6.5
Effective shear strength (intact)
The effective shear strength (Mohr Coulomb) parameters for intact rock have been determined from
regression analysis of p’-q data plots (refer to Figures E9 to E14 presented in Section E4 of Appendix
E).
Effective shear strength data was sourced from CRL Stage 2 and historical data and supplemented by
SH20 data which included the only available test data for EU3 material.
6.5.1
Typical values
The typical values for intact rock outlined in this section should not be used for design. They are
required inputs to determine rock mass effective shear strength parameters. The rock mass
parameters presented in Chapter 7 have been ‘factored’ to take into account the rock mass properties
and are the effective shear stress parameters that should be used for design.
Typical values were chosen from triaxial test results which yielded deduced UCS values equivalent to
median UCS values (refer to Section 6.3).
UCS deduced from triaxial tests was back-calculated from triaxial minor and major principal stress
data using the method described by Hoek and Brown (1997). One lab test of typical strength ECBF
sandstone from SH20 Waterview (BH705A 56.88m) yielded a deduced UCS of 2.4 MPa which is
approximately equivalent to the EUs2 UCS parameter of 2.5 MPa. The lab certificate reported (using
2
linear regression, R =0.9978) an effective friction angle (phi’) of 40.77 degrees and effective cohesion
(c’) of 664 kPa.
The deduced typical values are summarised in Table 6-7 below:
Table 6-7: Deduced effective stress typical values for intact ECBF rock
Material
EW†
Lab
specimen
identifier
–
Lab
Test
Type
Lab
reported
Phi’
(degrees)
Lab
reported
c’
(kPa)
Lab
Regression
Coefficient
2
R
Backcalculated
deduced
UCS (MPa)
Backcalculated
deduced
mi
Phi’
(deduced)
(degrees)
c’
(deduced)
(kPa)
–
–
–
–
–
–
35
15
EUs1
BH222
28.37m
1x
CUM
40.8
30
0.9998
0.095
50*
40
0****
EUs2
BH705A
56.88m
3x
CDS
40.77
664
0.9978
2.394
15.04
40
200***
EUz2
BH705A
51.05m
1x
CUM
32.66
653
0.9991
2.157
7.763
32
200***
EUz2
BH705A
38.00m
3x
CDS
31.55
750
0.9999
2.582
5.971
32
500***
EUs3
BH706A
51.39m**
3x
CDS
52.52
1099
0.9947
5.804
26.062**
45*****
500
†No triaxial tests with equivalent UCS in range of 0.5-0.9MPa. Used design parameters published in CRL enabling works
geotechnical parameters TA memo (Chung, 2014). Small values of effective cohesion have been adopted for weathered ECBF,
where relic rock structure is a plausible explanation for cementation.
*All triaxial tests with deduced UCS less than 1MPa gave unreliable mi value typically exceeding mi=50.
**All EU3 tests were carried as consolidated drained (CD) tests with each test stage carried out on different test specimens.
Therefore materials tested could be significantly different owing to the decimetre scale typical bedding within EU2 material. Also,
test pressures did to meet the requirements stipulated by Hoek and Brown (1997) to ensure an accurate estimate of mi is
attained. The confining pressure (sigma 3) of the final test stage should approximate 0.5 x UCS.
***For EUs2 lower bound c’ values have been chosen since weaker material (where failure through material is more likely to
occur) can generally be found over a 6m span.
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****The effective cohesion intercept was assumed to equal zero for EUs1 and the friction angle is the same as typical strength
EUs2 although some lower strength friction angles were observed that have been attributed to sample disturbance
*****friction coefficient (mi) unrealistically high. Expected value in range 10-16, therefore a phi value of 45 degrees has been
adopted.
6.5.2
Sensitivity
Plots of test data show the materials are highly variable with friction angles being relatively constant,
while cohesion which reflects the degree of cementation, accounts for the majority of the variability.
Friction angle appears to be sensitive to grain size and matrix clay content. Materials with less clay in
the matrix and siltstone rock fragments generally had lower friction angles and richer in volcanogenic
rock fragments and quartz had higher friction angles.
Plotting all p’-q points for a given material with highly variable cement strength (i.e. EUs2, EUs3)
commonly results in negative cohesion – refer the Figure E13 in Appendix E which shows ‘negative
cohesion’.
Figure 6-5: Indicative P’Q plot showing effect of cementation on effective strength
Some regressions built from single stage consolidated drained (CD) and undrained (CU) tests did not
result in good linear regression fits and it is suspected the test specimens were different materials
resulting in different strength due to variation in cementation.
It is suspected that effective stress phi values might be under estimated and effective cohesion
overestimated for the following two reasons:

Multi-stage consolidated undrained (CUM) tests that were over-sheared in initial stages may have
resulted overestimates of effective cohesion and underestimates of friction angle.

Analysis of the p’-q data showed that the failure envelope was commonly non-linear with higher Φ’
and lower c’ at lower normal stresses than determined from the linear ‘best fit’ regression.

At lower axial strains the cementation between the soil particles is the major strength component,
while at higher strains, when breakage of the cementing bonds occurs, the frictional component of
strength becomes predominant (Rad and Clough, 1982).
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
Testing by Collins and Sitar (2009) showed that weakly cemented quartz sand materials fail in a
brittle fashion and can be modelled effectively using linear Mohr-Coulomb strength parameters,
although for weakly cemented sands, curvature of the failure envelope is more evident with
decreasing friction and increasing cohesion at higher confinement. In contrast, the sand grains that
make ECBF are composed of a significant proportion of ‘partially plastic’ siltstone rock fragments
within a clay matrix, resulting often in a plastic response prior to the linear elastic phase.
To account for overestimates of cohesion, cohesion values are refined when the rock mass effective
stress parameters are defined – refer to Chapter 7.
6.6
6.6.1
Young’s Elastic Modulus (Intact stiffness)
Young’s modulus
Young’s modulus for unweathered ECBF (EU) was derived from stress-strain measurements taken
during UCS (method 1) and triaxial UU (method 2) lab testing.
Insitu moduli were derived from in-situ dilatometer (PMT) measurements (methods 3 and 4) and
deduced from a typical value range (method 5) and SPT testing using an empirical relationship
(method 6).
Refer to section 6.6.3 below for definition of moduli types.
Table 6-8: Tangent modulus
Material
Description
Parameter
Young’s
Tangent
Modulus E
(MPa)
Range
EW
Weathered ECBF
Method 1: UCS data: median = 130MPa; IQR=19-272MPa (n=28)
75
50 – 150
EUs1†
Uncemented sand†
Method 1: UCS data: median = 8MPa; IQR=19-272MPa (n=14) (disturbed by
sampling)
Method 4: PMT SH20+CRL2 data: median = 104MPa; IQR=72-159MPa (n=9)
Method 5: Bowles (1997) Es estimate for heavily over consolidated sand: 75 MPa
Method 6: Bowles (1997, p316) empirical estimate from lower bound SPT = 94 MPa
65
50 – 150
EU2
Typical strength ECBF interbedded sandstone and siltstone
Method 1: UCS data: median = 420MPa; IQR=231-715MPa (n=238)
Method 4: PMT SH20+CRL2 data: median = 430MPa; IQR=311-673MPa (n=49)
400
200 – 700
EU3
EUs3 well cemented, atypically strong sandstone
Method 1: UCS data: median = 1843MPa; IQR=1147-3251MPa (n=85)
Method 4: PMT SH20+CRL2 data: median = 1508MPa; IQR=1211-1724MPa (n=8)
1500
700 – 3000
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Table 6-9: Secant modulus determinations
Material
Description
EW
EU2
6.6.2
Parameter
Young’s
Secant50
Modulus E
(MPa)
Range
Weathered ECBF
Method 2: UCS data: median = 121MPa; IQR=19-272MPa (n=28)
75
60 – 150
Typical strength ECBF interbedded sandstone and siltstone
Method 2: UCS data: median = 314MPa; IQR=160-360MPa (n=250)
Note: To convert from secant to tangent modulus, multiply secant modulus by
160%.
250
150 – 400
Modulus ratio
Since EU2 material is variable in strength (1-5MPa), a tangent modulus ratio yields a more accurate
estimate of young’s modulus and is more applicable than a typical modulus value. Modulus ratio
should be used for estimates of modulus during design.
Moduli ratios are presented in Table 6-10 and Table 6-11 below.
Table 6-10: Tangent modulus ratio
Material
Description
EW
EUs1†
EU2
EU3
Parameter
Tangent
Modulus ratio
(dimensionless)
Range
Weathered ECBF
Method 1: UCS ALL sources: median = 102; IQR=53-141 (n=28)
100
50 – 140
Uncemented sand†
Method 1: UCS data: average = 50; IQR=39-67 (n=14) (disturbed by sampling)
2
Method 3: PMT SH20: median = 135 (weak regression, R = 0.54)
Method 4: PMT SH20 data: median = 148; IQR=111-166 (n=9)
140
110 – 170
Typical strength ECBF interbedded sandstone and siltstone
Method 1: UCS CRL2: median = 168; IQR=140-219 (n=38)
Method 1: UCS ALL sources: median = 149; IQR=112-200 (n=238)
2
Method 3: PMT CRL2: median = 209 (weak regression, R = 0.57)
2
Method 3: PMT SH20: median = 163 (weak regression, R = 0.77)
2
Method 3: PMT CRL2+SH20: median = 179 (weak regression, R = 0.66)
Method 4: PMT CRL2 data: median = 183; IQR=156-255 (n=17)
Method 4: PMT SH20 data: median = 159; IQR=116-183 (n=34)
Method 4: PMT SH20+CRL2 data: median = 166; IQR=133-198 (n=51)
160
120 – 220
EUs3 well cemented, atypically strong sandstone
Method 1: UCS CRL2: median = 213; IQR=180-232 (n=20)
Method 1: UCS ALL sources: median = 191; IQR=154-249 (n=85)
180
150 – 250
Parameter
Secant50
Modulus ratio
(dimensionless)
Range
Table 6-11: Secant modulus ratio
Material
Description
EW
Weathered ECBF
Method 2: UCS data: average = 67; IQR=50-123 (n=24)
67
50 – 125
EU2
Typical strength ECBF interbedded sandstone and siltstone
Method 2: UCS data: average = 96; IQR=75-123 (n=266)
Note: To convert from secant to tangent modulus, multiply secant modulus by
160%.
250
75 – 130
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Methods presented in Appendix E suggest the following:

Since EU2 material is variable in strength (1-5MPa), a tangent modulus ratio yields a better
estimate of young’s modulus and should be used for estimates of modulus.

The modulus ratio is measured Young’s modulus at failure divided by compressive strength at
failure
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 (𝑀𝑀𝑀𝑀) =
𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑔𝑔 ′ 𝑠𝑠 𝑀𝑀𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜
𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑈𝑈𝑈𝑈𝑈𝑈

A tangent modulus ratio (using tangent modulus) of 165 x UCS appears typical of EU2 material.
This value is in general agreement with UCS and pressuremeter tests.

Regression of PMT tests (using initial tangent modulus) yields a slightly higher tangent modulus
ratio of approximately 200 x UCS for typical strength ECBF. However this seems to be a function of
the regression as tangent modulus ratios averaged for each material type from pressuremeter are in
the 160 range.

There is a slight trend of increasing modulus with depth associated with the UU triaxial tests and
insitu PMT tests. However this trend is masked by the variability due to variation of cement strength
(which accounts for the majority of normal variation).

Modulus ratio does seem somewhat dependent on compressive strength. The typical range
observed is 140 x UCS for lower strength uncemented sandstone and up to 200 x UCS for wellcemented sandstones.

A very high quality dataset of UU triaxial tests was put together during the Auckland rapid transport
(ART76) investigation. This dataset includes 250 secant modulus determinations of material logged
as unweathered ECBF. The secant modulus ratio is pretty consistent at 100.

The tangent modulus ratio (UCS, PMT) is 160% of the secant modulus ratio for EU2 material.
Therefore estimates of secant modulus can be made by applying this factor.

Some low tangent and secant modulus ratios were noted for some EUs1 determinations. This is
thought to be the result of sample disturbance.

When analysing modulus ratio data with regression, EU3 which is a distinct material has to be
treated separately. If analysed together the regression will be influenced by the EU3 population
(effectively outliers) which will result in much higher modulus ratio determination. As a general rule,
filter out EU3 data, apply an upper bound cut off of 6MPa and restrict modulus determinations to
less than < 1GPa. Not statistically justifiable, but gives more realistic determinations.

Unload-reload Eur modulus was investigated as part of the CRL3 laboratory testing programme.
Unload-reload moduli were calculated for 3 x UCS and 1 x UU and compared with initial tangent
moduli. The testing revealed that unload-reload modulus is typically 150% of the tangent modulus.

Tangent modulus determinations from the PMT were in general agreement with tangent modulus
determinations of the lab UCS data so they should be directly comparable.

The ratio of unload-reload modulus to initial tangent modulus from EU2 determinations using the
PMT is 230% for the CRL2 dataset (n=17) and 260% for the SH20 dataset (n=50). PMT
determinations are therefore not comparable with unload-reload modulus to initial tangent modulus
ratios of 150% determined from lab testing.
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