empirical development of the rock mass deformation

7/25/2019 Empirical Development of the Rock Mass Deformation

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Journal of Geological Resource and Engineering 2 (2014) 55-67

Empirical Development of the Rock Mass Deformation

Modulus

Manouchehr Sanei and Lohrasb Faramarzi

Department of Mining Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran

Abstract: Rock mass deformation modulus is a fundamental factor for a safe and economical design of rock structures like large

underground openings, tunneling, and open pit mine as well as foundations in both the initial state of stresses act on rock mass and its

strength characteristics. The rock mass deformation modulus recently has been measured by in-situ loading tests and has been

estimated by use of empirical equation based on classification systems and data of laboratory tests. In-situ tests to measure modulus

directly are so expensive, times consuming and the reliability of the results of these tests is sometimes doubtful; subsequently, many

researches have been carried out to estimate this parameter based on classification systems. In this study, a new empirical equation wasproposed by use of statistical analyses based on a database of more than 142 in-situ tests, like plate load tests, dilatometer tests, flat jack

tests, and classification systems; in addition, properties of the intact rock.

Key words:Rock mass deformation modulus, in-situ tests, classification systems, empirical equation.

1. Introduction

The deformation modulus is the most representative

parameter describing the pre-failure mechanical

behavior of any engineering material. Also,

deformation modulus is an important parameter used inorder to estimate various rock mass properties in a rock

engineering projects. Many methods are available to

estimate the rock mass deformation modulus such as

in-situ tests, empirical equations between deformation

modulus and rock mass classification system, and

geophysical (usually seismic) methods as well as

estimating from laboratory test results [1]. In rock mass,

the existence of discontinuities makes the mechanical

properties of rock mass differ greatly from that of intact

rocks. Although the laboratory tests have existed for

estimating deformation modulus; however, the results

are not very suitable for this purpose since the

specimen is too small. Thus, the in-situ tests are

presently employed in major rock engineering projects,

to provide more rational data for the design of rock

Corresponding author: Manouchehr Sanei, M.Sc. in rockmechanic, research fields: rock mechanics, rock engineering

and geomechanics. E-mail: [email protected].

structures which are available for the prediction of rock

mass behavior under different loading conditions [2, 3].

Furthermore, the rock mass deformation modulus is

currently evaluated by means of different types of

in-situ loading tests such as the plate loading test, the

flat jack test, the borehole loading tests, and the radial

jacking test as well as the water chamber test and so on [4].

In-situ tests to measure modulus directly are so

expensive, times consuming and the reliability of the

results of these tests is sometimes doubtful;

consequently, many authors have proposed empirical

relations for estimating deformation modulus

indirectly by using various rock mass classification

systems such as the RMR (rock mass rating), the GSI

(geological strength index), the Q (tunneling qualityindex), the RMI (rock mass index) and the RQD (rock

mass quality designation) like Bieniawski [5], Serafim

and Pereira [6], Nicholson and Bieniawski [7],

Mehrotra [8], Grimstad and Barton [9], Mitri et al. [10],

Hoek and Brown [11], Read et al. [12], Palmstrom and

Singh [13], Barton [14-16], Galera et al. [17], Shen

et al. [18], and Sanei et al. [19].

Moreover, Zhang and Einstein [20] estimated the

DAVID PUBLISHING

D


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Empirical Development of the Rock Mass Deformation Modulus56

deformation modulus of rock masses by using of RQD.

Sonmez et al. [21] developed an empirical model to

determine the deformation modulus of rack masses

indirectly based on the GSI system. Also, Hoek and

Diederichs [22] proposed an empirical equation to

estimate rock mass modulus by use of a sigmoid

function. On the other hand, Chun et al. [23] presented

a model in order to predict deformation modulus based

on multiple and polynomial regression analyses of the

RMR systems. Furthermore, Sanei et al. [24]

developed the second-order polynomial equation for

estimating of rock mass deformation modulus by use of

JH (Japan Highway) corporation classification system.

In this study, the values of RMR, Q, GSI and JHclassification systems were determined and properties

of the intact rock like modulus of elasticity from

laboratory tests was calculated; in addition, according

to ISRM [25] the values of rock mass deformation

modulus from in-situ tests (plate load, dilatometer, and

flat jack test) were measured. Then, four new empirical

equations for estimating the rock mass deformation

modulus were developed by use of a database of 47

plate load tests, 86 dilatometer tests, and 9 flat jack test

at the Bakhtiary Dam site in Iran. All in all, by use of

the statistical analyses among them, the suitable

equation was select to estimate the rock mass

deformation modulus.

2. Bakhtiary Dam Site

The site of Bakhtiary Dam and Hydroelectric Power

plant project include the design and construction of a

315 m high, double curvature, concrete dam, and an

underground powerhouse, with a nominal capacity of

1,500 MW, are located in Lorestan Province, in the

southwest of Iran, northeast of the Tang-e-Panj railway

station on the Tehran-Ahwaz railway, with the

following coordinates: 484650E/3257'41N (Fig. 1).

2.1 Geological Characterization of the Dam Site

Limestone layers of Sarvak formation, which areMid-Cretaceous marine sediments, form the

foundation of the dam, powerhouse and other

appurtenant structures. These layers are generally

tightly folded. The bed rock consists of limestone and

marly limestone that contains nodules of siliceous

limestone (or Chert). These deposits, which were

sedimented between the formations of Garau (at the

bottom) and Gurpi (at the top), are marked as

Bangestan Group (Kazhdomi, Sarvak, Surgah and Ilam

formations) of Cretaceous age. The limestone of the

Bakhtiary Dam reservoir, which is overlying Garau

formation and underlying Gurpi formation, has been

Fig. 1 Location of Bakhtiary Dam site.


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Table 1 Physical and mechanical properties of intact rock specimens.

Physical and mechanical properties Index Unit Value

Density g/cm3 2.61-2.74

Uniaxial compressive strength c MPa 77-133

Modulus of elasticity E GPa 55-73Poissons ratio - 0.3

Tensile strength t MPa 6.3-11.2

Cohesion C MPa 29-36

Friction angle 35-45

Table 2 Estimated RMR, Q, GSI and JH values for different rock mass classifications at Bakhtiary Dam site.

Lithology RMR89 Q GSI JH

SV2 + SV3 30-51 0.002-80 35-50 67-83

SV2 + SV3 + SV4 48-66 0.002-100 45-60 75-89

SV5 + SV6 41-72 0.01-100 45-65 71-91

SV7 46-56 0.002-100 45-55 75-85

Table 3 Characteristics of bedding planes and joint sets.

Value or descriptionFrequency (%)

Bedding J1 J2 J3

Aperture (mm)0.1-1 90 90 95 95

1-5 10 10 5 5

Spacing (cm)

2-6 1.5 25 3 6

6-20 47 48.5 52 25

20-60 44.5 45 43.5 62.5

60-200 3.5 4 1.5 6.5

200-600 3.5 0 0 0

Infilling

Clay 42.5 10 2 0

Calcite 46 67.5 55 43Bitumen 4.5 1 0 0

FeO 2 0 0 0

Tight 5 21.5 43 57

Roughness

UndulatingSs 19 2 0 0

PlanarSs 41 2 1 0

UndulatingSm 5 1 1 0

PlanarSm 18 47 54.5 72.5

UndulatingRo 1 0 0 0

PlanarRo 16 48 43.5 27.5

SsSlickensided, SmSmooth, RoRough.

3. Evaluations of Rock Mass Classification

Systems at the Bakhtiary Dam

Rock mass classification systems were used for

various engineering design and stability analysis;

therefore, based on empirical relations between rock

mass parameters and engineering applications, such as

tunnels, slopes, and foundations, the values of rock

mass classification systems were calculated that are

given in Table 2.

3.1 Rock Mass Classification by JH Method

Akagi et al. [27] presented a new method for the

classification of rock masses that the JH rating system

was obtained from the study of 6,101 tunnel sections

constructed by the JH Corporation. It should be noted

that the range of JH system is from 0 to 100. Moreover,

in JH method rocks are divided into four classes

according to compressive strength in the fresh state and

the modes of subsequent weathering and deterioration


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Empirical Development of the Rock Mass Deformation Modulus 59

as well as investigated the degrees of contribution of

observation items in each class. Also, grouping of

rocks in JH classification method are given in

Table 4.

4. In-situ Measurements of Deformation

Modulus

In-situ deformation tests are expensive and difficult

to conduct and they are mostly conducted in special

works; in addition, initial preparations at each test site

are particularly time consuming. Today, several types

of in-situ tests are used to determine the modulus of

deformation. Therefore, in this study, totally, 47 PLT

(plate load tests), 86 DLT (dilatometer tests), and 9 FJT(flat jack tests) were performed at Bakhtiary Dam site.

Also, locations of plate load, dilatometer and flat jack

tests are shown in Fig. 3.

4.1 Interpretation of Plate Load Test Results

PLT were performed in the 6 exploratory galleries at

Bakhtiary Dam site (Fig. 3). In fact, plate load testing

using rigid bearing plates, were performed in

accordance ISRM method for determining of rock

mass deformability. Also, data of all PLTs at dam site

were analyzed and the values of deformation modulus

were measured based on the method proposed by

ISRM [25]. According to ISRM, for rigid plate tests,

the basic formula for calculating the rock mass

deformation modulus is:

2 2,0

2 1 cot 12 1

avm

z

q a zE arc an z

w z

(1)

wheremE , avq , a, wz,0, and z are modulus of

deformation (GPa), average stress on the loaded

surface (MPa), radius of the loaded circular area (m),

displacement in the direction of the applied load

beneath the center of circle (at the depth = 0) (mm),

Poissons ratio of rock mass (taken as 0.3 that

measured from petite seismic tests in exploratory

galleries) and depth from the surface (m), respectively.

Also, the values of in-situ deformation modulus of all

performed PLTs are given in Table 5.

4.2 Interpretation of Dilatometer Test Results

DLT were performed in 21 boreholes drilled at

Bakhtiary Dam site that they were performed in

accordance with ISRM method for measuring

deformability using a flexible dilatometer with radial

displacement measurements. Also, data of all DLTs at

dam site were analyzed and the values of deformation

modulus were measured based on the method proposed

by ISRM [25]. The basic formula for calculating the

rock mass deformation modulus is:

1 id RP

E DD

(2)

where,d

E , R , D, Pi and D are modulus of

deformation (MPa), Poissons ratio of rock mass (taken

Table 4 Grouping of rocks in JH classification method.

Strength

weatheringHard Medium Soft

Massive

Group l (1,650 [123] data)[massive hard rocks]

Group 2 (2,698 [673] data)[massive medium, soft rocks]

Grani (68),Paleo & Mesozoic,Sandstone (192),

Quartz porphyry (65),Granodioritc (695),

etc.

Tuff (1,201), tuffbreccia (331), phyolite (341),

andesite (479), sandstone (67), basalt (3), etc.

Planar

Group 3[planar medium rocks]

Group 4[planar soft rocks]

Paleo & MesozoicShale (1,279), etc.Total (1,279) [111] data

Green schist (218),

Black schist (27),Tertiary mudstone (229), etc.Total (474) [105] data

[] means number of samples.


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Fig. 3 Locations of plate load, dilatometer and FJT in the exploratory galleries in Bakhtiary Dam site.

Table 5 Values of deformation modulus in Bakhtiary Dam site.

In-situ test PLT DLT FJT

Deformation modulus (GPa) 1.7-35.5 1-22 3-19

as 0.3), diameter of borehole (mm), pressure increment

within the considered segment (MPa) and corresponding

average change in drill hole diameter D (mm),

respectively. Also, the values of in-situ deformation

modulus of all performed DLTs are given in

Table 5.

4.3 Interpretation of Flat Jack Test Results

FJT were performed in 3 exploratory galleries at

Bakhtiary Dam site that they were performed in

accordance with ISRM method for deformability

determination using flat jack technique. Also, data of


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all FJTs at dam site were analyzed and the values of

deformation modulus were measured based on the

following formula suggested by ISRM [25]:

D

P

vEd

)1(K2

i

(3)

where,d

E , , D, P and Ki are modulus of

deformation (MPa), Poissons ratio of rock mass (taken

as 0.3), slot opening (mm), pressure increment within

the considered segment (Bar) and a constant (related to

the stiffness, shape, configuration, and number of flat

jacks), respectively. Also, the values of in-situ

deformation modulus of all performed FJTs are given

in Table 5.

5. Results and Discussion

In-situ tests are expensive and difficult to conduct,

therefore, the value of the deformation modulus is

often estimated indirectly from the empirical

equations. In this study, by statistical analyses, four

new empirical equations were developed to estimate

the rock mass modulus by using a database of 142

in-situ test results at the Bakhtiary Dam site; then, by

use of statistical analyses among them, the suitable

equation would be select to estimate deformation

modulus.

5.1 Estimation of Deformation Modulus from RMR

System

In the first step, the values of RMR classification

system at the Bakhtiary Dam were determined and

properties of the intact rock like modulus of elasticity

from laboratory tests was calculated; in addition, the

values of the rock mass deformation modulus weremeasured from more than 142 in-situ tests. Then,

non-linear regression analysis was used between the

values of relation Em/Ei and the values of RMR. Eq. (4)

shows that the second-order polynomial withR2= 0.70

is optimum. Also, plot of the values of relation

E /Em i versus RMR classification system is shown in

Fig. 4.

)0199.10.0363RMR-(0.0003RMR2

i EEm (4)

where, Em, Ei and RMR are rock mass deformation

modulus, modulus of elasticity and rock mass rating

classification system, respectively.

5.2 Estimation of Deformation Modulus from Q System

In the first step, the values of Qclassification system

at the Bakhtiary Dam were determined and properties

of the intact rock like modulus of elasticity from

laboratory tests was calculated; in addition, the values

of the rock mass deformation modulus were measured

from more than 142 in-situ tests. Then, non-linear

regression analysis was used between the values of

relation (Em/Ei) and the values of Q. Eq. (5) shows that

the second-order polynomial with R2

= 0.69 isoptimum. Also, plot of the values of relation E /Em i

versus Qclassification system is shown in Fig. 5.

0.0595)0.0044(0.000022 QQEE

im (5)

where, Em, Ei and Q are rock mass deformation

modulus, modulus of elasticity, and tunneling quality

index classification system, respectively.

5.3 Estimation of Deformation Modulus from GSI

System

In the first step, the values of GSI classification




values of the rock mass deformation modulus were

measured from more than 142 in-situ tests. Then,


values of relation (Em/Ei) and the values of GSI. Eq. (6)

shows that the second-order polynomial withR2

= 0.69is optimum. Also, plot of the values of relation

(Em/Ei) versus GSI classification system is shown in

Fig. 6.

)88890GSI03450GSI00040(2 ..-.EE

im

(6)

where, Em, Ei and GSI are rock mass deformation

modulus, modulus of elasticity, and geological strength

index classification system, respectively.


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Fig. 4 The values of relation Em/Eivs. RMR classification system.

Fig. 5 The values of relationEm/Eivs. Qclassification system.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60 80 100

Em

/Ei

RMR

Em

/Ei= 0.0003RMR

2-0.0363RMR+ 1.0199

R2= 0.70

0

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60 80 100

Em/E

i= 0.00002Q

2+0.0044Q+0.0595

R2= 0.69

Q

Em

/Ei

RMR

Em/Ei= 0.00002Q2+ 0.0044Q +

Q

Em/Ei= 0.0003RMR - 0.0363RMR + 1.0199R

2= 0.70

Em

/Ei

Em

/Ei

R2= 0.69


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Fig. 6 The values of relation Em/Eivs. GSI classification system.

5.4 Estimation of Deformation Modulus from JH

System

In the first step, the values of JH classification




values of the rock mass deformation modulus were

measured from more than 142 in-situ tests. Then,


values of relation (Em/Ei) and the values of JH. Eq. (7)

shows that the exponential equation with 2 0.67R is

optimum. Also, plot of the values of relation E /Em i

versus JH classification system is shown in Fig. 7.0.1392

( 0.000002 )JH

m iE E e

(7)

where, Em, Ei and JH are rock mass deformation

modulus, modulus of elasticity, and JH corporation

classification system, respectively.

5.5 Proposed a New Empirical Equation to Estimate

the Rock Mass Deformation Modulus

In this study, the rock mass deformation modulus in

Bakhtiary Dam site was obtained from in-situ tests and

four new equations. Moreover, in a similar study, the

deformation modulus in dam site from different

empirical equations had been determined and the

results had compared with measured results;

subsequently, the results showed that the first equation

of Hoek and Diederichs [22] had the most coincidence

with measured results. On the other hand, the results of

in-situ test were compared with four new equations and

Hoek and Diederichs empirical equation in order to

choose the eligible empirical equation to estimate

deformation modulus. Hoek and Diederichs [22]

proposed the following empirical equation for

estimation of rock mass deformation modulus:

0

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60 80 100

Em

/Ei= 0.0004GSI

2-0.0345GSI+0.8889

R2= 0.69

GSI

Em

/Ei

Em/Ei= 0.0004GSI2 0.0345GSI+ 0.8889

R2= 0.69

GSI

Em

/Ei


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Fig. 7 The values of relation (Em/Ei) vs. JH classification system.

75 25

11

12100

1

m D GSI

DE

e

(8)

where, D, GSI andmE are distribution factor, geological

strength index classification system and rock mass

deformation modulus, respectively.

In this study, the standard descriptive measure of

goodness-of-fit was employed to evaluate the accuracy

of deformation modulus calculated from empirical

equations. RMSE (root mean squared error) is:

n

imm ii

EEn 1

2)(1

RMSE '

I = 1, 2, , n

(9)

where, n, Em andim

E are the number of data i,

measured value of deformation modulus, and estimated

value of deformation modulus by empirical equations,

respectively. Also, MARPE (mean absolute relative

prediction error) is:

n

i m

mm

i

ii

E

EE

n 1

'1MARPE i=1, 2, , n

(10)

Furthermore, the ER (error ratio) or MER (meanerror ratio) is:

i

i

m

m

E

E 'ER

i=1, 2,, n

(11)

In this study, based on the above equations, the

values of RMSE and MARPE equations which are

close to zero and the value of MER equation which is

close to one, the suitable empirical equation was

suggested in order that it can carefully estimate the

values of deformation modulus. A list of the equations

for selecting the suitable equation in order to estimate

the deformation modulus is given in Table 6.

In Table 6, the validation of four new equation by

use of statistical analyses were examined; subsequently,

the results showed that Eq. (7) was highly suitable to

estimate deformation modulus owing to R2 = 0.67,

RMSE = 0.07, and MARPE = 0.46 as well as

MER = 1.28.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60 80 100

Em/E

i= 0.000002e

(0.1392JH)

R2= 0.67

JH

Em

/Ei

JH

Em/Ei= 0.000002e0.1392JH

R

2

= 0.67

Em

/Ei


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Table 6 List of the equations for selecting of the suitable equation in order to estimate the deformation modulus.

Equations 2R RMSE MARPE MER

Eq. (4) 0.70 0.20 1.73 -0.73

Eq. (5) 0.69 0.06 0.53 1.31

Eq. (6) 0.69 0.17 1.85 2.85

Eq. (7) 0.67 0.07 0.46 1.28

Eq. (8) - 6.89 0.76 1.65

Fig. 8 Comparison between the measured and estimated deformation moduli from eq. (7).

Moreover, the best results can be considered when

the values of modulus were predicted by Eq. (7). Also,

the comparison between the measured and estimated

deformation modulus from Eq. (7) is shown in Fig. 8.

6. Conclusions

In this paper, the rock mass deformation modulus by

actual data collected from Bakhtiary Dam site was

measured. Then, four new empirical equations to

estimate rock mass deformation modulus based on

modulus of elasticity and the RMR, the Q and the GSI

as well as the corporation JH classification systems was

developed.

Then, through statistical analysis (RMSE, MARPE,

ER and 2R , the rock mass deformation modulus was

estimated by empirical equations and the results were

compared with the results of measured deformation

modulus. All in all, the results showed that Eq. (7) was

the suitable equation for estimating the rock mass

deformation modulus.

Acknowledgments

The authors express their thanks to the Iran Water

and Power Resources Development Committee staff,

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35 40

Estim

ateddeformationmodulusfrom

JH

system,

GPa

Measured deformation modulus from in-situ tests, GPa(Gpa)

(Gpa)


12/13


Poyry Cu. Engineering Staff, Moshanir Cu.

Engineering Staff, Dezab Cu. Engineering Staff,

Stucky Pars Cu. Engineering Staff for providing data

support, and Isfahan University Of Technology, where

the research was carried out.

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