Design Techniques in Rock and Soil Engineering

At the initial stage of tunnel design, the tunnel stability can be assessed by different design techniques which are broadly classified into three categories i.e. Mathematical Analysis, Empirical Methods and Numerical Analysis. Mathematical methods or closed form solutions are more precise methods; however, its use is limited to simple geometries and almost impossible for complex geometries due to complex and tedious calculations involved. In practice, Empirical and Numerical Methods are usually used for stability analysis of tunnels. It should be noted that it is not the replacement of final design. Empirical design methods use information about the structural geology and other rock mass properties as input that can be easily obtained at the initial stage of a project. Numerical Methods commonly require mechanical properties, especially strength and deformation of rocks. Numerical methods are also considered as precise due to provision of allowance for variable inputs and geometry and having ability for sensitivity analysis. It is good practice to evaluate the stability of tunnels using at least two Empirical methods and validated through Numerical methods.


Introduction
The process of engineering design comprises of devising a scheme/module, or process to achieve the required goal or target. It can also be defined as an assessment -making procedure, which utilized the knowledge of basic sciences, mathematics and engineering sciences to convert resources optimally to meet quantified objectives. In other words, engineering design is the procedure of formulating framework, segment, or procedure to address desired problems [1]. General goal of engineering design is to develop a solution (the design) to a known problem. However, there is no single solution, and depends upon the approach used by different engineers resulting different solution. Among the solution obtained some will work well than others, but it is necessary that all solutions should 'work'. The reason behind the fact that solutions to engineering design problem are not unique is perhaps due to very broader spectrum of the concerns encountered in design [2].

The design process
Each and every engineering problem/task passes through a design process. According to Hill (1983), as discussed by Biniawski (1988), the design process is: a) logical development of design inside organization of actions and b) a work plan process for planning the design program. For satisfactory design results, a define process can work as agenda of activities. The defined process or methodology can be considered as a form of quality control that ensures that all aspects that should be considered in the design are considered [2]. Response to a complex engineering problem does not shortly seem in a vacuum. Well-meaning description of engineering problem needs exercise or approach. Design processes generally depend upon the number of engineers analyzing design. The process described here is general, and one can adapt it to the problem, they are trying to solve [3]. Following are the different stages of design process [1] illustrated in

Recognition of need or a problem
Engineering design activity always occurs in response to a human need [3]. Before attempting any solution for design, the presence and nature of a problem must be. This is not an easy task. It needs the rather rare skill of inquiring the right kind of question and call for a clear identification of the problem to be solved. In design it involves the recognition of a genuine social need want or opportunity.

Statement of the problem
If there is any problem involves, it is then necessary to clearly define it. This may involve a list of specification or criteria. These must be stated clearly and concisely. A poorly recognized and expressed problem cannot be anticipated to result in a good solution. In rock mechanics design, this means to set design objectives in terms of economy, safety and stability.

Collection of information
This stage comprises the collecting, investigation, processing and analyzing of information to obtain the explicit nature of the targeted problem. In rock engineering collection of information include site investigations, conducting in-situ and laboratory tests to determine the characteristics of the rock strata and assessment of applied loads and field stresses.

Analysis of solution component
The selection of approach to either search for the most promising method of solution or certain hypothesis is selected or conceived depends upon the nature of the problem. Design approaches at this phase involve numerical analysis and mathematical, physical modal studies, observation and monitoring or the empirical analyses based on experience.

Synthesis to create a detailed solution
On the basis of analysis of the individual solution component, all design is focused to furnish comprehensive alternative solutions. In this phase of design, calculations, specifications, performance predictions, cost estimates, scheduling procedures and the experimentation are involved.

Evaluation of ideas and solutions
In this phase the solution is interpreted and compare with the original hypothesis, specification, facts assumptions, requirements or constraints. This demand for a clear understanding of the all relevant interacting factors that's needed for the engineering judgments. The solution for engineering problems should be balanced involving all the factors with interact.

Optimization
Optimization is the assortment of a best solution (with regard to some criteria) from some set of available alternative solutions [4]. There are always multiple solutions available to any engineering problem. Refinement and modification of a solution may then be required to reach a practicable agreement between the generally contradictory constraint and assets. The effectiveness of an optimization process mostly depends upon simplicity and clarity with which problem and solution are specified.

Recommendation
Recommendation is the principle of the whole Engineering design process. It provides a refined endorsement of the solution to problem, point out limitations and shows the trend to be followed in applying the solution.

Communication
The conclusive aim of the all design stages is the creation or instigation of a progression accomplishment. In order to achieve the objective requires the engineer must communicate the finding effectively. Effective communication means that all relevant aspects should be appropriately presented. If a mathematician were to sum up these thoughts, he might well do so by the Eq. (1).
Where, E means effectiveness of the subject, M mean the mastery of the subject matter and C means the communication.
So for effective communication one should have sound knowledge of the subject matter and good communication skills. The design engineer must have the capability to communicate views and ideas concisely and clearly and to convey technical knowledge effectively.

Implementation
This is the final stage of design procedures. The finding or results communicated are applied under the given circumstance and proper monitoring is carried out for further refining the result or design that has been recommended for action. The main objective of the design is to ensure that a desire goal and quality will achieved within the time frame and the budget allocated.

Feed back
After implementation of the design, its performance is monitored and recorded. Remedial measurements are suggested for more improvement of the performance the solution design.

Design techniques in soil and rock engineering
There are different significant design techniques in rock engineering. They are classified into three groups which are Analytical, Empirical and Observational. Rock masses having more complex in nature. Due to the very complex nature of rock masses and the difficulties encountered with their characterization, the analytical approach is the least used in the present engineering practice. Due to this reason, it does not lie in the analytical techniques themselves, since some have been developed to a high degree of sophistication, but in the inability to furnish the necessary input data as the ground conditions are adequately explored. Consequently, such analytical techniques as the finite element method, the boundary element method, closed form mathematical solutions, photo-elasticity or analogue simulation are mainly useful for assessing the influence of the various parameters or processes and for comparing alternative design schemes; they are the methods of the future not as yet acceptable as the practical engineering means for the design of rock tunnels [5]. Empirical methods of design are commonly applied as these are built on earlier practices derived from creation of rock structures owning alike physical characteristics [6]. It is a good practice to evaluate the stability of tunnels using at least two Empirical methods and validate through Numerical methods. Therefore, these two groups of tunnel design methods will be discussed in detail [7].

Empirical methods of design
The empirical approach relates the experience encountered at previous projects to the conditions anticipated at a proposed site. If an empirical design is backed by a systematic approach to ground classification, it can effectively utilize the valuable practical experience gained at many projects, which is so helpful to exercising one's engineering judgment. This is particularly important since, a good engineering design is a balanced design in which all the factors which interact, even those which cannot be quantified, are taken into account; the responsibility of the design engineers is not to compute accurately but to judge soundly. Rock mass classifications, which the main part of the empirical design methods, are extensively used tunnels within rock. At present, most of the tunnels excavated in the United States make use of some classification system. Terzaghi classification which was presented over 40 years ago is the most broadly used. In fact, rock mass classifications have been successfully applied throughout the world [5].
The empirical methods of design may be used in association with other engineering assessment and design Techniques [6]. These methods are very essential and beneficial for the design in the earlier stages of the project, when minimum evidence about the behavior of rock mass, stress conditions and hydrological characteristics are obtainable [8].

Rock mass classification systems
Rock mass classification is a tool for the assessment of the rock behavior and performance based on the essential inherent and structural parameters [9]. Rock mass classification systems are the most and widely used empirical methods of design Different rock mass classification systems are RMR, Q-System, RQD, RSR, GSI etc. [6]. Rocks have been classified on the basis of origin, mineralogical compositions and distinct physical properties and ground condition. Rock Classification provides a mutual basis of communication to recognize rock mass in a category having same and well define characterization and basic input parameters for rock engineering design. For designing purposes in several attempts were made to classify rock based on rock and site characterization. Such simplified classification systems have served to understand the upper bound response of the rocks [10]. Rock mass classification systems effectively combined the results comes observation, experience and other engineering judgment for providing a quantitative evaluation of rock mass situations. Rock mass classification systems has the below mentioned purposes in tunneling design [5].

Terzaghi's rock mass classification
A well-known classification system for support of tunnels. This explanatory system was developed in the U.S.A in 1946. Terzaghi's (1946) formulate the first rational method of evaluating the rock loads suitable to the design of steel sets. This classification is appropriate for the estimating rock loads for steel arch supported tunnels. It is not so suitable for modern tunneling methods using shotcrete and rock bolts [5].
Terzaghi's classify rocks as under [11]: 1. Intact Rock: Rocks that's having no joints and cracks, it breaks crossways a sound rock or loose block may drops off the top for many hours and days due to blasting. It is called sapling condition.
Stratified rock: that rock composed those distinct sections having slightly or no confrontation to parting beside the margins stuck between the strata. In such rock the spalling condition is generally happened.

Moderately jointed rock:
That rock having joints and hair cracks, but the blocks among joints are locally developed collectively or so closely joined that perpendicular walls do not need on the sides support. In this type of rock, both spalling and popping conditions may be happened.
3. Blocky and seamy rock: Such rocks consist of chemically intact or almost intact rock fragments which are totally detached from each other and erroneously joined. In such rock, vertical walls may need sides support.

4.
Crushed rock: such rocks are chemically intact rock but have the characteristic of crusher outing. If maximum or completely all the fragments are as small as fine sand particles and no cementation has taken place, crushed rock below the water table demonstrate the properties of water-bearing sand.
5. Squeezing rock: Squeezing rock gradually progresses into the tunnel without noticeable increase in volume. An obligation for squeeze is a high percentage of microscopic and sub-microscopic elements of micaceous minerals or clay minerals with a low swelling capability.
6. Swelling rock: Such rock moves inside the tunnel mainly because of expansion. The capability to swell seems to be insufficient to those rocks that have clay minerals such as montmorillonite, with a high swelling capability.

Classifications containing stand-up time
Lauffer (1958) anticipated that stand up time for an excavation span is associated with the quality of rock mass in which the width is mined. The Unsupported span may be defined as the width of the tunnel or the distance between the face and the adjacent support, if such is grater that the tunnels width. Laufer's (1958) advanced classification has been improved by various researchers especially Pacher et al., (1974) and currently formulae the part of the worldwide tunneling attitude so called the New Austrian Tunneling Method (NTAM). The importance of the standup time is to increase in the tunnel width results in a substantial decrease in the period available for the fixing of support. The NATM comprises numerous systems for workable, safe and stable excavation in rock situations where the stand-up time is restricted before collapse occurred. These systems are:

Rock mass classification system
• The use of small headings and benching • The use of several small drifts to form a reinforced ring inside which the unpackaged of the tunnel can be mined As described by Terzaghi (1946), these practices are appropriate to apply in squeezing soft rock mass i.e. shale's, phyllites and mudstones. The practices are also appropriate when tunneling in exceptionally jointed rock, but needs excessive attention to apply these practices to underground excavations designed in hard rocks having dissimilar failure mechanisms. For hard rock excavation support design, it is practical to accept the assumption that the stability of the rock mass adjacent to the underground excavation is not time-dependent. A defined wedge visible in the roof of an excavation will fall as soon as after excavation. This can happen after blasting or during the succeeding scaling process. Early support is demanded do keep such a wedge in place, or to improve the limit of safety preferably before the rock supporting the full wedge is removed. On the other hand, in a highly stressed rock condition, failure will generally be induced by some change in the stress condition adjoining the excavation. The failure may occur gradually and apparent it as spalling or it may occur rapidly in the form of a rock burst. In either case, the support system design must take into account the modification in the stress condition rather than the 'stand-up' time of the excavation.

Rock quality designation index (RQD)
It is developed by Deere et al., (1967). Such system provides the quantities estimation of rock mass quality from the drill core logs. RQD is defined as the percentage sum of all intact core pieces having length more than 10 cm in the total length of the core provided that the core should be of NX size (54 mm in diameter). The precise practices for the estimation of the size of core portions and the approximation of Rock Quality Designation Index are summarized as shown in Figure 2 [11].
In 1982, Plastron suggested that when core is not available and discontinuity traces are visible in surface disclosure or exploratory adits, the RQD may be calculated from the number of discontinuities per unit volume. The suggested relationship is for clay free masses and is given below by Eq. (2).
Where, RQD is the Rock Quality Designation Index, J v is the number of all joints per unit length for all joint (discontinuity) sets, so called volumetric joint count.

Rock structure rating
Wickham et al. (1972) established another quantitatively rock mass classification system termed as Rock Structure Rating (RSR). RSR is used to describe and measure the quality of rock mass for selecting of appropriate support and reinforced system. Such classification system not applied generally as compared to other classification systems, but it has its important role in the emergent of other empirical classification schemes. Many investigators advised that for good, reliable and suitable results for planning of excavation more than one rock mass classification systems should be used at initial stage of the project. The significance of the rock structure rating, in the context of this conversation, is to bring forward the idea of assessment of each of the constituents recorded below to calculate a mathematical value of RSR = A + B + C.
Where, Factor A: Area Geology: It includes Common evaluation of geological structure based on: • Rock type Origin (sedimentary, metamorphic and igneous).
• Rock Hardness (it means hard, medium, soft and decomposed).
Factor B: Geometry of the geological structures: it consists of effect of disjointedness arrangement with consideration to the tunnel alignment on the basis of: • Joint spaces.
• Orientation of joints (dip and strike).
• Direction of tunnel drive.
Factor C: it includes influence of groundwater inrush and joint situation on the basis of: • Whole rock mass class based previous parameter combined (A and B).
• Situation of Joint (poor, fair and good).
The following tables are used for the calculation of RSR (maximum RSR is 100) [9] ( Tables 2-4 Table 2.
Rock structure rating, parameter a: General area geology [9].  The RSR value calculated for the above tables are then used for the calculation support system recommendation. The support recommendation chart for the RSR value is given in Figure 3.

Rock mass rating system (RMR system)
The rock mass rating system was produced by Biniawski in 1976; it is sometimes also called geo-mechanics classification system. It was developed taking into account the distinctive case histories in the field of structural designing This classification system was altered in 1974, 1976, 1979 and 1989, because of considering of more contextual analyses identified related to tunnels, mines, chambers, slopes and foundations [1]. The Geo-mechanics classification system has a widespread  Table 4. Rock structure rating, parameter C: Groundwater, joint condition [11].

11
Design While using this classification system, the rock masses are divided into a number of structural regions. Each region is classified independently [12]. These six parameters are being given different rating based on different geological and geotechnical condition as shown in Table 5.
Based on the overall rating of RMR calculated form above mentioned parameters support systems are being recommended for the project site. Support recommendation based on RMR value is given in Table 6.

Q-system
This system of rock mass classification was devised by Barton et al., (1979) in Norwegian Geotechnical Institute (NGI), explicitly for the design of tunnel established on 212 case histories. The rock mass classification system is generally used for tunnel design throughout the world and has been used in approximately 1260 various projects and considered as one of the best classification systems for design of tunnels (Kumar N., 2002). The extreme ratings of Q-System shows good quality of rock mass and the lowest ratings designate poor quality of rock mass. The minimum and maximum of Q-index ranges from 0.001 to 10000 on logarithmic scale. According to this classification system Q is the function of six independent parameters as defined by Eq. (3).
Where, RQD Rock Quality designation index, Jn shows joint set number, Jr shows number of joint roughness estimated for the set of joint that is most terrible and dangerous to alignment of tunnel, Ja show joint alteration number estimated for the most dangerous and unfavorable set of joint along the alignment of tunnel, Jw is joint water condition which shows the water reduction factor, Stress Reduction Factor, SRF is comprised to consider the consequence of in-situ stress condition on the whole quality of Rock. The following comments are offered by Barton et al. (1974) for explaining the meaning of the parameters used to decide the value of Q.
The first quotient RQD Jn demonstrating the organization of the rock mass, is a rough measure of the block size.  The second quotient Jr Ja communicates the unevenness and frictional features of the joint walls or infill materials. This measure is taken in favor of uneven, unchanged joints in direct interacted. The strength is reduced significantly in case where rock joints have coating of thin clay mineral and fillings. It defines the interblock shear strength of rock mass.

A. CLASSIFICATION PARAMETERS AND THEIR RATINGS
The third quotient Jw SRF incorporates two stress related parameters. SRF is a degree of 1) untying load when the excavation passes through clay bearing rock and shear zones, 2) rock stress when the excavation is within competent rock, and 3) squeezing loads in plastic weak rock masses. It is also as a total stress parameter. The Jw parameter is amount of water pressure, adversely affect the shear strength of joints as it reduces the effective normal stress. In addition, presence of water may create softening and ultimately the possibility of outwash when clay infill the joints. It generally shows the active stress component and that is determined empirically.     High professionalism is required for estimation of the values of parameter used in this system. The poor professional users may face trouble while approximating the score of the parameters and may approximate the lesser value for Q-System, which is considered the weakness of this classification system [14].
The  G Strongly over-consolidated, non-softening, clay mineral fillings (less than 5 mm Continuous thickness).

12-16°8
I Swilling clay fillings, i.e., montmorillonite (less than 5 mm continuous thickness).   Note: ii. For strongly anisotropic virgin stress field (if measured): when 5 ≤ σ1/σ3 ≤ 10 reduce σc to 0.8 σc, and σΘ to 0.8 σΘ, when σ1/σ3 > 10 reduce σc to 0.5 σc, and σΘ to 0.5 σΘ. iii. Few case records available where depth of crown below surface is less than span width Suggest SRF increase from 2.5 to 5 for such cases (see H).  Figure 4,is based on the Q-system ratings and equivalent dimension for the endorsement of permanent support system for underground excavations. This chart provides a   wide-ranging framework established on the empirical data that what kind of support system is recommended in case of rock bolt's center to center spacing and the thickness sprayed concrete, and also give the energy absorption of fiber strengthened sprayed concrete.

Geological strength index (GSI)
This classification system established and improved by Hoek and other researchers including the block size and its shear strength in order to estimate value of GSI quantitatively. The GSI index value for any rock mass is depend on the estimation techniques, expertise and reliability of these two input parameters. Sonmez and Ulusay developed the arithmetical basis for GSI value calculation and present quantitatively GSI chart as given in Figure 5 [16]. Further research were carried out for quantification of GSI value by (Cai, et al.,2004), they present the assessment method for block size, joint and joints wall condition for GSI value quantification.
GSI system should not be considered as the replacement for other classification systems like RMR and Q-System, as this system cannot recommend any support system for stability of rock mass. This system can only be used in estimation of rock mass properties and input parameters for numerical modeling [15]. The comprehensive practice for estimation of input parameters for numerical analysis of stress condition and the remedial measures is presented in Figure 5 (Hoek, 2013).
The GSI index may be estimated by subsequent various methods used for assessment of rock mass.
Method A: Using this method the GSI is estimated by skilled geologist or mining engineers from the data collected (observational data) at site and then the value of GSI is evaluated from chart [17]. Method B: In this method the GSI index is estimated by using other classification systems like RQD and RMR etc. when limited data is available. The GSI can be estimate from the well-known relationship presented by various researchers [17].
Method C: The sonmez and Ulusay considered structure rating (SR) and surface condition rating (SCR) for approximation of GSI value [17].
The Cai et al. (2004) used block volume (V b ) and joint surface condition factor (J c ) to approximation the GSI. The block volume having greater number of joint sets indicated as: where, S is joint spacing. The Jc defined by the roughness of joint, weathering and infilling, these are used to measure the joint surface condition factor by using the Eq. (6).
The V b and Jc are used to precisely quantify the GSI value [17]. The quantitative chart for estimation of GSI suggested by sonmez and Ulusay [1999] is shown in Figure 6.

Numerical methods of design
The empirical methods of design do not estimate accurately the reliability supports, redistribution of stresses, rock mass deformation [18]. These parameters are very important in designing and analysis of any excavation therefore, numerical Geological strength index chart [15].
analysis should be carried out for appropriate designing. The numerical methods are considered very useful to estimate the above parameters precisely and in minimum time as compared to other methods of design. Numerical methods used physical and strength properties of rock as input for analysis. For efficient and viable design the numerical and empirical methods are used in parallel [19][20][21][22][23].
Different researchers developed and present various numerical methods and models. These are divided into eight classes on the basis of four methods and two levels as shown in Figure 7 [24,25].

Numerical methods of modeling for rock/soil engineering
The numerical methods of design uses in rock/soil engineering are grouped into three classes for modeling in rock mechanics as discussed above.

Continuum methods
The different continuum methods of design are as under. Quantitative estimation of GSI chart [15].

Finite Difference Method (FDM).
The Finite difference method (FDM) is the direct calculation of PDEs and transmitted the creative PDEs in term of unknown at grid point into a system of algebraic equations by interchange the fractional derivatives with difference at irregular or regular grid forced over problem areas. This system is solved due to establishing the required initial and boundary condition. This method is old but widely applied in the numerical modeling in rock mechanics. This method is based for explicit approach of discreet element method (DEM) [26].

Finite Element Method (FEM).
The Finite element method (FEM) splits the problem into sub-elements of smaller sizes and shapes with fitting the number of nodes at the vertices and at the side of discretization. FEM is mostly used to estimate the behavior of PDEs at elemental level and for signifying the behavior of elements; it produces the local algebraic equation. After creating the local equation the FEM gathered it according to topographic relation of node and elements and further put it into worldwide system of algebraic equation for receiving the required information after establishing the definite initial and boundary situations.

Boundary Element Method (BEM).
The Boundary element method is the precise method then FEM and FDM because of its easiness. This method involves the discretization of solution areas at boundary and thus decreases the problem dimension by simplifying the design Division of numerical models and methods [24,25]. input parameters. This method computes separately the essential information in the solution domains from the information at the boundary, which is achieved by the solution of boundary integral equation rather than direct solution of PDEs [26].

Discontinuum methods
The different discontinuum methods of design are given below.

Finite element method (FEM)
This method of design was developed by Clough et al., (1950). Due to wide application of this method in mining engineering especially tunneling, it get more attention for solving mining problems and popularity in this field [19]. The FEM divide problem into small parts and connect these parts at a point/nodes at the apexes and at the boundaries of meshing/discretization. The FEM has many applications in modeling in rock engineering design due to dealing with nonlinearity, boundary conditions and heterogeneity problems [26,27].
The unidentified function over each element in FEM estimated through test function having its nodal values of anonymous system (in polynomial form). This practice is the fundamental supposition of FEM. For experimental function, it is mandatory to satisfy the principal of PDFs. In this research the FEM based software Phase2 was used for analysis of stresses and total displacement around tunnel. For experimental function it must be satisfied the principal of PDFs, which is given in Eq. (7).
Where, Nij is the shape function or interpolation function; this must be defined into inherent coordinates for use of Gaussian quadratic integration, M is the element order.
Using shape function the problem original PDFs can be substituted by the arithmetical equation as given below.

Relation between strain and displacement
For two dimensional element domain the relation between strain and displacement represent by Eq. (12) [28].

Relation between stress and strain
It may express as: Where, Δσ is the vector of stress components, Δε represents corresponding components of strains and DT is a square matrix that is constant in the elastic case.

Global stiffness matrix
It is formed when added the stiffness matrices of all elements. The equation for global stiffness is given as: Where. Δδ is unknown vector having increments of nodal displacement due to increment force ΔR.
For material linear elastic material behavior the equation may by write as (Scheldt, 2002).

Finite element based software's
Following are finite element based software's.
1. Displacement Analyzers Finite Element program (DIANA) software is developed by TNO Building and Construction Research, Netherlands. It is a flexible software and used in solving of linear and nonlinear structural engineering in 2D and 3D [28].
2. Phase2 developed by rock science for solving 2D non-linear problems like analysis of displacements and stresses around underground openings, in the field of mining and civil engineering [29].
3. ABAQUS software is developed by Hibbitt et al. (1978) in USA. It is used for linear and non-linear, problems and analyzes the stresses of any structure in 3D [28].
4. ANSYS software is developed for solving both linear and non-linear problems for isotropic and non-isotropic properties of materials [28].

Conclusion
Engineering design is the valuation using knowledge of basic sciences, mathematics and engineering sciences to convert resources optimally to meet quantified objectives. Its goal is to develop a solution to a known problem. There are different stages of design process; one can adapt it to the particular problem for solving it. We have variety of design techniques in rock engineering. They are classified in to three groups i.e. are Analytical, Empirical and Observational. Among, these empirical approaches can effectively be used for engineering judgment. Rock mass classification is one of the widely used empirical methods for the assessment of the rock mass behavior. The empirical methods of design do not estimate accurately the reliability of support systems, redistribution of stresses and rock mass deformation. Numerical methods are considered very useful to be used for estimate these parameters precisely and in short time as compared to other methods of design. So it is recommended that for efficient and viable design the numerical and empirical methods should be used in parallel for the assessment of soil/rock mass behavior to design any underground structure. diversion tunnel at Guledar dam site, turkey. Engineering Geology, 131-[