Empirical Strength Models, Elastic Modulus and
Stiffness of Weathered Sandstone and Shale as a
Composite Rock
By
Zainab Mohamed, PhD.
Assoc. Prof., Faculty of Civil Engineering, Universiti Teknologi MARA, Malaysia
zainab556@salam.uitm.edu.my
Kamaruzzaman Mohamed, Haryati Awang
Postgraduate students, Faculty of Civil Engineering,
Universiti Teknologi MARA Malaysia
ABSTRACT
A geotechnical studies has been carried out on the typically weathered Kenny Hill
sedimentary rock. The objectives are to determine the geotechnical properties related to wet
tropical weathering. The mandatory classification by weathering grade was adopted to classify
the interbedded rock mass which is mainly constitutes of sandstone and shale. The purposes
are to characterize and classify the engineering properties, stiffness characteristics and
behavior of weathered sandstones and shale and consequently their behaviour as a composite
rock material. A series of rock material strength tests were carried out, i.e. a uniaxial
compressive strength and point load strength. The empirical strength models were developed
based on sandstone and shale experimental data. Thus the rock materials composite strength,
elastic modulus and stiffness were mathematically modeled with respect to their respective
weathering grades. Conclusively it was found that as a composite rock the strength models,
modulus and stiffness were influenced by their state of weathering and deteriorated nonlinearly.
KEYWORDS: weathering grade; sandstone; shale; rock strength; composite rock
INTRODUCTION
The rock mass assessment system and rock characterization methods have been previously established
on a single type of rock which was assumed as an isotropic and homogenous. However practitioners
reported that none of the established systems are relevant to interbedded rock mass which was also
known as a problematic or difficult ground (Mohamed, 2004). It was reported that it would be a very
tedious exercises to predict the behavior of such rock mass without first carrying out a thorough and
systematic physical and engineering assessment. The engineering problems of interbedded rock are
due to the differences in rock lithology, complex mode of failures and non-homogenous behaviour.
Since early 90’s, some research studies had been initiated into heterogeneous rock formation which is
also known as composite rock mass. The rock mass engineering model can be predicted either by
simple rock classification system; empirical model, numerical modeling or a combination of any of
them.
A geotechnical research study has been carried out to characterize, classify and determine the
engineering properties and behavior of weathered sandstones and shale named as composite material,
dominating a Kenny Hill formation (Mohamed, 2004). From a rigorous experimental works the
1
empirical strength models are established and later become a mean to further understand and predict
the modulus and stiffness characteristics of the composite rock with respect to their respective
weathering state. The advancement of powerful statistical software has helped to expedite the analysis
and hence developed an empirical rock mass model. Shakor et al. (1991) and Ulusay et al. (1994) had
developed empirical models for sandstone rock mass by using multiple regression analysis from
petrography and geo-mechanics data. Meanwhile Habimana et al. (2002) characterized the catalyst of
quartzite sandstone and phyllite schist by adopting the Hoek-Brown failure criterion. However,
Gokceoglu et al. (2003) has predicted the empirical model of rock mass based on the ratio of rock
modulus and its quality index to the weathering grade of weak rock. They had respectively emphasis
on the success of precise prediction of a single rock mass behavior hence contributed to the reduction
to the cost of site investigation.
This paper highlighted and discuss the development of an empirical relationship that express the
strength and stiffness behavior of composite rock determine from the rigorous study on the typical
rock formation of composite material (Kenny Hill rock mass). Figure 1 below illustrated four possible
observed vertical profiles of weathered sandstone and shale by assuming the layers representing an
ideal horizontal interbedding as recommended by Mohamed (2004).
Highly
weathered
sandstone
Moderately
weathered
sandstone
Slightly
weathered
sandstone
Slightly/highly
weathered
shale
Highly
weathered
shale
Highly
weathered
shale
Slightly
weathered
shale
Highly
weathered
sandstone
Highly
weathered
sandstone
Moderately
weathered
sandstone
Slightly
weathered
sandstone
Slightly/highly
weathered
shale
Figure 1: A typical four ideal interbedding profile of weathered sandstone and shale named as
composite rocks (after Mohamed, 2004)
The figure above clearly indicated the heterogeneity of composite Kenny Hill rock mass. Generally as
the state of weathering changes from slightly weathered to highly weathered, the physical and
mechanical properties also deteriorate and degrade accordingly. Thus any combination of rock mass
profile is expected to be unique which explained the difficulties often encountered and reported by
practitioners working with Kenny Hill rock mass that resulted to possible unexpected delay on
geotechnical work
CHARACTERISATION AND CLASSIFICATION BY
WEATHERING GRADE
The outcrop of sedimentary cut slope at Section 8, Shah Alam, Selangor was selected as a case study.
The outcrop is geologically known as Kenny Hill rock mass. From the field mapping, the cut slope
constituted of slightly to highly weathered sandstone and shale with traces of quartz veins. The two
dominating materials were differentiated physically, where weathered sandstone is a fine grained
gritty texture while weathered shale is smooth and powdery. It was very difficult to ascertain the
grade of weathering through physical observation therefore some methods of testings had been used
2
to characterize and classify the weathered sandstone and shale. The objective is to determine the
degree of deterioration and disintegration of both materials hence explained the complex mode of
slope failure observed in-situ. The details of finding have been discussed by Zainab 2004. Table 1
summarizes the physical classification of weathered sandstone and shale looking from the quality of
weathering grade, hand sample hardness, rebound hardness, surface texture, dry density and slake
durability. It was found to be a gradual physical degradation and deterioration of both materials with
respect to the increase in grade of tropical weathering. Hence, the type of composite rock models as
shown in Figure 1 , each is expected to has different strength and stiffness characteristics with any
combination of the respected weathered materials.
Table 1: Physical properties of weathered sandstone and shale of Kenny hill formation
Rock
samples
Hardness
(hand sample)
Slightly weathered
Sandstone
(BP2g, BP2s)
Very hard and intact
Moderately
weathered Sandstone
(BP3)
BP4
Hard and slightly
disintegrate
Highly weathered
Sandstone (BP5)
Slightly weathered
shale ( S2 )
Rebound
hardness
Surface texture and
lamination
Dry density
kN/m3
> 30
Smooth and intact
2.4 – 2.6
Slake
durability
index (%)
98
5-30
Slightly massive and gritty
2.2 – 2.7
94
10-15
Partially massive and
gritty
2.0 – 2.7
-
dented
Very gritty and massive
1.5 – 1.9
46
< 20
Soapy and intact
2.4 – 2.5
92
Breakable and easily slake
10-20
Powdery and slightly
massive
2.2 – 2.4
96
Breakable and slake
dented
Powdery, gritty and
massive
2.5 – 2.6
92
Breakable and easily
disintegrate
Easily broken and
disintegrate
Hard and slake
Moderately to Highly
weathered shale
S5
S5a
GEOMECHANICAL STRENGTH
A series of strength test was carried out according to ISRM 1981, suggested method of testing. Some
blocks of sandstone and shale have been sampled from the site according to the weathering grade and
later prepared for uniaxial compressive strength and point load strength tests. The objective is to
determine the material strength as it varies from slightly weathered to highly weathered i.e from rock
to soil like state. The strength and stiffness of the weathered composite materials i.e a matrix of
weathered sandstone and weathered shale are then formulated.
Uniaxial Compressive Strength
The test was carried out according to the suggested method with some modification to the procedure
of testing .The non-homogeneity of weathered sandstone from Kenny Hill formation constitute of a
wide range in uniaxial compressive strength values. The broad varieties are due to the aggressive
tropical rock weathering and the unique weathering pattern of the sedimentary rock. The removal of
inherited physical properties of weathered sandstone and shale materials due to sample preparation
process resulted to the mechanical properties obtained was a representative of tropical weathering
3
characteristics of the tested samples. However by repeating the test on as many samples with the same
quality of weathering has enabled the comparison of the strength deterioration of sandstone and shale
being concluded. Table 2 summarized the uniaxial compressive strength (c) of weathered sandstone
and shale which has been physically characterized and clustered accordingly. The data obtained in the
first column was statistically analyzed and has been reclassified to reflect the true uniaxial
compressive strength of the weathered rock by its quality of weathering grade.
Point Load Strength
A point load strength test is not popular as a method for geotechnical assessment among civil engineer
in Malaysia however result shows that by using a lower scale of load cell and higher sensitivity of
strain measurement, the point load strength (Isp50) of slightly to highly weathered sandstone and shale
has been successfully measured. Table 3 summarized the result of the point load strength index tested
perpendicular to the sample lamination.
Table 2: Summary of σc2 for weathered sandstone and shale samples from Kenny Hill rock mass
Rock samples
BP2G (*22)
BP2S (*26)
BP3 (*15 )
BP5a (*8)
BP2a
BP5b
S2 (*8)
S2’
S5’
S5a’
c Range ( MPa)
12.64 - 100.24
17.18 - 102.25
13.03 - 87.40
9.96 - 39.64
10.98 - 36.64
-
c2 Range (average) (MPa)
12.63 - 97.22 (48.34)
17.03 - 97.26 (54.16)
12.76 - 85.55 (42.95)
18.88 - 64.49 (42.79)
8.85 - 35.23 (18.41)
6.26 - 34.89 (15.24)
6.83 - 20.79 (10.87)
5.33 - 28.70 (10.86)
(*) no.of samples, BP2: weathered sandstone,
c2: UCS equivalent to diameter to length ration equal to 2
Standard deviation
21.07
21.27
23.98
16.33
-
Reclassified c2 (MPa)
27.91 - 71.36 (*17)
32.53 - 72.31 (*17)
20.81 - 45.12 (*9)
34.73 - 59.56 (*5)
71.23 - 97.26 (*12)
12.63 - 31.67 (*11)
-
S2’,S5’,S5a’: c2 of weathered shale derived from
empirical correlation
Table 3: Summary of Isp and Isp50 for sandstone and shale perpendicular to sample lamination
Rock
samples
BP3 (32)
BP4 (30)
BP5b (29)
S2 (30)
S5 (51)
S5a (29)
Isp
Range (MPa)
Isp50
0.08 - 9.52
0.02 - 0.43
0.01- 0.43
0.11-2.07
0.14 -2.26
0.05-1.88
0.09 - 9.94
0.03 - 0.46
0.01 - 0.53
0.13-2.08
0.18 - 2.56
0.06 - 1.41
Average (MPa)
Isp
Isp50
3.13
0.17
0.06
0.73
0.47
0.45
3.36
0.18
0.07
0.76
0.50
0.45
(..) no. of samples , Isp: Point load perpendicular to sample lamination, Isp50: Point load equivalent to 50 mm diameter-
4
Fresh to slightly
weathered
Highly
weathered
Fresh to slightly
weathered
Isd – slake durability (%)
σc- Uniaxial cpmressive strength
Iks –%tage of medium quartz
It - Stiffness index
Ikj-% of quartz
Ktt – Confined compressive strength (MPa)
Is –Point load strength (parallel) (MPa)
Ia – Point load anisotropy index
Figure 2: Summary of the physical and mechanical properties of sandstone and shale by
the quality of weathering grade.
The summary of the physical and mechanical properties of sandstone and shale with respect to their
degree of tropical weathering is tabulated in Table 2, Table 3 and Figure 2. From the results the
qualitative and quantitative methods of assessment have conclusively showed the gradually decreased
of weathered sandstone physical properties and strength differences from 6% to 33% from BP2 to
BP5. Similarly the complex properties of weathered shale resulted to strength differences from 17% to
28% from S2 to S5’.
EMPIRICAL STRENGTH MODEL
The principles of empirical strength model of sedimentary rock is based on the assumptions that the
physical properties of sandstone and shale gradually changed from fresh to highly weathered, hence
their respective strength reduces proportionately with the grade of weathering . It was assumed that
the four empirical models in Figure 1 were based on a column weathering profile of rock mass. The
analyses were carried out in sequence of the strength of weathered sandstone; weathered shale ;
weathered composite material dominated by sandstone and weathered composite material dominated
5
by shale . In the composite rock material models, the structure orientation was assumed to be ideally
horizontally paralleled.
In summary, the research design of the empirical models were based on the following assumptions:
 quality of weathered rocks below the ground increases with depth
 quality of rock weathering is based on strength envelopes.
 broad range in strength index are due to inherited non-homogeneity of weathered rock
 the highest and the lowest strength indices are recorded for each weathered group of rock
 the average strength index of rock from each group was used as a guideline
 the empirical correlations of material strength was used to predict the mechanical properties of
composite rock material.
Uniaxial Compressive Strength to Point Load Strength of
Weathered Sandstone
From the laboratory results, the uniaxial compressive strength of the weathered sandstone, (σ, σ1 or σ2)
versus the respective point load strength index, Isp50 , were plotted on semi-log graph as shown in Fig
3. The strength correlation had two different profiles. The uniaxial compressive strength of slightly
weathered to moderately weathered sandstone has relatively linear correlation to point load strength as
shown by equation (1), meanwhile moderately weathered to highly weathered sandstone strength
concludes logarithmic correlation as shown by equation (2). Both equations have significant strength
correlation of more than 90%.
 1 10 I sp50  40.8 with R2 = 0.93
(1)
 2  12.6 ln( I sp50 )  65.4 with R2 = 0.97
(2)
Further data regression from slightly to highly weathered sandstones produced power regression line
as in equation (3), with degree of significant equal to 0.91.
  60.6( I sp50 ) 0.3 with R2 = 0.91
(3)
Strength to Elastic Modulus and Stiffness of Weathered Sandstone
The elastic modulus of weathered sandstone was determined from uniaxial compressive strength test.
Graphical plot of the uniaxial compressive strength (σ2) with respect to elastic modulus (E50) and
stiffness index (Ii) is as shown in Fig. 4. From Eqn. 4 and Eqn. 5 respectively with each R2 value
equal to 0.52 and 0.23 had concluded a low significant of correlations obviously observed from the
scattered data.
E50  0.4  2  12
with R2 = 0.52
(4)
I i   0.0053 2  0.94
with R2 = 0.23
(5)
6
Highly
weathered
Moderately140
140
weathered
Slightly
weathered
120
120
y1 = 9.8823x + 40.839
R2 = 0.9305
UCS index (MPa)
y1 =9.8823x + 40.839
100
100
Indeks KMS (MPa)
80
80
60
60
y2 = 12.563Ln(x) + 65.396
2
y2 = 12.563Ln(x) + 65.396
R = 0.9719
40
40
R2 = 0.9719
20
20
0.001
0.001
0.010.010
1
0
1.000
100
0.100
10
Isp (50) (MPa)
10.000
-20
Isp50 (MPa)
Figure 3: Correlation of σ versus Isp50 of weathered sandstone
60.00
60
y = 0.3989x + 11.975
R2 = 0.5201
y = 0.3989x + 11.975
R2 = 0.5201
1.20
1.2
50
50.00
1.0
1.00
40
0.8
0.80
Indeks tegar
E50(MPa)
40.00
30
30.00
0.6
0.60
20
0.4
0.40
20.00
y = -0.0052x + 0.9497
R2 = 0.23
y = - 0.0052x + 0.9497
R2 = 0.23
10
10.00
E50
0
0.2
0.20
It
0.00
0
Stiffness index, It
Modulus elasticity, E50
1.40
1.4
20
40
20
40
E50
60
80
60 KMS (MPa) 80
100
Indeks
UCSLinear
Index
Indeks tegar
(Indeks(MPa)
tegar)
Linear (E50)
100
120
0.00
120
Figure 4: Correlation of σ2 versus E50 and Ii of weathered sandstone.
Strength Index, Is of
R2 = 0.9305
Weathered Sandstone
Strength index, Is, is defined as the ratio of uniaxial compressive strength to point load strength and is
a dimensionless parameter. It represents the ratio of compressive strength to the tensile strength
properties of a rock material. Based on the plotted data as shown in Fig 5 and Fig 6, the strength index
of sandstone correlated exponentially to σ2 (Eqn. 6) and Isp50 (Eqn. 7) as follows:
I s  1853 e 0.005 2 with R2 = 0.9
(6)
7
I s  0.02( I sp50 )0.7 with R2 = 0.98
(7)
Based on the above correlations, it is observed that at σ2 > 60 MPa , Is< 125, the strength index
reduction rate is not significant probably due to the high brittleness of weathered sandstone. On the
contrarily the weathered sandstone having σ2 < 60 MPa and Is>125, can be due to reduction in the
brittleness indicated by a large increment of strength index at low compressive strength. The profile
revealed the boundary between rock-like weathered sandstone and soil-like highly weathered
sandstone. The similar behaviour was also observed at the boundary of point loads strength of 1 MPa.
The sandstone behaved as a brittle material when the point load strength is more than 1 MPa,
otherwise it can be considered as a ductile material.
1250
1250
1000
750
Indeks Kekuatan Ik
Strength index, Ik
1000
750
500
500
-0.0513x
1853e
y =y = 1853e
R = 0.8987
R2 = 0.8987
-0.0513x
2
250
250
0
0
0
0
20
20
40
40
60
80
100
60
80 100
UCS Index (MPa)
Indeks KMS (MPa)
120
120
140
140
Figure 5: Correlation of strength index to uniaxial compressive strength of weathered sandstone
0.08
40
0.07
0.08
0.07
0.06
Strength index
0.06
0.05
Nisbah kekuatan
0.05
0.04
0.04
0.03
0.03
yy = 0.0164x
= 0.0164x0.7133
R2= 0.9839
R = 0.9839
0.7133
2
0.02
0.02
0.01
0.01
0.01
0.01
0.1
0.10
0.00
1.00
1
Isp(50) (MPa)
Isp50 (MPa)
10
10.00
Figure 6: Correlation of strength index to point load index of weathered sandstone
Empirical Model of Weathered Shale
The indirect method of empirical strength model for weathered shale is an alternative method for
predicting its equivalent uniaxial compressive strength.At the same time, the correlation between
material properties with respect to its quality of weathering grade can been predicted. From the
minimal experimental results of uniaxial compressive strength test and point load test on slightly
8
weathered shale, a semi-log graph was established. The correlation between the two strength indices
showed a curvilinear correlation as shown in Fig 7 producing an empirical correlation as in eqn (8),
 2 s 14.10 Is sp50  4.50 with R2 = 0.94
(8)
Hence the reduction in strength of weathered shale is predicted from the point load strength index.
The uniaxial compressive strength of the shale is in the range of 6 MPa to 29 MPa for moderately
weathered. For slightly weathered shale, the ranges of strengths are slightly higher range from 29 MPa
to 35 MPa.
40
35
40
y = 14.104x + 4.5026
2
R = 0.9359
Indeks KMS (MPa)
UCS index (MPa)
35
30
30
25
25
y =14.104x + 4.5026
R2 = 0.9359
30
15
10
20
15
10
5
5
0.001
0.010
0.001
0.100
0
1.000
0.01
1
Isp(50) (MPa)
Isp(50) (MPa)
10.000
10
Figure 7: Correlation of UCS to Isp(50) of slightly weathered shale
Uniaxial Compressive Strength to Elastic Modulus and Stiffness
The correlation between the uniaxial compressive strength with elastic modulus, E50, and intact
properties, Ii are plotted in the same graph as shown in Fig 8. The graphical plot produced two
empirical correlations. The correlation of elastic modulus of the shale with respect to compressive
strength can be predicted using Eqn. 9,
E50 '  0.46 2 '  8.03 with R2 = 1.0
(9)
and similarly the strength index of weathered shale is predicted by using eqn (10) below,
I c  4.8 2 s ' ( 0.57) with R2 = 0.99
(10)
It was found that the elastic modulus decreases linearly with the decrease in uniaxial compressive
strength, meanwhile the stiffness of material exponential increases with a decrease in uniaxial
compressive strength . The intersection of the two lines indicated the boundary between soil-like
weathered shale on the left and rock-like weathered shale on the right hand side.
9
3030
2.5
2.5
25
25
2
2.0
y = 0.4563x
+ 8.0298
y = 0.4563x
+ 8.0298
R =1
R2 = 1
20
E50 (MPa)
20
1.5
1.5
15
15
1
1.0
10
10
-0.572
y = 4.7759x
y = 4.7759x
R = 0.9896
R2 = 0.9896
-0.572
0.5
2
5
Stiffness index, It
Modulus elasticity,
E50
2
0.5
5
0
0.000
5.000
00
5
10.000
15.000
10
20.000
25.000
15
20
25
UCS Index (MPa)
Indeks KMS (MPa)
30.000
0
40.000
35.000
30
35
040
Figure 8: Uniaxial compressive strength w.r.t. elastic modulus and stiffness index of weathered
shale.
Empirical Strength Model of Composite Rock
The empirical strength model of each type of composite rock was determined by the same approach of
analysing individual strength of sandstone and shale. Each composite model was developed base on
the combination of each group of experimental data for weathered sandstone and shale. It was found
that the strength boundary of weathered materials changes from soil-like material to rock-like material
at σ2 = 35 MPa or equivalent Isp50 = 0.3 MPa. The strength correlation for the respective weathered
state was plotted by using normal scale graph as shown in Fig 9 and Fig 10. The respective empirical
strength correlations are simplified below:
2
Rock-like composite
or
Soil-like composite
or
General composite material
composite
 24 ln ( Issp50 )  51 with R2 = 0.94
(11)
composite
 25 ln ( Issp50 )  49 with R2 = 0.97
(12)
2
2
composite
 52 ( Issp50 )  3 with R2 = 0.90
(13)
2
composite
 28 ( Issp50 )  6 with R2 = 0.94
(14)
composite
18 ln ( Issp50 )  50 with R2 = 0.85
(15)
2
Subsequently the correlation between the uniaxial compressive strength with elastic modulus, E50, and
stiffness Ii of composite is as shown in Fig. 11. The graphical plot produced two empirical
correlations. The elastic modulus and stiffness index of the composite can be predicted by the
following equations,
E50 '  0.45 2 '  8.2 with R2 = 0.7
(16)
I s   0.42 ln  2  2.24 with R2 = 0.72
(17)
Equation (16) for composite material is close to that weathered shale (Eqn. 9) and the stiffness index
(Eqn. 17) is close to Eqn. 10. Hence it can be deduced that the presence of shale has greatly
influenced the strength of Kenny Hill rock mass.
10
Boundry soil/rock? BP n Syal
140
140.000
120
120.000
100
80
Indeks KMS (MPa)
UCS index, (MPa)
100.000
60
80.000
y = 24.622Ln(x) + 49.162
R2 = 0.9695
40
60.000
20
y = 24.622Ln(x) + 49.162
R2 = 0.9695
0
40.000
Isp(50) > 0.3
Isp(50) < 0.3
20.000
y = 27.653x + 5.7399
y = 27.653x
+ 5.7399
R2 =2 0.9382
R = 0.9382
0.000
0.000
0
11.000 2
2.000
3
3.000
4
54.000 6 5.0007 6.000
8 97.00010 8.000 9.000
Isp50 (MPa)
Isp(50) (MPa) Isp < 0.3 Isp > 0.3"
10.000
Figure 9: Plot of UCS wrt ISp for weathered composite using boundary Isp =0.3 MPa
Figure 10: Plot of UCS wrt Isp for weathered composite using boundary UCS=35 MPa
11
Figure 11: Correlation of UCS to Elastic modulus and stiffness of composite rock
CONCLUSION
The systematic assessment method and the comprehensive data analysis on the weathered sandstone
and weathered shale had been carried out to establish their respective strength models as individual
material and composite material. Even though there is no direct laboratory works has been carried out
on composite sample the results have shown some promising findings on the prediction of the strength
behaviour of composite sandstone and shale rock of Kenny Hill formation. The respective empirical
equations can be used either to predict the elastic modulus, stiffness or strength indices from a simple
test result as simple as a point load strength test. In real life problem, it is very important to the
practitioner to be able to characterise and determine the geotechnical behaviour of weathered
sandstone and shale as a composite rock mass for cost saving and safe geotechnical design.
ACKNOWLEDGEMENT
This paper only highlighted and discuss a sub topic of a comprehensive research studies funded by
Ministry of Science, Technology and Innovation Malaysia ( IRPA 09-02-01-0006EA006 ) and is
gratefully acknowledge. The authors would like to thank , Institute of Research and Consultancy and
the Faculty of Civil Engineering UiTM for their support.
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