Preliminary study of karst collapse : forecast method
ENDINS, n.' 13.1987. Clutat de Malloma.
PRELlMlNARY STUDY OF KARST COLLAPSE.
FORECAST METHOD
by Tan JIANYI * and Chen JlAN **
Resurn
L'objecte d'aquest treball és analitzar diversos rnetodes de predicció d'enfonsarnents carstics.
S'estableixen dos rnodels de predicció, en diferents condicions, d'acord arnb el principi d'equilibri
limit.
Es contrasten arnbdós models arnb les dades procedents de Yulin, Guilin, Guangxi i d'altres
Ilocs. Els resultats de I'aplicació d'aquests rnodels mostren I'existencia de concordancia entre el re-
sultat calculat pel model i la realitat. Aixi, els dos rnodels es poden usar en la predicció d'abisa-
rnents carstics i en I'estimació de I'estabilitat de la cobertura superficial del terreny.
Aquesta nota s'ocupa detalladarnent de la relació entre els rnodels i els factors que influeixen
en ells, en base a la situació dels coneixernents actuals; tarnbe s'apunta, rnés generalrnent, el con-
tingut dels esmentats rnetodes quant a la predicció d'eventuals abisarnents. Per acabar, la predicció
d'enfonsarnents ha estat realitzada a San Lidian, Guilin, Guangxi, usant els dos rnodels.
Abstract
The object of this paper is to discuss forecast rnethods of karst collapse. According to lirnit
equilibriurn principie two collapse forecast rnodels are established in different conditions of the
level.
Two rnodels are checked by the data in Yulin, Guilin of Guangxi and other places. The checking
result show to be consistency beíween the calculating result by the model and realiiy. So the iwo
models can be used in forecast of karst collapse and estirnation of the cover stabiliiy.
The paper dealt in detail with the relationship between the rnodel and its affecting factors in the
light of actually situation and also generally point out the collapse forecast content. Finally the co-
llapse forecast is carried out using the two rnodels in San Lidian, Guilin, Guangxi.
lntroduction
Karst collapse is the most projecting problem
tend continuously up until collapse with gravity.
of environmental engineering geology in covered
Karst collapse result from many factors such
karst area. Collapse serious consequences have
as karst development degree, groundwater fluctua-
been widly paid attention to. In order to avert and
tion, cover thickness and its physical mechanic
reduce collapse and losses the research on diffe-
property. These factor affect the formation of co-
rent aspects of collapse has been done. The co-
Ilapse.
llapse genesis and type research are focal point,
the collapse forecast research is the gap yet. The-
refore it is necessary to do collapse forecast.
Premise condition
The formation of collapse is a complex pro-
cess. The cover up karst cave slack and peel with
Premise conditions of establishing model are
the groundwater erosion, vacuum draw erosion,
assumed in the paper, they include:
aero-erosion etc, t o form the soil cave, the one ex-
1. Karst developed under cover and there are karst
cave;
*
2. The collapse t o be assumed cylinder;
Central Station of Environmental Hydrogeological Observa-
3. There is flowing groundwater; and
tion of Guilin, Guangxi. China.
** lnstitute of Karst Geology of Guilin, Guangxi, China.
4. The cover may be slacking or peel.

Model establishment
1. The First Model
According to different conditions of groundwa-
The first model is established in the condition
ter level two models of collapse forecast are esta-
of confined water. In this case, there are several
blished.
acting force of the cover. They are:
1) gravity of soil body
H - v t
,
r r [(y -
- (
+ M ) DZ
lo + 1
lo + 1
2) interna1 friction force
H - v t
(Y - ~t --
- M )
lo + 1
1 - sinp
(
tgp rh + 1000c) dh
1 + sin9
1
1 - sin9
H - v t
- -
r r D tgp
M)Z + 1000 .rrc D (Y - vt)
2
1 + sinp
3) buoyancy
rD2rw (H - vt - AH)
N =
4
The state to be forced in cover show in Figu-
re 1.
Thus according to acting direction of force the
first collapse forecast model is:
Figure 1. Sketch forced cover.
-
K =-
-
G
H - v t
H - v t
D r ( y - vt --
- M) + Dri (-
+ M)
lo + 1
lo + 1

where,
K = equilibrium factor;
c = internal cohesion (Kg/cmZ);
D = diameter of assuming collapse (cm);
p = internal friction angle (degree);
y = covering thickness (cm);
t = time of collapse formation (year);
H = groundwater level (cm);
1 o - initial hydraulic gradient (lo assume 1.11
A H = groundwater level amplitude (cm);
in the paper);
r = natural unit weight (g/cm3);
M = capillarity height (cm) (measured volume
ri = saturation unit weight (g/cm3);
is about 100 cm); and
rw = water specific gravity (g/cm3);
v = slacking or peel rate (cm/year).
2. The Second Model
The model is established in the condition that
the groundwater is unconfined. In the case there
are three main force in the cover. They are:'
,, gravity ofsoil
a r D2 (y - vt)
G =
4
Figure 2. Sketch forced cover.
2) internal friction force
(Y - vt)
1
1 - sinp
= a D [
- rtgp
(y - vt)2 + 1 0 0 0 ~
(y - Vt) 1
2
1 + sinq
tgp rh + 1000~)
dh
1 + sinp
3) attraction frorn the change of groundwater level
The state to be forced in the cover show in Fi-
aD2 AH rw
gure 2.
P =
According to the acting direction of force the
4
second model is established. It is:,
1 - sinq
2r tgp
(y - vt)2 + 4 0 0 0 ~( y - M)
1 + sin@
-
K 7-
-
G + P
r D (y - vt) + rw AHD

Model analyse and discussion
creasing, that is, the K is increasing with the y. For
example, measured data are:
Above two models are established now follow-
ing to only analyse the first model.
AH = 384 (cm),
The model (1) show that: if K > 1, the cover is
H = 705 (cm),
relative stable state; K = 1, the one critica1 state;
r = 1.85 (g/cm3),
K < 1, the one unstable state (that is collapse).
ri = 2.06 (g/cm3),
c = 0.13 (kg/cm2),
1) The Relationship between the Equilibrium
cp = 13 (degree),
Factor (K) and Covering Thickness (y)
Assuming other variable value to be no varia-
letting t = O, D = 447 (cm) and assuming y to be va-
tion experct the covering thickness (y), the K is a
riable, the calculating result show that the larger
function of tfie y. To seek the derivative for the y
the cover thickness, the larger the K is. If the cover
and t o identify monotone increasing or decreasing
is more than 11 meter, the cover is no collapse in
of the function show that the K is a monotone in-
present (Table 1 ).
Table 1. The relationship between the equilibriurn factor (K)
and the covering thickness (y)
According to preliminary statistics of collapse
number are related to draw-off. As draw-off are
number with covering thickness in Guilin. Collapse
made with larger drawdown, the AH is larger and K
number mainly distributed over the cover that its
value is less. Therefore, the cover produce easily
thickness is less than 10 meter and show that the
collapse. In addition, the cover often produce co-
less the thickness, the more the collapse number is
llapse after heavy rain. The reason is that the level
(Table 2). This phenomenon is consistency with the
rapidly rise with the larger value of H soon after
result calculating by model.
heavy rain and that the groundwater level rapidly
fall with larger value of AH in several day.
2) The Relationship between the Equilibrium
3) The Relationship between the Equilibrium
Factor (K) and Groundwater Leve1 (H)
Factor (K) and the Physical Mechanic Property
and Amplitude
(C and cp)
To seek derivation for the H and AH and to
c and cp are main index representing physical
identify monotone of function show that the K is
mechanic property. The model show that the K is
monotone decreasing, that is, the K is decreasing
decreasing with decrease of c and cp value. There-
with the increasing of H and AH. It also show that
fore, the less the K, the easier the collapse in the
the larger thenH and H, the easier the collapse is in
cover is.
cover. This conclusion is consistency with reality.
In face, the water is,a active factor in the forming
4) The Relationship between the Equilibriurn
course of collapse. lt not only directly affect the
Factor (K) and the Slacking and Peel Rate (v)
physical mechanic property of cover, but also exert
or Time (t)
influence on the collapse formation by its action.
The first model show that the equilibrium fac-
According to incomplete statistics 80 % of collapse
tor (K) is decrease with the increase of slacking (or
covering thickness range (m)
0 - 5
5 - 10
1 0 - 15
> 15
collapse nurnber
94
46
11
O
percentage (%)
62.3
30.5
7.2
O
Table 2. Statistical data of relationship between collapse nurnber
and covering thickness

peel) rate (v) and time (t). It is say the faster the
or not? It must be forecast. Letting t = O and analy-
slacking or peel rate, the easier the collapse in the
sing cover stability is status quo estimation; letting
cover is. Thus the cover can be transformed stable
K = 1 and solving t is forecast, the t is the need
state into unstable with time. That is, there is a
time that the cover transfred stable state into uns-
evolution i n collapse formation.
table. There are t w o case in forecast. The first case
is that the forescast result show that the cover may
be collapse using the first model, if H 3 vt. The
Model check
second case is that the cover may be stable if
H
Can the model use in collapse forecasting or
H = vt. In the case, at first, the t is equal to -, then
v
not? H o w do w e check the model? The most effica-
using the second model forecast, finally t w o time
cious and simplist method t o check the model is
add together t o make total time from stable t o
comparing the result calculating by the model with
unstable.
the reality o f collapse in the cover. This paper
For example, at the 9th site in Sanlidian, G'ui-
check t h e model by the reality data in Yulin, Guilin
lin, the data are:
and other places.
AH = 420 (cm)
The checking result show that the area of lar-
H = 713 (cm)
ger equilibrium factor is no collapse at present,
r = 1.99 (g/cm3)
and the collapse is always in the area of equili-
ri = 2.06 (g/cm3)
b r i u m less than 1 (Table 3).
y = 1498 (cm)
It also show that the result o f calculating by the
c = 0.47 (kg/cm2)
model is consistency with reality, and the model
q = 20.5 (degree)
can be used i n collapse forecast.
lo = 1.1 I (empiric value)
v = 0.20 (cm/year, assuming value)
Collapse forecast
D = 345 (cm, statistical value)
According t o above analyse stage and putting each
The main content of collapse forecast are:
value into the first model, the K is 3.08 if v product
1. collapse site or range;
t is equal t o H. This result show that the cover w i l l
2. collapse time; and
be stable, the time is equal t o 3565 year. Then put-
3. drawdown causing collapse.
ting y being equal t o 785 c m (1498-713) into the
Collapse site and range is important forecast
second model and letting K t o be equal t o 1, seek
content. There are three methods and techniques
tirne (t), the t is 3355 years. That is the cover need
t o determine distribution o f karst cave or soil cave
about 6920 years transforming stable state into uns-
under the cover. They include: (1) airborne remote
table (That is collapse).
sensing, ground geophysics and direct ground in-
For the covered karst area suppling groundwa-
vestigation. The discussion about the methods and
ter i n order t o avert or reduce collapse production
techniques have gone beyond the scope of this pa-
the limit drawdown must be controlled, this aim
per. Therefore, here is no more discussion.
m a y be realized b y controlling amplitute oH at criti-
Will the cover that is stable at present is stable
cal state that the K is equal t o 1.
site
A H
H
Y
r
D
cP
c
K
reality
(cm)
(cm)
(cm) (g/cm3) (cm)
( O )
(kg/cm2)
1
280
129
379
1.94
(500)
11.4
0.15
0.57
2
280
699
919
1.94
(500)
11.4
0.15
0.80
C
.-
-
8
3
280
294
544
1.94
(500)
11.4
0.15
0.70
5
4
280
284
1234
1.94
(500)
11.4
0.15
0.85
-
ca
5
280
1034
1284
1.94
(500)
11.4
0.15
0.70
8
6
600
425
850
1.91
230
21
0.04
0.88
7
124
360
734
1.82
423
19
0.02
0.44
c
.-
- c 8
413
580
1706
1.96
(345)
23.4
0.43
3.52
a
l,
n
.
ca
ü 9
420
713
1498
1.99
(345)
20.5
0.47
3.28
O
Q
"
-
1
220
1770
2649
1.95
(345)
18.1
0.64
4.01
8
11
385
1034
1789
1.78
(345)
24
0.42
3.12
Table 3. Cornparing data between status quo estirnation and
reality. (ri assurne all 2.06 (kg/crns), The data with brac-
kets is quoting one)

Conclusions
Karst collapse result from many factors. Two
Collapse forecast is a new topic o f engineering
models based on affecting factor such as covering
stability evaluation. Forecast key is t o define the
thickness; physical mechanic property of soil;
distribution of karst or soil cave and t o measure
groundwater level fluctuation; time can be used in
slacking or peel rate of soil etc. All o f these are
collapse forecast. The model analysis show that
pending further discussion and study in practice.
collapse is produced easily as the covering thíck-
ness (y) and the c or cp value representing the phy-
sical mechanic property o f soil is less, the ampli-
Referencec
tute larger, and the cover can be transform stable
state into unstable (collapse) with time.
ZHANG ZHONGYIN: (con Bond Water Dynamics Paoblemn.