Estimating cement take and grout efficiency on foundation
improvement for Li-Yu-Tan dam
Yang , Chau-Ping
Department of Civil Engineering, Chuag-Hau University,
30 Tung Shiang, Hsinchu, Taiwan, 30067
Fax: +886-3-5372188; E-mail address: ycp@chu.edu.tw
Abstract
The cement take needed for dam foundation improvement with grout-curtain is difficult to
estimate due to the complexity of the rock foundation and the great number of Lugeon tests
involved in the analysis. Therefore, this study adopted the mean method, the linear regression
method, and the back-propagation neural network (BPN) method to analyze the grout-curtain
construction data of the Li-Yu-Tan dam, Taiwan, 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 grout-curtain construction were used to derive the parameters of the predictive schemes,
and then the second half of the grout-curtain construction’s data were used to test the
accuracy of those schemes. The accuracy levels estimated by these three methods on gross
cement take were 71.8%, 59.8%, and 75.3% for the mean method, the linear regression
method and the BNP method respectively. All accuracy levels estimated by these three
methods were higher than the original design level of 43.4%. Furthermore, the efficiency of
the grout improvement in the studied cases were confirmed by observing the changes of the
distribution curve of the Lugeon value following each grout sequence. The method
proposed is intelligible and can be applied in other situations.
Keywords: Dam foundation; Grouting; Cement take; Estimation; BPN
1
1.
Introduction
Taiwan is located on a sedimentary rock with rugged terrain and complicated geological
properties. 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 grouting to
improve bedrock has been quite common (Baker, 1982; Jaroslavl, 1989; Houlsby, 1990;
JSIDRE, 1994), and there are numerous examples of its application to the engineering of
dam-foundation improvement (Ewert, 1985; Weaver, 1991). However, since the dam
foundation is below the surface of the ground, the expense for cement grouting is the most
difficult construction expense to estimate. The expense of cement grouting mainly includes
the operational part and the material part. The expense of materials is calculated based on the
cement take. Then the expense of the grouting operation is determined based on the material’s
expense. Therefore, it is necessary to study various methods of estimating the cement take of
the grouting based on actual construction data.
In general, the status of the discontinuities in the dam foundation is indirectly expressed by
the Lugeon value determined from the Lugeon tests. The information gained from the
Lugeon tests 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 . 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.
L u g e ovna l u=eLu =
VPs
(l / m / min)
TPi L
(1)
Where V is the water take ( l ), Ps is the standard injection pressure (981 kPa ), T is
the injection time ( min . ), Pi is the injection pressure used ( kPa ), L is the length of grout
section ( m ).
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
2
cement take and the Lugeon value (Yamaguchi and Matsumoto, 1989; Hirota et al., 1990).
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 of Li-Yu-Tan dam was
115 kgf / m (Taiwan Water Resources Agency, 1993). This difference resulted in a doubling
of the amount of gross cement take from what was required in the original design. This
experience illustrates the difficulty in cement take estimation.
Consequently, this study focuses on the practical application of cement take estimation by
adopting the mean method, the linear regression method, and the back-propagation neural
network (BPN) method 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
efficiency of the grouting for this dam site is also addressed in this article.
As shown in Fig.1, the Li-Yu-Tan dam is located at about 500 m in the upper stream of the
Jing-San brook, a tributary of the Da-An river, which is in the mountainous regions of
northwestern Taiwan. 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 volume of 3,700,000 m 3 .
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 2 cm ~5 cm above. (Taiwan Water
Resources Agency, 1986a).
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 .
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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. All of these properties may have
combined effects on cement take. If a dam foundation consists of different rock layers, it may
have more hidden discontinuities. Shallow bedrock tends to have a high density of cracks or
openings and is subjected to grout leakage and hole 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. 2, the strata in the dam site vicinity are northeastwards and meet the river
valley 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 coefficient of
permeability 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 coefficient of permeability is 3.4  10 6 cm / sec . If the mudstone has good
cementation and low permeability, it is considered as the bedrock layer because of the better
engineering properties. 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 above. On the surface layer, seepage paths
can form that cause deterioration of the shale into fragments or even seams. The width of
fragments is about 20 cm ~30 cm above.
2.2. Zone of dam foundation
Runoffs flush weak parts of the ground to form river valleys. When the pressure of ground
is relieved, riverbanks will move inwards, and tensile fractures will occur in the banks. This
development will result in more cracks on the upper half of the dam abutments and induce
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
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the right lower zone, as shown in Fig.3 and Fig. 4, 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. 4 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. If during the
grouting process, the operator increases injection pressure to fill the cracks with more grout,
this action may cause the loosening and cracking of bedrock. As a result, the extent of the
grout area may become larger. 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 (Kutzner, 1985; Shibata, 1989). In Taiwan, the field of dam engineering,
considers 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
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bottom of the grout hole (Taiwan Water Resources Agency, 1986b).
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. In the Li-Yu-Tan dam, 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 the Lugeon value , which gives the permeability
of that specific grout section, and determines the water to cement ratio.
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
analysis began.
For the convenience of anal ysis, this study has adopted the symbol Lu to
represent the Lugeon value of a specific grout section. In addition, because
6
the lengths of the grout sections anal yzed 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. Secondl y, the major material expense in
grout construction is the quantit y of cement. Thirdl y, many documents related
to grouting refer to cement take in place of cement mortar take (Ennto, 1988;
Tano, 1988). Generally speaking, a grout section with a higher Lu needs a
greater amount of Lg for grout improvement.
4. Estimation method of cement take
4.1. The mean method
The relationship between Lu and Lg is complicated because it is affected by many
factors including geological properties, injection pressure, and grout operation. Nowadays, in
practical application, researchers still think that Lu is a major factor affecting Lg . Since
there are enough samples gathered in this study, either the middle value method or the mean
method can be adopted to find the regression formula that expresses the relationship of Lg
and Lu .
Hirota, et al. (1990) tried to use the middle value of Lu and Lg as a representative
value to observe their relationship. Lu50 was defined as the middle value in the distribution
curve Lu (refer to Fig. 14 and Fig. 15) and Lg 50 as the middle value in the distribution
curve Lg . Next, Lu50 and Lg 50 were determined for primary holes and secondary holes
etc. Then, regression was applied at Lg 50 over Lu50 for different sequences to derive the
formula in Eq. (2).
Lg 50    Lu50  
(2)
However, Hirota, et al. (1990) also pointed out that the accuracy of the estimation derived
from Eq. (2) was based on the frequency distribution pattern of the samples. That is, samples
7
with normal distribution were more applicable to Eq. (2). Furthermore, Fig.5 and Fig.6 are
the Lg histograms of the samples used in this study. The histograms clearly show that the
samples were not normally distributed but skewed. Most of the samples fell into zones of a
small value of Lg <200 kgf / m . Therefore, it was not appropriate to use the middle value
method to estimate cement take in this case. Consequently, in place of the middle value
method, this study adopted the mean method to regress the relationship of Lg and Lu , then
defined Lu av as the mean of Lu , and Lg av as the mean of Lg for each zone in the dam
foundation.
Since different dam foundations rarely have the same geological properties, a predictive
scheme may be applicable only to the specific dam foundations under analysis and cannot be
applied to other cases. However, in the same dam foundation, since the operation load for
grout improvement is usually in large quantities and the construction period is usually long, it
is possible to use the data collected from the completed grout sections to estimate the cement
take needed for the remaining sections. Therefore, this study used the data collected from the
first half of the grout-curtain construction in four zones to calculate its Lu av and Lg av . Then,
the four sets of ( Lu av , Lg av ) points were regressed to derive Eq. (3).
Lg av  8.06Lu av  36.3
(3)
The relationship of Lu av and Lg av in Fig. 7 is obtained from different zones that are
highly correlative (with a correlation coefficient R 2 as 0.95). It was found that the accuracy
of the estimation derived from Eq. (3) was mainly affected by the similarity of the
distribution pattern of the samples instead of the normal distribution. The distribution patterns
of the samples of the two upper zones were similar (see Fig. 5 and Fig. 6). Therefore, the
mean method (i.e. Eq. (3)) was adopted as one of preference scheme to estimate cement take
in this case.
4.2. The linear regression method
Yang (2002) observed the corresponding relationship of spatial distribution between Lu
and Lg in this case, and found that the spatial distribution of the contours of Lu and Lg
8
corresponded. Thus, this study attempted to find the linear regression equation that directly
expressed the relationship of Lu and Lg . The Lu - Lg relationship collected from the first
half of the grout-curtain construction is shown in Fig. 8 and Fig. 9. As a whole, Lg had a
tendency to increase along with the increase of Lu , but there was little correlation between Lg
and Lu.
With the help of ms-Excel software, several types of equations were tried. Among
these types of equations, although the correlation demonstrated by the quadratic type of Eq.
(4.a), Eq. (4.b), Eq. (4.c), Eq. (4.d) was higher, still the values of R 2 were small. However,
because the geological properties of a dam foundation are complicated, it is hard to observe
the factors that might affect Lg . Accordingly, the linear regression method is still often used
(Ewert, 1985; Yamaguchi and Matsumoto, 1989; Hirota, et al., 1990).
Left upper zone
Lg  0.05Lu 2  9.94Lu  1.02
R 2 =0.36
(4.a)
Left lower zone
Lg  0.07 Lu 2  13.3Lu  2.11
R 2 =0.43
(4.b)
Right upper zone
Lg  0.05Lu 2  7.86Lu  0.92 R 2 =0.41
(4.c)
Right lower zone
Lg  0.06Lu 2  10.29Lu  1.07 R 2 =0.49
(4.d)
4.3. Back-propagation neural network (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 (Goh, 1995). ANN has
been widely applied to research in the field of geotechnical engineering in recent years. For
example, Goh (1994) used ANN to evaluate the liquefaction potential of soil. The
comparisons indicated that such a model was more reliable than the conventional dynamic
stress method. Schaap et al. (1998) used the hierarchical neural network model for the
prediction of water retention parameters and saturated hydraulic conductivity from basic soil
properties. Such a model is attractive because of high accuracy and because it permits a
considerable degree of flexibility toward available input data.
9
Huang and Wanstedt (1998) 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, such law 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 soil (Ellis et al., 1995; Zhu et al., 1998; Imad, 2000; Yang, 2002).
4.3.1. Mechanism of BPN
The typical architecture of BPN used in this study is shown in Fig. 10. 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.
b. 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 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
10
processing element to complete the learning of one cycle.
d. Repeat the computation described above until convergence or approximately 3,000
learning cycles are reached.
The BPN software used in this research was PC-Neuron, written in C   language (Yeh,
1997). 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.
4.3.2.
Architecture of BPN for estimating cement take
This study focuses on the practical application of research related to the input variables that
were taken from the data collected in the grout-curtain construction phase. 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.
Similar to the mean method and the linear regression method mentioned above, the learning
samples for these phases were also 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. (5) is used to calculate SSE :
M
S S E
N
 (T
p
p
j
 Y jp ) 2
j
(5)
M N
11
Where T jp is the actual output value of processing element j in example p, 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 processing element in the output layer.
So, a 5  5  1 network was set up as shown in Fig.11. 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.11).
4.3.3.
Performance of BPN for estimating cement take
In the learning process, a change in the SSE with respect to the number of the learning
cycle is shown in Fig. 12. The results indicate that convergence was achieved for the training
and testing phase. That means the amounts of the samples were sufficient and there was some
degree of correlation between the input variables and the output variables. The performance
of BPN is shown in Fig. 13. 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
5.1. The mean method
The procedure requires that one, first, changes the Lu av in Eq. (3) to Lu , and
the Lg av to Lg to get Eq. (6).
Lg  8.06 Lu  36.3
(6)
Then, according to the different zones of the dam foundation, one replaces the Lu value of
each grout section of the second half of the grout-curtain construction into Eq. (6) to get Lg .
Next, multiply this Lg value by the length of that grout section to get the cement take.
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Calculate the sum of cement take for all grout sections to get the estimated gross cement take.
The estimated accuracy was defined as a ratio of estimated gross cement take to gross cement
take of grout-curtain construction. The estimated accuracy levels of the mean method are
68.0%, 74.0%, 71.0% and 76.0% 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 71.8% (see Table 3).
5.2. The linear regression method
Put the Lu values of each grout section of each zone in the second half of the grout
construction into Eq. (4.a), Eq. (4.b), Eq. (4.c) and Eq. (4.d) to get Lg values, and further to
get the estimated gross cement take. The estimated accuracy levels of the linear regression
method are 64.9%, 69.8%, 57.9% and 50.1% 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 59.8% (see Table 3).
5.3. The BPN method
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.
10 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 all the zones is 75.3% (see Table
3).
6.
Grout efficiency
When the grout improvement is finished, one uses the changes of the distribution curve
Lu and its middle value Lu50 to observe the efficiency of the grout improvement. From the
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distribution curves of Lu plotted in Fig. 14 and Fig. 15, it is clear that after a sequence of
grout improvement, the Lu values of the grout sections in each zone were reduced. Then,
after the fourth sequence of grout improvement was performed, 90% of the grout sections had
a permeability less than 4 Lugeon , 3 Lugeon , 9 Lugeon , 8 Lugeon , for the left upper zone,
the left lower zone, the right upper zone and the right lower zone, respectively. Furthermore,
one uses the changes of Lu50 plotted in Fig. 16 to show the efficiency of the grout
improvement in the four zones. Along with the increase of the grout sequence, Lu50 tends to
become smaller. For example, the Lu50 obtained from the left upper zone decreased from
7.12 to 1.96, and the same value obtained from the right upper zone decreased from 9.36 to
2.52. That is to say, the efficiency of the grout improvement in the Li-Yu-Tan dam’s
foundation was confirmed.
7.
Summary and conclusions
This study adopted the mean method, the linear regression method, and the BPN method to
estimate the cement take needed for the grout improvement on the Li-Yu-Tan dam’s
foundation. The levels of average estimated accuracy on gross cement take are 71.8%, 59.8%
and 75.3% for the mean value method, the regression method and the BPN method
respectively. All of these levels were higher than the designed level of 43.4%.
As to the mean method, because the mean of the samples analyzed was calculated with the
intention to draw on the strength of each to offset the weakness of the other, the mean can
supplement the low correlation between Lu and Lg . Therefore, the level of average
estimated accuracy obtained is 71.8%, higher than 59.8% from the linear regression method
and slightly lower than 75.3% from the BPN method. In comparison, the analytical process of
the mean method was simpler than BPN method, whereas its level of estimated accuracy is
acceptable. In addition, because 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 such as Eq. (3) and Eq. (4). It must be declared that the coefficients in Eq.
(3), Eq. (4) and Fig. 10 are only suitable to the Li-Yu-Tan dam. The three methods mentioned
above can be applied in other situations only when using the data collected from the
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completed parts of the grouting to estimate the rest of the grout take at the same site.
The efficiency of the grout improvement in the studied case was confirmed by observing
the changes of the distribution curve Lu and its middle value Lu50 following each grout
sequence. This method is intelligible and can be applied in other situations.
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.
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Berlin, Heidelberg, Germany.
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of Geotechnical Engineering, American Society of Civil Engineers, 120(9), 1467-1480.
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foundation grouting - a case of Granite -, Journal of Japan Society of Civil Engineering,
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application in rock engineering, Engineering Geology, Elsevier Ltd., 49, 253-260.
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16
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17
Table 1
Number of grout holes and grout sections at each zone of the grout-curtain of the Li-Yu-Tan
dam.
Zone
Sequence
Number of grout Total length Number of
holes
of grout holes grout sections
Primary
11
591
83
Secondary
9
543
76
Left upper Tertiary
20
1,158
163
zone
Quaternary
36
1,869
262
Supplementary
11
540
76
Inspection
14
739
104
Primary
15
828
108
Secondary
15
826
108
Left lower Tertiary
30
1,655
216
zone
Quaternary
51
2,326
303
Supplementary
3
166
22
Inspection
14
772
101
Primary
16
976
133
Secondary
15
987
134
Right upper Tertiary
30
1,949
265
zone
Quaternary
52
3,029
412
Supplementary
28
1,422
194
Inspection
20
1,193
162
Primary
9
480
79
Secondary
9
472
78
Right lower Tertiary
17
906
150
zone
Quaternary
26
879
145
Supplementary
4
221
37
Inspection
14
749
124
Sum
469
25,276
3,532
Table 2
The 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
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
18
Code Depth of grout Code
section ( m )
1
0~20
1
Table 3
Amount of gross cement take estimated by three methods at each zone for the second half of
the grout-curtain construction.
Item
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 )
(mean method)
(4)
Gross cement take
( kgf )
(regression method)
(5)
Gross cement take
( kgf )
(BPN method)
(6)
(3)
(%)
( 2)
( 4)
Estimated
(%)
( 2)
accuracy
levels
( 5)
(%)
( 2)
(6)
(%)
( 2)
Left upper
zone
Left lower Right upper Right lower Sum for
zone
zone
zone
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
201,366
169,099
476,079
199,290
1,045,832
192,169
159,477
388,266
131,362
871,273
231,570
186,007
482,034
198,156
1,097,767
45.9
71.9
35.6
35.3
43.4
68.0
74.0
71.0
76.0
71.8
64.9
69.8
57.9
50.1
59.8
78.2
81.4
71.9
75.6
75.3
19
(Kcy: Muddy sandstone, Siltstone and shale; l: gravelly terra rossa)
Fig. 1. The location and geological map of Li-Yu-Tan dam
Fig. 2. 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).
20
Fig. 3. Characteristic Zones of the grout-curtain in the dam foundation.
Original ground surface
Grouting tunnel
Crest
Dam
Design excavation surface
Grouting tunnel
Grouting hole
Fig. 4. Longitudinal section of the Li-Yu-Tan dam indicating the extent of the
grout-curtain.
21
No.of sections in grout hole
600
Left upper zone
500
400
300
200
100
0
0-200
201-400
401-600
601-800 801-1000
Lg (kgf/m)
Fig. 5. Histogram of Lg in the left upper zone.
No.of sections in grout hole
1000
Right upper zone
800
600
400
200
0
0-200
201-400
401-600
601-800 801-1000
Lg (kgf/m)
Fig. 6. Histogram of Lg in the right upper zone.
160
y=8.0569x+36.273
R2=0.9486
Lgav (kgf/m)
140
120
Right upper
zone
Right lower
zone
Left upper
zone
100
80
Left lower
zone
60
40
0
2
4
6
8
10
12
14
16
Luav (Lugeon)
Fig. 7. Linear regression of Lg av over Lu av in the left and right zones of the
abutments of the dam.
22
Fig. 8. Relationship between Lu and Lg in the left upper zone.
Fig. 9. Relationship between Lu and Lg in the right upper zone.
23
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
Y5
W45
T5
¡µW45
X2
W24
2
H4
4
¡µW24
net h4
£ch4 ¡µ£ch4
£_h4
Fig. 10. Typical BPN architecture.
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
Weights and Biases
item
node 0 node 1
weight weight
node 5 0.34
0.59
node 6 0.18
-0.81
node 7 0.23
-1.24
node 8 -0.22
2.01
node 9 -0.17
2.32
node 10
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
24
Ouput layer
10
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
Lg
Fig. 11. Architecture of BPN for estimating Lg , indicating the connection weights,
and the biases.
25
Training phase
Testing phase
Fig. 12. Convergence characteristics of BPN for estimating cement take.
Fig. 13. Comparison of actual and target Lg values.
26
Fig. 14. The changes of distribution curve Lu after each grout sequence
(left upper zone).
Fig.15. The changes of distribution curve Lu after each grout sequence
(right upper zone).
Fig.16. Grout efficiency in the four zones.
27
28