Estimation of Rock Mass Deformation Modulus and Strength of Jointed Hard Rock Masses Using the GSI System

Introduction

Rock mass characterization is essential for excavation and rock support design.
Design parameters like deformation moduli and strength are crucial for numerical modeling.
In-situ tests are definitive but often impractical during preliminary design due to limited access.
Rock mass classification systems (RQD, RMR, Q, GSI) bridge this gap by estimating parameters.
The GSI system is unique because it directly links to Mohr–Coulomb and Hoek–Brown parameters.
The subjective nature and experience needed for GSI application can be limiting.
This study introduces a quantitative approach using block volume and joint condition factor.
The approach connects geological terms with measurable parameters (joint spacing, roughness).
The GSI system is applied to characterize rock masses at Japanese underground powerhouses.
GSI values, derived from construction documents and field data, inform strength parameter calculations.
Point Estimate Method (PEM) is used to estimate means and variances of mechanical properties, matching field data.
Renewed global interest exists in underground powerhouses, nuclear repositories, and deep mining.
Knowing rock mass properties is crucial for safe and economical excavation.
Rock mass deformation modulus and strength are required for numerical models.
Determining mechanical properties of jointed rock masses remains challenging.
Numerous parameters influence deformability and strength, making universal laws impractical.
Traditional methods (plate-loading, in situ shear tests) are costly and require excavation.
The GSI system, developed by Hoek et al., uses intact rock and jointing properties to estimate deformability and strength.
GSI is suitable for characterization without direct tunnel access, focusing on structure and surface conditions.
Applicability tested in Japan, addressing the need for quantitative output from qualitative input.
The GSI system provides a complete set of mechanical properties for design (Hoek–Brown parameters $m_b$ and $s$ , Mohr–Coulomb parameters $c$ and $\,!\phi$ and elastic modulus $E$ ).
Efforts were undertaken to quantify GSI system parameters for better classification of jointed rock masses.
A supplementary, quantitative approach links descriptive geological terms to measurable field parameters.
This quantitative approach aims to facilitate consistent ratings from field mapping parameters.

Rock Mass Characterization for Mechanical Properties

Rock mass characterization collects and analyzes data, providing indices and descriptive terms of rock mass properties.
Rock mass classification estimates support requirements, strength, and deformation properties.
It also supplies quantitative data for support estimation and facilitates communication between project teams.
The study focuses on GSI use for estimating mechanical properties of jointed rock masses.
Various rock mass classification systems exist (RQD, RMR, Q, GSI, RMi), with modifications for specific applications.
The Denken system is used in Japan for dam and cavern construction, primarily for rock mass grouping.
Rock mass classification estimates mechanical properties at the preliminary design stage.
The GSI system is preferred for design due to its comprehensive input parameters for panel stability analysis.
When describing a rock mass, many parameters should be considered.
Inherent parameters (intact rock, joints, faults) are crucial for estimating strength and deformation.
Numerical analysis requires rock mass deformation modulus and strength as primary inputs.
The GSI system fits the criterion of a universal rock mass classification system using a finite set of parameters.
It provides a rating in the range of 0–100.

Rock Mass Strength

Mohr–Coulomb and Hoek–Brown failure criteria are widely used in rock engineering.
Jointed rock mass strength depends on intact rock strength and joint conditions.
Mohr–Coulomb failure criterion links major and minor principal stresses $(\sigma1$ and $\sigma3)$ :
$\sigma1 = 2c \cos \phi \frac{1 + \sin \phi}{1 - \sin \phi} + \frac{1 + \sin \phi}{1 - \sin \phi} \sigma3$
Where $c$ is cohesive strength and $\,!\phi$ is the angle of friction.
The generalized Hoek–Brown criterion for jointed rock masses is:
$\sigma1 = \sigma3 + \sigmac (mb \frac{\sigma3}{\sigmac} + s)^a$
Where $mb$ , $s$ , and $a$ are constants, with $\sigmac$ being the uniaxial compressive strength of intact rock.
Applying the Hoek–Brown criterion requires estimating: uniaxial compressive strength, Hoek–Brown constant $m_i$ , and GSI value.
Values of $\sigmac$ and $mi$ should be determined by statistical analysis of triaxial tests results.
Simple index tests (point load, Schmidt hammer) can estimate $\sigma_c$
When rock testing is limited, sc and mi can be estimated from published tables.
Mohr–Coulomb parameters can be obtained from block shear tests or in situ triaxial tests, but these are costly.
Hoek and Brown suggested rock mass classification could estimate Hoek–Brown constants $m_b$ and $s$ .
Experiences gained from using tables showed reasonable estimates on a large number of projects.
In a later update, Hoek and Brown suggested the material parameters for a jointed rock mass could be estimated from the modified 1976-version of Bieniawski’s RMR, assuming completely dry conditions and a favorable joint orientation.
A new index called GSI was introduced for very poor rock with RMR less than 25.
The GSI system consolidates various versions of the Hoek–Brown criterion into a single simplified and generalized criterion that covers all of the rock types normally encountered in underground engineering.
A GSI value is determined from the structure interlocking and joint surface conditions.
It ranges from 0 to 100.

Rock Yielding in a Ductile Manner

When GSI is known, the parameters in Eq. (2) are given as:

$mb = mi \exp \left( \frac{GSI - 100}{28 - 14D} \right)$

$s = \exp \left( \frac{GSI - 100}{9 - 3D} \right)$

$a = 0.5 + \frac{1}{6} \left( e^{-GSI/15} - e^{-20/3} \right)$

Where $D$ is a disturbance factor (controlled blasting implies $D = 0$ ).

Equivalent Mohr–Coulomb parameters are obtained from the Hoek–Brown envelope and a range of $\sigma_3$ values.
Hoek and Brown suggested using equally spaced $\sigma3$ values in the range of $0 \le \sigma3 \le 0.25 \sigma_c$ to obtain $c$ and $\,!\phi$ .
For hard rocks, e.g., $\sigmac = 85 \text{ MPa}$ , this gives a $\sigma3$ range of 0-21 MPa.
The recent update suggests obtaining a maximum confining level ( $\sigma{3\text{max}}$ ) for deep tunnels from the equation: $\frac{\sigma{3\text{max}}}{\sigma{cm}} = 0.47 \left( \frac{\gamma H}{\sigma{cm}} \right)^{-0.94}$
Where $\sigma_{cm}$ is rock mass strength, $\gamma$ is unit weight, and $H$ is overburden depth.
For caverns around 400 m deep, the $\sigma_{3\text{max}}$ is around 5 MPa.
The resulting $\,!\phi$ is higher and $c$ is lower for a range $\sigma3 = 0$ –5 MPa compared to a wider range (0 to $0.25 \sigmac$ ).
This lower confinement range aligns with the normal stress during in situ shear block tests in Japan.

Rock Failing in a Brittle Manner

Pelli et al. found that the parameters obtained did not predict the observed failure locations and extend near a tunnel in a cemented sand or siltstone.
They found that lower mb and higher s values were required to match predictions with observations.
Further analyses of underground excavations in brittle rocks lead to the development of brittle Hoek–Brown parameters ( $m_b = 0$ , $s = 0.11$ ) by Martin et al. for massive to moderately fractured rock masses with tight interlocks that fail by spalling or slabbing rather than by shear failure.
Accordingly, Eqs. (3) and (4) are clearly not applicable for GSI>75 in massive to moderately or discontinuously jointed hard rocks.
Empirical evidence suggests that brittle Hoek–Brown parameters are applicable for strong rocks ( $\sigmac > 50 \text{ MPa}$ ) with moderate to high modulus ratios (E/\sigmac > 200) and $Vb > 10 - 100 \times 10^3 \text{ cm}^3$ , JC > 1 - 2 and GSI > 65 - 75, where $Vb$ and $JC$ are block volume and joint condition factor, respectively.

Deformation

The mean deformation modulus is related to the GSI system as

$E = \left( \frac{1 - D}{2} \right) \sqrt{\frac{\sigmac}{100}} 10^{\frac{GSI - 10}{40}} \text{ GPa for } \sigmac \le 100 \text{ MPa}$

Equation (7) shows the influence of the intact rock modulus ( $E_0$ ) on the rock mass deformation modulus.
Good correlation between the modulus $E0$ and $\sigmac$ of the intact rock exists.

GSI Determination Based on Block Volume and Joint Condition

The GSI system has evolved based on experience and field observations.
GSI is estimated based on geological descriptions of rock mass, involving rock structure/block size and joint/block surface conditions.
GSI table/chart use involves some subjectivity, requiring experience and judgment.
A different approach builds on block size and conditions using block volume and joint condition factor.
This adds measurable quantitative input to render the system more objective.
The proposed GSI chart supplements descriptive block size and joint condition with quantitative measures.
Vb = Block Volume
JC = Joint Condition Factor
The influence of $Vb$ and $JC$ on GSI was calibrated using published data and applied to caverns for verification.
The original GSI chart covers four structure categories: blocky, very blocky, blocky/disturbed, disintegrated.
Extensions include a ‘‘massive’’ and ‘‘foliated/laminated/sheared’’ category for different block volumes.

Block Volume

Block size, determined from joint spacing, orientation, number of joint sets, and persistence, is important for rock mass quality.
When three or more joint sets are present, block volume can be calculated as:
$Vb = s1 s2 s3 \sin \gamma1 \sin \gamma2 \sin \gamma_3$
Where $si$ and $\gammai$ are joint spacing and angles between joint sets.
For practical purposes, the block volume can be approximated as:
$Vb = s1 s2 s3$
When irregular jointing is encountered, block volume can be measured in the field.
Other methods using RQD, volumetric joint count $J_V$ , and weighted joint density can also be used.
If joints are not persistent (rock bridges exist), apparent block volume should be larger.
Joint persistence is considered in the GSI system by the block interlocking description.
A joint persistence factor quantifies the degree of interlocking.
If $si$ and $\%li$ are average joint spacing and accumulated joint length of set $i$ in the sampling plane, and $L$ is the characteristic length, then:

$pi = \frac{\%li}{L} \begin{cases} \%li \le L \ 1 \quad \%li > L \end{cases}$

The equivalent spacing for continuous joint has to be found to use Eq. (8) to calculate the block volume.
Based on the consideration that short joints are insignificant to the stability of the underground excavation with a larger span, or are insignificant to the rock mass properties with a longer characteristic length, the equivalent spacing for discontinuous joints is defined as:
$s'i = si \sqrt[3]{p_i}$
The equivalent block volume is expressed as:

$Vb = s1 s2 s3 \sqrt[3]{p1p2p3} \sin \gamma1 \sin \gamma2 \sin \gamma3$

Example: For three orthogonal joints with characteristic length 10 m and average joint length 2 m, $Vb = 5Vb^0$ , meaning the equivalent volume is 5 times larger.

Joint Condition Factor

The GSI system defines joint surface condition by roughness, weathering, and infilling.
A joint condition factor, similar to Palmstrøm's factor, quantifies the joint surface condition:

$JC = \frac{JW JS}{JA}$
Where
* $JW$ is large-scale waviness (meters from 1 to 10 m) * $JS$ is small-scale smoothness (centimeters from 1 to 20 cm)
* $J_A$ is the joint alteration factor

Ratings from the Q-system and RMi-system are adopted for $JW$ , $JS$ , and $J_A$ .
Waviness is measured by undulation (percentage); both large and small-scale roughness are estimated by asperity amplitude $a$ .
The joint alteration factor has the most impact on the joint condition factor.

Examples

The values of GSI predicted from the GSI chart fit the ones back-calculated from other systems well.
Cases 1 and 2 stem from the thesis of Palmstrøm, Cases 3 and 4 from underground mapping of two mine sites in Canada, and Case 5 is from the well-known Gjovik Olympic Hall, Norway.
There are situations that may render the quantified approach difficult to be applied; For example, in rock masses that are disintegrated, foliated, or sheared.
The quantitative system helps less experienced engineers arrive at consistent ratings.
The block volume spectrum ranges from 1 m3 to 1 dm3 for rock masses, and for rocks, from 1000 to o1 cm3.

Application

The quantitative GSI chart estimates mechanical properties at two cavern sites in Japan.
The quantitative approach allows consideration of strength and deformation parameter variability, compared to in situ test data.

Kannagawa Site

Kannagawa pumped hydropower project is under construction with a maximum output of 2700 MW.
The powerhouse cavern at 500 m depth measures 33 m wide, 52 m high, and 216 m long.
Excavation began in 1998 and finished in 2000.
The rock mass consists of conglomerate, sandstone, and mudstone, classified into five groups.
The Geological Strength Index (GSI) system characterizes the rock masses, using lab tests results and field mapping data.
The Point Estimate Method (PEM) represents the variability of rock mass properties.
PEM evaluates the model at discrete points, and computes the mean and variance of predictions.
Sixty-four uniaxial compressive tests were conducted (data for CG1, CG2, FS1, M1 shown), with $m_i$ estimated from triaxial tests.
Joint frequencies in zones CG1 and CG2 are 0.74 and 0.85 joint/m, respectively. The average joint frequency is 1.1 joint/min FS1 zone, and 3.7 joint/min M1 zone.
Block size is estimated from $V_b = b((\frac{115 - RQD}{3.3}))^3$ , where RQD is calculated from joint frequency.
During the site visit to Kannagawa powerhouse construction site, the joint conditions were rated.
In CG1 zone, the joints are stepped on a large scale and rough on a small scale with no weathering; in CG2, FS1/FS2 and M1 zones, the joints are moderately undulated with slightly rough surfaces and have no alteration; joints in M1 zone are moderately altered.
Based on the PEM and using the GSI chart, the average and standard deviation of GSI is obtained using two variables $Vb$ and $JC$ .
The resulting coefficients of variation of GSI are in the range of 2–3.2%.
Equivalent Mohr–Coulomb parameters and elastic modulus averages and standard deviations are calculated based on $\sigmac$ , $mi$ and GSI.
Test data from 21 in situ block shear tests and 29 plate-load tests are shown.

Kazunogawa Site

Kazunogawa power station has a capacity of 1600 MW.
The rock mass consists of sandstone and composite rock of sandstone and mudstone.
75 uniaxial compressive tests were conducted . Three joint sets were observed, with spacing in the range of 1–20 cm.
Joint spacing usually follows a negative exponential distribution.
Based on the PEM and using the GSI chart, the average and standard deviation of GSI are obtained.
The coefficients of variation of GSI for CH and CM rock masses are 4.1% and 3.5%, respectively.
The results for the two rock types are presented along with c and f determined from 12 in situ block shear tests and deformation moduli determined from 29 in situ plate- load tests.

Discussion Of Results

In situ tests can be used to verify the GSI prediction or the observational method will be required to confirm the GSI predictions.
The joint surface condition factor and the block volume are proposed as inputs to determine the GSI value.
It is shown that the variability of inherent parameters can be explicitly considered in the calculation process to estimate c, f, and E.

Conclusion:

The GSI system is a universal rock mass classification system linked to Mohr–Coulomb and Hoek–Brown parameters.
It is particularly useful in the design phase where information is limited.
By incorporating block volume and joint condition factors a supplementary approach is proposed to add quantitative measures to the GSI system.
It represents the quantification of the original qualitative system.
Hence, the quantitative approach added to the GSI system provides a means for consistent rock mass characterization and thus improves the utility of the GSI system.