Using BPN Method for Estimating Cement Take of Grouting
Chau-Ping, Yang
Department of Civil Engineering and Engineering Informatics, Chung-Hau University,
30 Tung Shiang, Hsinchu, Taiwan, 30067, E-mail address: ycp@chu.edu.tw
Keywords: Dam foundation; Grouting; Cement take; BPN
Abstract
Using cement grout to improve bedrock has been quite common. However, the cost for cement grout is the
most difficult one to estimate. This study adopted the Back-Propagation Neural network (BPN) to analyze the
grouting construction data of the Li-Yu-Tan dam, in order to estimate the cement take needed. The samples
analyzed included data from 3,532 grout sections. The data from the first half of the grouting construction were
used to derive the parameters of the predictive schemes, and then the second half of the grouting construction’s
data were used to test the accuracy of those schemes. The accuracy level estimated by BPN on gross cement
take was 75.3%. It was higher than the original design level of 43.4%.
1. Introduction
The bedrock inherently has discontinuities such as
faults, folds, beddings, joints, and fractures, which
are the major factors that affect the engineering
properties of rock foundations such as permeability,
shear strength, and deformation. When a dam is
located on bedrock that has unknown discontinuities,
the underlying foundation needs to be improved to
raise its engineering properties and ensure a
watertight reservoir. Using cement grout to improve
bedrock has been quite common, and there are
numerous examples of its application in foundation
improvement [1, 2, 3, 4, 5, 6]. However, since the
dam foundation is below the surface of the ground,
the cost for cement grout is the most difficult one to
estimate. The cost of cement grout mainly includes
the operational part and the material part. The cost of
materials is calculated based on the cement take.
Then the cost of the grouting operation is determined
based on the material’s cost. Therefore, it is
necessary to study various methods to estimate the
cement take of the grouting based on actual
construction data. The methods commonly used are
mean method and linear regression method [7, 8].
In general, the status of the discontinuities in the
dam foundation is indirectly expressed by the
Lugeon value determined from the Lugeon tests.
This information can also be used to design the water
to cement ratio and the injection pressure used in the
grouting process. Eq. (1) is the definition of
the Lugeon value .
Lugeon value = Lu =
VPs
(l / m / min) (1)
TPi L
T is the
Pi is the injection pressure
used ( kPa ), L is the length of grout section ( m ).
standard injection pressure (981 kPa ),
injection time ( min . ),
Generally speaking, if a dam foundation has a
high Lugeon value , it will have more
discontinuities with high permeability and more
cement take is needed for the grout improvement.
The Lugeon value is the best physical
parameter to express the status of discontinuities in a
dam foundation. Theoretically, it is quite difficult to
define the relationship between cement take and
the Lugeon value [7, 8]. Additionally, when
researchers estimate the cement take needed for a
new dam foundation from past experiences, they still
encounter the problems of different geological
properties for the proposed dam site. For example,
the cement take designed for the improvement of the
foundation of the Li-Yu-Tan dam, Miao-Li County,
Taiwan, was 50 kgf / m . However, the average
reading of cement take from the construction records
was 115 kgf / m [9]. This difference resulted in a
doubling of the amount of gross cement take from
what was required in the stage of original design.
This experience illustrates the difficulty in cement
take estimation.
This study adopted the Back-Propagation Neural
network (BPN) to analyze the construction data from
the grout-curtain improvement of the Li-Yu-Tan
dam’s foundation, and indicate how to estimate the
cement take needed. The dam is located at the upper
stream of the Jing-San brook, a tributary of the
Da-An river. The dam is a zone-type-earth-dam with
a height of 96 m , a bottom width along the
foundation of the river of about 500 m and a gross
3
Where V is the water take ( l ),
Ps is the
volume of 3,700,000 m . The major terrain includes
gravelly terra rossa and some riverbank outcrops.
There are no faults or obvious folds on either side of
the river. The major discontinuities in the foundation
of the dam site are dozens of developed shear zones.
Most shear zones are distributed in the right side of
the abutments of the dam with slips of more than
2 cm ~5 cm [10].
2. Factors affecting cement take
Theoretically, there are many factors that affect the
cement take needed for improving dam foundations.
Moreover, since some factors may have combined
effects, it is not possible to clearly define the role of
each factor. Some factors that can be categorized or
quantified are the strata, zone of dam foundation,
depth of grout section, injection pressure, and
the Lugeon value .
2.1
Strata
This category covers properties such as the rock
layers, the nature of discontinuities, the rock strength,
the mineral components, and the cementation.
Shallow bedrock tends to have a high density of
cracks or openings and is subjected to grout leakage
and hole’s collapse. If a rock foundation has little
strength, the grout hole will be less independent. The
disadvantages of bedrock mentioned above increase
the amount of cement take needed for grout
improvement.
As shown in Fig. 1, the strata in the dam site
vicinity are northeastwards and meet the river valley
vertically at 28~34 degrees. All the strata are leaning
towards the upper stream at 30~34 degrees. The
strata of the Li-Yu-Tan dam’s foundation include
clean sandstone (CS), mudstone (MS), and
alternations with sandstone and shale (AL). The
major formation of clean sandstone contains quartz
sand, which has a tensile strength of about
1,050 kPa and a hydraulic conductivity of about
6.5  10 5 cm / sec . However, since quartz sand
has a poor cementation quality, the seepage paths are
more likely to cause a loss of fine material. Mudstone
contains different amounts of mud; therefore, its
tensile strength ranges from 1,140 kPa to
2,010 kPa , and the average hydraulic conductivity
6
is 3.4  10
cm / sec . Alternations with
sandstone and shale have intertwined clean sandstone
and shale or mudstone and shale in small alternating
thickness. The thickness of mud accumulation
between layers can reach 30 cm . On the surface
layer, seepage paths can form that cause deterioration
of the shale into fragments or even seams.
2.2
Zone of dam foundation
When the overburden of ground is relieved,
riverbanks will move inwards, and tensile fractures
will occur in the banks. This phase results in more
cracks on the upper half of the dam’s abutments and
induces greater permeability. For this reason, the
cement takes needed for the grout improvement in
the right zone, left zone, and the valley are different.
This research has divided the dam foundation into the
riverbed, the left upper zone, the left lower zone, the
right upper zone and the right lower zone, as shown
in Fig.2 and Fig. 3, according to the tunnel locations
for the grout-curtain construction. However, because
the riverbed has been dug to the level of fresh
bedrock with a permeability lower than 10 Lugeon ,
there are only a few in-place grout holes. Thus, the
analytical extent of this research covers only the left
upper zone, the left lower zone, the right upper zone,
and the right lower zone. The shaded part in Fig. 3 is
the outcome of the grout-curtain in the Li-Yu-Tan
dam’s foundation. For the shallower parts, grouting
can be performed from the top, but, in the deeper
areas, the grouting will have to be performed from
tunnels.
2.3
Depth of grout section
In a rock layers deeper into the underground, the
cracks are narrow and comparatively do not take in
grout because of the greater tectonic stresses in lower
elevation. When the tectonic stress is taken into
consideration, the depth of the grout section is
considered as one of the factors that affect cement
take. As to the grout-curtain construction in the
Li-Yu-Tan dam, the diameter of the grout holes was
3.8 cm and the greatest vertical depth of a grout
hole was limited to 50 m . Inside of each grout hole,
there were several grout sections, and the grout
process was conducted from the bottom to the top of
the grout hole. If the depth of the grout section was
smaller than 30 m , the grout section length was 5 m .
When the depth of a grout section was greater than
30 m , the section length was 10 m .
2.4
Injection pressure
The injection pressure is the major technical factor
affecting cement take. Theoretically, the injection
pressure should be smaller than the tectonic stress
corresponding to the depth of a grout section, which
is obtained from the hydraulic fracturing test.
Moreover, the injection pressure should be smaller
than the tensile strength of the rocks [11, 12]. In
Taiwan, dam engineers consider that the injection
pressure is determined based on the principle of
additional pressure increasing about 30 kPa per
meter depth. The injection pressure adopted for the
grout-curtain construction of the Li-Yu-Tan dam was
150 kPa to 1200 kPa from top to the bottom of
the grout hole [13].
2.5
Lugeon value
The Lugeon value is the only physical
parameter that the researcher could obtain to evaluate
the multiple factors that affect cement take. This
value shows the degree of permeability in the dam
foundation. Basically, in grout improvement, a dam
foundation that has a high Lugeon value
requires more cement take.
3.
Data analysis
In the Li-Yu-Tan dam’s grout-curtain construction,
the grout holes were of the split-spacing type.
Split-spacing means that the grout holes were
arranged in the sequence of primary holes, secondary
holes, tertiary holes, and quaternary holes.
Supplementary holes may be added to enhance the
locations with more discontinuities in the bedrock or
near the holes that required more cement take.
Basically, the arrangement of grout holes was based
on the quality of bedrock. The grout holes were
arranged at intervals of 1 m to 3 m . When the
grouting process of a specific hole lasts for 60
minutes, but the amount of cement take does not
reach 70 l , the grouting for this section should be
stopped. Finally, the drill inspection holes used for
performing the Lugeon test to check the permeability
of the dam foundation were improved. The process
of grouting in each grout section was arranged in the
following sequence: drilling, washing, water testing,
and grouting. During water testing, the Lugeon tests
need to be performed to obtain Lugeon value .
Table 1 lists the data analyzed for 469 grout holes
and 3,532 grout sections. Each grout section had data
such as zone, sequence, hole depth, length of grout
section, rock nature, Lugeon value , injection
pressure, and cement take. All of the data were
collected from the inspection chart of the
grout-curtain construction for the Li-Yu-Tan dam in
1993. Then, all the data were entered into an Excel
application program for calculations before the BPN
analysis began.
For the convenience of analysis, this study has
adopted the symbol Lu to represent the Lugeon
value of a specific grout section. In addition,
because the lengths of the grout sections analyzed
were not the same (between 5 m and 10 m ), the
cement take of a grout section was divided by its
length to obtain the cement take per unit length Lg
( kgf / m ). There were three reasons to use cement
take instead of cement mortar take to define Lg .
First, the voids in the cracks were filled by solid
cement. Secondly, the major material expense in
grout construction is the quantity of cement. Thirdly,
many documents related to grouting refer to cement
take in place of cement mortar take [14, 15].
4. BPN method
The BPN is a branch of artificial neural networks
(ANN). The growing interest in ANN among
researchers is due to its excellent performance in
learning ability, fault tolerance, pattern recognition,
and the modeling of nonlinear relationships
especially involving a multitude of non-digital
variables in place of conventional techniques.
Generally, a complex domain is characterized by a
number of interacting factors. Yet, such factors are
often incomplete or unreliable. If ANN is used to
analyze complex engineering systems, it can alleviate
noise interference and raise the accuracy level of the
analysis. ANN has been widely applied to research in
the field of geotechnical engineering in recent years
[16,17,18].
Huang and Wanstedt [19] applied BPN to the
categorization of rocks and found that the
categorizing ability of BPN was much better than
statistical methods. Additionally, a conventional
method for modeling the stress-strain behavior of soil
is the constitutive law. However, it is characterized
by the difficulties in obtaining correct parameters,
conducting mathematical calculations, and the
oversimplification of the hypothesis. In a quite
different way of research thinking the constitutive
law was replaced with BPN to simulate the
stress-strain behavior of soils [20, 21, 22].
4.1
Mechanism of BPN
The typical architecture of BPN used in this study
is shown in Fig. 4. The input layer uses linear
transfer functions to handle the input variables in the
network. The number of processing elements in the
input layer depends on the problem. In the hidden
layer, it learns how each processing element in the
input layer affects the others through association of
the connection weights. In the output layer, an
S-shaped sigmoid transfer function is used to handle
output variables to make the domain to be [0, 1].
The number of processing elements in the output
layer depends on the problem. BPN learns by
modifying the connection weights of the elements in
response to the errors between the actual output
values and the target output values. This is carried
out through the gradient descent on the sum of
squared error for all the training patterns.
The learning algorithm of BPN requires the
following steps:
a. Use the connection weight W to show the
correlation between the input variable X and
each processing element. Meanwhile, biases 
and activity function net value will come out.
Then, convert the net value to either the target
output value H in the hidden layer and to the
target output value Y in the output layer.
As to the processing elements in the output layer,
use Y and the actual output value T to calculate
the offset  y . The calculation of the processing
b.
elements in the hidden layer also adopts
W , H and  y to calculate the offset  h .
c.
In the input layer and the hidden layer, use the
learning rate  ,  h and X to calculate the
correction value of the connection weight W .
In the hidden layer and the output layer, use the
learning rate  ,  y and H to calculate W .
Then, update the W in each processing element
to complete the learning of one cycle.
Repeat the computation described above until
convergence or approximately 3,000 learning
cycles are reached.
d.
The BPN software used in this research was

PC-Neuron, written in C
language [23]. With the
assistance of the original programmer, a new
subprogram was written to return to the target output
value from the original domain [0, 1]. Then, this
value was converted to a data file that Excel software
can treat.
4 .2
Architecture o f B P N f o r est i ma ti ng
ce me nt t a ke
The input variables which needed to be fed into
the BPN program were the zone of the dam
foundation, the type of rock layers, the injection
pressure, the depth of grout section, and Lu . The
output variable was the Lg of each grout section.
Among these variables, both Lu and Lg are
measured digital data and the others are represented
by the classification codes. The codes of these input
variables are listed in Table 2.
The learning algorithm of BPN can be divided into
the training phase and the testing phase. The learning
samples for these phases were collected from the first
half of the grout construction in the four zones. The
samples were randomly categorized into the training
set and testing set in the first phase of data processing.
The initial learning rate, the initial inertial factor, and
the initial connection weight were set to be 5.0, 0.5
and 0.3 respectively. After a number of different
hidden layers were tried, one hidden layer was used
in the BPN model employed here. In the preliminary
task, a network with different elements ranging from
2 to 8 in the hidden layer was trained for the same
number of 3,000 cycles. It was found that the value
of the average sum squared error ( SSE ) would
reach the minimum value of 0.11 when the number
of elements was equal to 5. Eq. (2) is used to
calculate SSE :
M
S S E
Where
N
 (T
p
p
j
 Y jp ) 2
j
M N
(2)
T jp is the actual output value of processing
Y jp is the target output
value of processing element j in example p, M is
the number of example, N is the number of
element j in example p,
processing element in the output layer.
So, a 5  5  1 network was set up as shown in
Fig.5. The learning process was performed with a
Pentium 586 computer, which took about 110 min. of
CPU time. Finally, BPN was applied to the training
set and produced the connection weights and biases.
Then, the architecture of BPN for estimating cement
take was built (see Fig.5). The accuracy for the
training and testing data sets are described by the
degree of correlation between output target values
and actual values. The scatter of the target output
Lg values versus the actual output Lg values
were assessed using regression analysis and its
degree of correlation of 0.82 was an acceptable one
5. Estimated results of cement take
According to the different zones of the dam
foundation, use the data of grout sections in the
second half of the grout-curtain construction as the
input variables. Key the input variables of each grout
section into the BPN program with the architecture as
shown in Fig. 5 to predict the Lg value of that
grout section and further to obtain its cement take.
Repeat the prediction process described above one by
one until all of the grout sections have been covered.
Then, calculate the sum of cement take for all the
grout sections to get the estimated gross cement take.
The estimated accuracy levels of BPN method are
78.2%, 81.4%, 71.9% and 75.6% for the left upper
zone, the left lower zone, the right upper zone, and
the right lower zone respectively. The average
estimated accuracy for the four zones is 75.3% (see
Table 3).
6. Summary and conclusions
This study adopted the BPN method to estimate
the cement take needed for the grout improvement on
the Li-Yu-Tan dam’s foundation. The level of
average estimated accuracy on gross cement take is
75.3%. This level is higher than the designed level of
43.4% calculated in Table 3. Because the BPN
method takes into consideration the effects of factors
on Lg , such a structure, which naturally increases
the level of estimated accuracy. However, the
construction of the network, testing and data input
process still tend to be more time-consuming.
Moreover, its estimation tool is a network program
instead of just a regression equation. It must be
declared that the coefficients in Fig. 5 are only
suitable to the Li-Yu-Tan dam. The method
mentioned above can be applied in other situations
only when using the data collected from the
completed parts of the grouting to estimate the rest of
the grout take at the same site.
11.
12.
13.
14.
Acknowledgements
Thanks are expressed to the National Science
Council, Taiwan (NSC85-2211-E-216-004), for
research funding and to the Water Resources Agency,
Ministry of Economic Affairs, Taiwan, for the data
collection.
15.
16.
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Table 1
Zone
Number of grout holes and grout sections at each zone of the grout-curtain
Sequence
Primary
Secondary
Left upper zone Tertiary
Quaternary
Supplementary
Inspection
Primary
Secondary
Left lower zone Tertiary
Quaternary
Supplementary
Inspection
Primary
Secondary
Right upper
Tertiary
zone
Quaternary
Supplementary
Inspection
Primary
Secondary
Right lower
Tertiary
zone
Quaternary
Supplementary
Inspection
Sum
Table 2
Number of grout
holes
11
9
20
36
11
14
15
15
30
51
3
14
16
15
30
52
28
20
9
9
17
26
4
14
469
Total length of
grout holes
591
543
1,158
1,869
540
739
828
826
1,655
2,326
166
772
976
987
1,949
3,029
1,422
1,193
480
472
906
879
221
749
25,276
Number of grout
sections
83
76
163
262
76
104
108
108
216
303
22
101
133
134
265
412
194
162
79
78
150
145
37
124
3,532
Codes of input variables for BPN analysis.
Zone of dam Code Type of rock layer
foundation
Left upper
1 Clean sandstone
zone
Right upper
2 Mudstone
zone
Left lower
3 Alternation with
zone
sandstone and shale
Right lower
4
zone
Code
1
Injection pressure
( kPa )
0~200
Code Depth of grout Code
section ( m )
1
0~20
1
2
201~400
2
21~40
2
3
401~600
3
41~60
3
601~800
4
61~80
4
801~1,000
1,001~1,200
5
6
81~100
5
Table 3
Amount of gross cement take at each zone for the second half of the grout-curtain construction.
Item
Left upper
zone
Left lower
zone
Right upper
zone
Right lower
zone
Sum for
four zones
2,721
3,287
4,778
1,854
12,638
296,126
228,512
670,533
262,223
1,457,393
136,050
164,350
238,900
92,700
631,900
231,570
186,007
482,034
198,156
1,097,767
(3)
(%)
( 2)
45.9
71.9
35.6
35.3
43.4
( 4)
(%)
( 2)
78.2
81.4
71.9
75.6
75.3
Zone
Total length of grout holes
(m)
(1)
Gross cement take ( kgf )
(construction)
(2)
Gross cement take ( kgf )
(1)  50( kgf / m )
(design)
(3)
Gross cement take ( kgf )
(BPN method)
(4)
Estimated
Accuracy
levels
Fig. 1. Longitudinal section of the Li-Yu-Tan dam indicating the rock layers in dam
foundation (CS=clean sandstone, MS=mudstone, AL=alternation of sandstone
and shale).
Fig. 2. Characteristic zones of the grout-curtain in the dam foundation.
Original ground surface
Grouting tunnel
Crest
Design excavation surface
Dam
Grouting tunnel
Grouting hole
Fig. 3. Longitudinal section of the Li-Yu-Tan dam indicating the extent of the grout-curtain.
Input layer
Hidden layer
Output layer
net h3
£ch3 ¡µ£ch3
£_h3
X1
W13
1
3
¡µW13
W14
W35
W23
¡µW35
net y5
H3
£cy5 ¡µ£cy5
¡µW23
¡µW14
5
Y5
W45
¡µW45
X2
2
W24
4
£_y5
H4
¡µW24
net h4
£ch4 ¡µ£ch4
£_h4
Fig. 4. Typical BPN architecture.
T5
Input layer
Hidden layer
Region
0
5
Kind of rock
1
6
Injection pressure
2
7
Depth of grout hole
3
8
Lu
4
9
Ouput layer
10
Lg
Weights and Biases
item
node 5
node 6
node 7
node 8
node 9
node 10
node 0
weight
0.34
0.18
0.23
-0.22
-0.17
Fig. 5.
node 1
weight
0.59
-0.81
-1.24
2.01
2.32
node 2
weight
0.92
0.50
-0.71
-1.24
0.63
Node3
weight
-0.52
-1.09
-0.14
0.45
-0.16
node 4
weight
1.57
1.74
1.48
1.74
1.36
Architecture of BPN for estimating Lg
node 10
weight
-0.79
-0.63
-0.35
-0.36
-0.36
biases
0.95
0.04
0.79
0.84
0.36
0.50