiringan 50o dan arah kemiringan
130o telah tergambar.

Penentuan kedudukan umum
bidang-bidang diskontinu
• Setelah terbentuk garis-
garis kontur, maka akan
didapat kutub kontur,
yaitu daerah yang
menggambarkan
konsentrasi kutub bidang
tertinggi.
• Titik pusat kutub kontur
merupakan kutub
kedudukan umum bidang-
bidang diskontinu,
• Kedudukan umum bidang-
bidang diskontinu adalah
kebalikan dari cara
penentuan kutub bidang
diskontinu.

LATIHAN

Dua bidang mempunyai kemiringan 50o
dan 30o dan arah kemiringan 130o dan
250o, yang saling berpotongan, sehingga
perlu ditentukan arah (trend) dan
penunjaman (plunge) dari garis
perpotongannya
Langkah 1 : Satu bidang (50o/130o) telah
tergambarkan, dan penentuan lingkaran
besar bidang kedua ditentukan dengan
arah kemiringan 250o diputar sampai
berimpit dengan sumbu W – E. Dan
gambarkan lingkaran besar menurut
kemiringan 30o.
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Penentuan arah dan penunjaman garis perpotongan dua bidang

Langkah 2 : Titik perpotongan dua
lingkaran besar diputar sampai
berimpit dengan sumbu W – E jaring
dan plunge dari garis perpotongan
diukur sebesar 20,5o.
Langkah 3 : Kemudian gambar
tersebut dikembalikan ke kedudukan
semula sehingga tanda utara pada
gambar berimpit dengan titik utara
pada stereonet. Dan arah (trend) dari
garis perpotongan didapat sebesar
200,5o.
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Main types of block failures in slopes, and structural
geology conditions likely to cause these failures: (a) plane
failure in rock containing persistent joints dipping out of
the slope face, and striking parallel to the face; (b) wedge
failure on two intersecting discontinuities; (c) toppling
failure in strong rock containing discontinuities dipping
steeply into the face; and (d) circular failure in rock fill,
very weak rock or closely fractured rock with randomly
oriented discontinuities.

Figure 2.1: Stereographic projections of the requirements
for kinematically possible plane,wedge, and toppling
failures (from Hoek and Bray, 1981).

Identification of plane and wedge failures on a stereonet: (a) sliding
along the line of intersection of planes A and B (αi) is possible where
the plunge of this line is less than the dip of the slope face,
measured in the direction of sliding, that is ψi < ψf; (b) wedge failure
occurs along the line of intersection (dip direction αi) on slope with
dip direction αf because dip directions of planes A and B (αA and αB)
lie outside included angle between αi and αf; (c) plane failure occurs
on plane A (dip direction αA) on slope with dip direction αf because
dip direction of planes A lies inside included angle between αi and αf.

Planar failure
In Figure 2.18a, a potentially unstable planar block is
formed by plane AA, which dips at a flatter angle than the
face (ψA < ψf) and is said to ‘daylight’ on the face.
However, sliding is not possible on plane BB which dips
steeper than the face (ψB > ψf) and does not daylight.
Similarly, discontinuity set CC dips into the face and
sliding cannot occur on these planes, although toppling is
possible.
ψA < ψf

The poles of the slope face and the discontinuity sets (symbol P) are plotted on the stereonet in Figure
2.18b, assuming that all the discontinuities strike parallel to the face. The position of these poles in
relation to the slope face shows that the poles of all planes that daylight and are potentially unstable lie
inside the pole of the slope face. This area is termed the daylight envelope and can be used to quickly
identify potentially unstable blocks.
The dip direction of the discontinuity sets will also influence stability. Plane sliding is not possible if the
dip direction of the discontinuity differs from the dip direction of the face by more than about 20°. That
is, the block of rock formed by the joints will have intact rock at one end that will have sufficient strength
to resist instability. On the stereonet, this restriction on the dip direction of the planes is shown by two
lines defining dip directions of (αf + 20°) and (αf − 20°). These two lines designate the lateral limits of
the daylight envelope in Figure 2.18b.

27
Example of a plane failure within a
slope consisting mostly of sandstone.

Wedge failure
Kinematics analysis of wedge failures (Figure 2.16b) can
be carried out in a similar manner to that of plane failures.
In this case, the pole of the line of intersection of the two
discontinuities is plotted on the stereonet and sliding is
possible if the pole daylights on the face, that is, (ψI < ψf).
The direction of sliding of kinematically permissible
wedges is less restrictive than that of plane failures
because two planes with a wide range of orientations form
release surfaces. A daylighting envelope for the line of
intersection, as shown in Figure 2.18b, is wider than the
envelope for plane failures. The wedge daylight envelope
is the locus of all poles representing lines of intersection
whose dip directions lie in the plane of the slope face.

Figure 1.6:
Example of a
wedge failure in
shale bedrock,
State Route 2,
West Virginia.

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Toppling failure
For a toppling failure to occur, the dip direction of the discontinuities dipping into the face must be within
about 20° of the dip direction of the face so that a series of slabs are formed parallel to the face. Also, the dip
of the planes must be steep enough for interlayer slip to occur. If the faces of the layers have a friction angle
ϕj, then slip will only occur if the direction of the applied compressive stress is at angle greater than ϕj with the
normal to the layers. The direction of the major principal stress is parallel to the slope face (dip angle ψf), so
interlayer slip and toppling failure will occur on planes with dip ψp when the following conditions are met
(Goodman and Bray, 1976):
These conditions on the dip and dip
direction of planes that can develop
toppling failures are defined in Figure
2.18b. The envelope defining the
orientation of these planes lies at the
opposite side of the stereonet from
the sliding envelopes.

Figure 2.2: (A) Kinematics of toppling failure; (B) stereographic projection of the requirement for
toppling failure, indicating that the normals (poles to discontinuities) should plot in the shaded zone
(Goodman, 1989).
A toppling failure is likely to result when steep discontinuities are parallel to the slope face and dip into it
(Hoek and Bray, 1981). According to Goodman (1989), a toppling failure involves inter-layer slip movement.
While describing requirements for the occurrence of a toppling failure, Goodman (1989) stated: “If layers
have an angle of friction Φj, slip will occur only if the direction of the applied compression makes an angle
greater than the friction angle with the normal to the layers. Thus, as shown in Figure 2.2, a pre-condition for
inter-layer slip is that the normals be inclined less steeply than a line inclined Φj above the plane of the slope.
If the dip of the layers is σ, then toppling failure with a slope inclined α degrees with the horizontal
can occur if (90 - σ) + Φj < α”.

Longsoran bidang, baji, guling
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