Basics of Rock Mechanics

This module is intended to provide a basic understanding of the engineering principles used in the analysis of rock materials when these materials are intended to be used for an engineering purpose.  These principles form the foundation of the science of rock mechanics and have been widely adopted and used.  At the introductory level provided here, the applicability of these principles should be easily grasped by each  student. 

These notes are, in part, from my course Geology for Engineers, GeoE 221, a first-level course in geology.  The course is presented as a systematic study of Earth and how natural geologic processes are applied in engineering practice.  This course is a freshman-level Geological Engineering course but is also taken by students of all grades from other disciplines such as Civil and Environmental Engineering and Mechanical Engineering.

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Part I

I. Rock Basics

A. Engineering Uses:  Rock is used for engineering purposes in 2 primary ways: 1. as a building material:  items such as cut stones, beams, support columns, decorative panels, etc.  Each student can envision examples where rock has been used in one of these ways.
2. as a foundation:  For example, on Manhattan Island, the skyscapers are founded on granite.  In Central Park, just a short distance to the south, there are no buildings over a few stories.  Why?  The bedrock under the Park consists of marine shale and metamorphic rocks that will not support the weight of a skyscraper.Thus, knowing and understanding basic rock properties will allow structures to be founded correctly so the required support will be there.
B. Rock Measurements:  the physical characteristics of a rock mass are a fundamental geologic property and are extremely important to engineers.  Analytical data on theses characteristics are generally derived in 2 ways:
1. laboratory measures:  are generally referred to as 'rock properties' and are acquired using small samples taken from the field site and analyzed in a laboratory setting.
2. field-scale measures:  most often referred to as 'rock mass properties' and are descriptions of the bulk strength properties of the rock mass.  The nature of these properties are governed primarily by 'discontinuities', or planes of weakness, that are present in the rock mass.  Examples of discontinuities are fractures, bedding planes, faults, etc.  The measured distance between fractures, bedding planes, and other structural features are also important when collecting field-scale data.C. Definitions:  From an engineering standpoint, there is a difference between a rock and a stone.  There is also a difference between soil and dirt.  'Rock' is used to denote the mass of material in-situ, it is a part of the bedrock and has not been moved or disturbed.  'Stone' is used to denote rock material that has been removed from its bedrock location.  In the same way, 'soil' refers to that material naturally in place and 'dirt' is most often used to define soil that has been removed and is, or has, been transported.

II. Rock Properties

Not all rock is the same and it must be treated differently in an engineering project.  There are 3 fundamental processes which form rock, igneous, metamorphic, and sedimentary processes.  Each of these basic rock types have inherent structural characteristics that define it strength and durability, and hence, its usefulness in an engineering situation.  It is strongly suggested that the student not familiar with these basic rock types review a basic Physical Geology textbook, or better yet, enroll in a fundamental geology course with a laboratory.

It is very important to assess some basic properties of rock before it is used as a building or founding material.  Some of the more important properties of rocks are:

A. Specific Gravity:  this term describes the weight of a volume of rock with respect to an equal volume of water, which weighs 1.0 gm/cm³. By weighing equal volumes of water and different rocks, a 'specific gravity' (SG) for that rock can be determined.  These experiments are conducted in a controlled laboratory using very specific guidelines so there are no unexpected variations.  After such work has been performed, typical SG's for common rock types are:
Shale: ~2.75
Granite: ~2.65
Sandstone: ~2.2
Basalt: ~2.65
Marble: ~2.7
Limestone: ~2.45
Steel: 7.85
Gold: ~14The meaning of the SG is that it represents the factor increase in weight of the rock per unit volume over the same unit volume of water.  For example, if the unit weight of water happened to be 750 gm, the the weight of an equal volume of shale would be about 2.75 x 750, or 2060 gm.  Specific gravity is reported as a dimensionless number.
B. Mass Density:  this is derived by multiplying the specific gravity by the density of water, specified as 1000 kg/m³.  So, for the above examples, the mass densities would be:

Shale: 2.75 x 1000 kg/m³ = 2750 kg/m³
Granite: 2.65 x 1000 kg/m³ = 2650 kg/m³
Sandstone: 2.2 x 1000 kg/m³ = 2200 kg/m³
Basalt: 2.65 x 1000 kg/m³ = 2650 kg/m³
Marble: 2.7 x 1000 kg/m³ = 2700 kg/m³
Limestone: 2.45 x 1000 kg/m³ = 2450 kg/m³
Steel: 7.85 x 1000 kg/m³ = 7850 kg/m³
Gold: 14 x 1000 kg/m³ = 14,000 kg/m³C. Unit Weight:  in construction situations in the US, it is often desirable to describe all materials as a 'unit' weight.  It is essentially the same as the mass density except it is calculated in English units, not metric, and so the standard reference unit is 1.0 ft³.  Again, this measure is made in relation to water which weights 62.4 lb/ft³.  So, the unit weight of the above samples are:

Shale: 2.75 x 62.4 lb/ft³ = 172 lb/ft³
Granite: 2.65 x 62.4 lb/ft³ = 165 lb/ft³
Sandstone: 2.2 x 62.4 lb/ft³ = 137 lb/ft³
Basalt: 2.65 x 62.4 lb/ft³ = 165 lb/ft³
Marble: 2.7 x 62.4 lb/ft³ = 168 lb/ft³
Limestone: 2.45 x 62.4 lb/ft³ = 153 lb/ft³
Steel: 7.85 x 62.4 lb/ft³ = 490 lb/ft³
Gold: 14 x 62.4 lb/ft³ =874 lb/ft³D. Rock Strength:  is a measure of the strength of a rock mass when subjected to any one or a combination of three primary forces:

1. Compressive Stress:  this stress consists of two opposing forces acting on a rock which decreases the volume of the rock per unit area.
'Compressive strength' is the maximum force that can be applied to a rock sample without breaking it.  Units of stress are either reported in pounds per square inch (psi in English units) or Newtons per square meter (N/m² in metric units).  1.0 Newton is equal to 1.0 Kg-m/s² and is derived by multiplying the mass by the gravity force, 9.81m/s².
Using this method, the force on the bottom of a 1.0 m³ block of granite due to gravity is:

2.65 x 1000 kg/m³ = 2600 kg (this is the mass of the block)
We know that F = ma, so F = (2600 kg) x (9.81 m/s²) = 2.55 x 10⁴ kg-m/s², or 2.55 x 10⁴ NThis resulting force is acting on the total area at the bottom of the block, which is 1.0 m², so the total force exerted by the 1.0 m³ block of granite is 2.55 x 10⁴ N/m².           Metric units of stress are equal to Pascals (Pa), which are units of pressure.  The equality is: 1.0 N/m² = 1.0 Pa.

Compressive strength is derived by dividing the force over the area upon which it acts and is specified as the Greek letter s.  The stress formula is given as:

s = P/A,  where P is the engineering way of expressing force, F.For example, we wish to determine the compressive force on a 6.0 m³ (1m wide, 1m deep, 6m high) block of granite that has an applied load (force) of 2000 KN. Does this load exceed the compressive strength for granite?

Solution: Using the above formula, we find the stress on the block as force divided by area:
s = P/A = 2,000,000 N / 1.0 m² = 2,000,000 N/m² which is well below the compressive strength of granite which ranges upward from about 200 x 10⁶ N/m².2. Tensile Strength:  rocks placed in tension will show a decrease in the total volume of the rock per unit area due to forces directed outward, opposite in action.

Tensile strength for a rock is usually much lower than its compressive strength, i.e., rocks are most likely to fail under tension well before they would fail under compression.  Thus, it is very important to know the stress regime a rock will be subjected to when used in an engineering project.  Most rock materials are never placed in a situation where tension is the primary force.
3. Shear Strength:  shearing action is caused by two forces acting in opposite directions along a plane of weakness (fracture, fault, bedding plane, etc.) that is inclined at some angle to the forces. The result is a force couple which effectively tears the material.

Rifting in tectonic environment is nothing more than a large shearing of the solid crust of the Earth where the actual rift itself is usually inclined at about 30^o to the tension forces.  In the case of rifting, tension is generally supplied by the upwelling of mantle material below the crust.  The US Geological Survey has a web site demonstrating tectonic principles at this site.

E. Elasticity:  this property describes the ability of rock material to rebound to its original shape after an applied stress is relieved, or removed.  While under stress, rock material often deformes and when the load is removed, it is possible that not all of the deformation will, or can be, restored, particularly when the load was excessively heavy.  There are 2 ranges used to describe deformation of the rock:

1. elastic deformation:  occurs when all of the deformation caused by the stress is restored upon its release.2. plastic deformation:  when stress that is below a critical threshold value is released, all of the deformation is restored.  However, if the applied stress exceeds the threshold value (which differs for various materials and rock types), permanent deformation results due to the load.  This means that when the load is removed, there is a permanent alteration to the original shape of the rock or material.  This may, or may not, be a critical concern in an engineering project.F. Strain:  is a property that is somewhat related to elasticity.  Materials that are subjected to a load, whether it be compressive, tensile, or shear, will deform and either stretch or shrink in length.  This action is referred to as 'strain' and is described mathematically as:

e = DL/L,  where L is length and DL is the change in length.This is a dimensionless number.  It is usually spoken as "...the strain on the marble column was determined to be 0.001 mm per mm."  It is a length divided by a length which is dimensionless.

The ratio between stress and strain is referred to as the 'Modulus of Elasticity', or Young's Modulus and is denoted as E.  Mathematically:

E = P/A   =  s
      DL/L     eThe last rock strength parameter we will explore is a property that describes the amount of lateral extension (strain) of a material that is under a vertical (axial) strain:

lateral strain   =   DB/B
axial strain          DL/Lwhere B is in terms of lateral dimensions.  This ratio is designated m, or 'Poisson's ratio'.  m varies in natural rock from between 0.1 to 0.5.  One example of the use of Poisson's ratio is in the analysis of the propagation of an energy wave generated by an earthquake.  This wave moves through solid rock and is, therefore, somewhat subjected to rock properties.  The speed of propagation, or wave velocity, is dependent upon the Poisson's ratio of the rock.  As rock type changes, wave velocity changes as a function of rock properties.

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Web Links

A companion page on Merlot that discusses basics soil mechanicsThe American Rock Mechanics Association, ARMA
The International Society of Rock Mechanics, ISRM

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 Content from http://webpages.sdsmt.edu/~lstetler/merlot/rock_mechanics.htm

The General Geology and Structures in Nepalese Himalaya

About 40 million years ago the Indian Plate came in contact with the Eurasian Plate. Before that there was a sea in between the two plates which is called the Tehtys Sea, when the two continents got closer and closer the sea retarded and the land mass got lifted up. After the contact the Indian Plate started getting subducted under the Eurasian Plate, since the Indian Plate was much lighter than the Eurasian Plate so it did not get sinked into the mantle. Since then this subduction and thrusting has become a continuous process. The Himalaya was formed around 2 million years ago. The rocks of Himalaya are thrusting upward about 2 to 5 mm per year and horizontally southward. It ranges about 2400 km from Punjab Himalaya in the west to Aarnanchal Himalaya in the east. Nepal lies in the central region of this Himalaya range. Since the formation of these Himalayan range is comparatively younger than geology of other continents so the rock are generally younger than on other parts of the world and are relatively weaker and more unstable.

The continuous process of collision of two plates has resulted in many thrusts and faults in Himalaya region and these thrust and fault separate Nepal in different zones. These zones and the thrusts that separate them are:

      1.       Indo Gangetic Zone / Terai Zone

Separated by Main Frontal Thrust (MFT)

      2.       Siwalik Zone

Separated by Main Boundary Thrust (MBT)

      3.       Lesser Himalaya Zone

Separated by Main Central Thrust (MCT)

      4.       Higher Himalaya Zone

Separated by South Tibetian Detachment System (STDS)

      5.       Tibetian Tethys Zone

Separated from the Eurasian Plate by Indus-Tsangpo Suture Zone (ITS)

  1.       Indo Gangetic Plain / Terai Zone

It lies in the southern most part of Nepal and is separated from the Siwalik Zone by Main Frontal Thrust (MFT) or also called Himalayan Frontal Thrust. The Terai region gradually rises from 100m in South to 200m in North. It mostly contains alluvial deposit (in average about 1500 m). It contains alluvium from Pleistocene era to recent time. It lies continuously from west to east except along Nepal India border at Chitwan and Rapti Valley where it coincides with the Siwalik Zone This zone is also further divided into three zones namely Bhabar Zone, Middle Terai or Marshy Zone and Southern Zone.

a.       Bhabar Zone

It is well developed around the mouth of major rivers whereas in other parts it is filled with debris derived from the Churia Hills.

b.      Middle Terai or Marshy Zone

It consists of flat land with marshy nature and there exists artesian nature. The alluvium deposit can be found from gravel, pebble, cobble, sand to yellow clay deposits.

c.       Southern Zone

The sediment deposits get finer as it moves southwards. It consists of fine sands, silts and clays.

  2.       Siwalik Zone

The Siwalik Zone lies just north of the Indo-Gangetic Plain and lies on the foot hill of Lesser Himalaya. It is bounded by MFT in the south and MBT to the north. Physiographic units Chure Pahad and Dun valleys lie in this zone. The sediments in this region was transported by rivers and accumulated due to uplift and denudation of the Himalaya. It is generally covered with thick forest and youngest sedimentary rock in the range. Sediments found are usually mudstone, sandstone, conglomerate usually getting coarse upwards. The age of sediments ranges from Middle Miocene to Early Pleistocene era (about 1-16 million years). It can be sub-divided into three regions Lower Siwalik, Middle Siwalik and Upper Siwalik.

a.       Lower Siwalik

It generally consists of interbedded fine grained mudstone and sandstone. The proportion of mudstone is larger than sandstone. Sediments are derived from the Thethys zone and Lesser Himalaya Zone in this region and were deposited by meandering action of river system which used to flow from north-east to south-west direction at that time. The age of this region is from Middle Miocene to Early Pliocene era (about 16-10 million years).

b.      Middle Siwalik

Rocks in this region are usually coarser, thick interbedded sandstone and mudstone with larger proportion of sandstone. These rocks have acquired the nickname "pepper and salt". The sediments in this region were derived from Higher Himalaya region and deposited by braided river system which was flowing from North to South Direction. It age ranges from Early Pliocene to Late Pliocene era (about 10-3 million years).

c.       Upper Siwalik

It is usually characterized by very coarse grained rocks like cobble and pebble conglomerate with lenses of mud and sand. Sediments were also deposited by braided river system which was also flowing from North to South Direction as in Middle Siwalik. The sediments were derived from Lesser Himalaya as well as from Siwalik itself. It ages from Early Pleistocene to Late Pleistocene (about 3-1 million years).

  3.       Lesser Himalaya Zone

The Lesser Himalaya is bounded by MBT in the south and MCT in the north. The three physiographic units The Mahabharat Range, Midlands and frontal parts or southern parts of the Fore Himalaya belong to this zone. This zone is made mostly of sedimentary rocks and metamorphic rocks like Shale, Sandstone, Limestone, Dolomite, Slate, Phyllite, Schist, Gneiss, Amphibolites, Quartzite, Marble. The rocks in this region are highly folded and faulted and have resulted in complex structures. Its age range is from Precambrian to Oligocene era.

  4.       Higher Himalaya Zone

The Higher Himalaya Zone is bounded by MCT to south and STDS to north. This region has extremely rugged terrain with very stiff slopes and deep cut valleys. Generally all terrain level above 5000m from sea level can be considered Higher Himalaya Zone. The world's tallest peak lies in this zone, the Mount Everest but, not only the tallest but also highest number of peaks above 8000m lie in this range. Rocks found in this region are high grade metamorphic rocks, which are in succession of 10-12 km, these rocks are gneissies, migmatites, schist, quartzite, marble, etc.

  5.       Tibetian Thetys Zone

This zone lies north of the Higher Himalaya Zone and is bounded by the STDS in south and separated by Indus-Tsangpo Suture Zone (ITS) in north from the Eurasian plate. This zone is composed of sedimentary rocks such as shale, limestone and sandstones aging from Cambrian to Cretaceous.  The rocks are highly fossiliferous. In Nepali places like Manang, Mustang and Dolpa are name "Himal Pari Ko Gaun" (i.e. Villages across the Himalaya) since they lie north of the Himalayan range.

The main structures that are present in Nepalese Himalaya are these thrust zones, namely Main Frontal Thrust (MFT), Main Boundary Thrust (MBT), Main Central Thrust (MCT), South Tibetian Detachment System (STDS) and Indus-Tsangpo Suture Zone (ITS). The locations of these thrust zones are also explained above paragraphs and schematic diagram is given below showing different geologic zones of Nepal and Thrust Zones separating them.

Thrusts are not lines but are weakness plane. When the Indian Plate collided with the Eurasian Plate these thrusts were formed and since Indian Plate is still getting sub-ducted into the Eurasian Plate it is believed that still more thrusts are being created in the southern direction. The rocks in these thrust zones are highly fracture or crushed. The geodetic measurement has shown that MBT is quite active nowadays. This movement along the MBT appears obvious due to geomorphic features like pressure ridges.

Significance in Geotechnical Engineering

The knowledge of these zones and structures are very important for a geotechnical engineer. Since characteristics of certain zone can be favorable for certain purpose while unfavorable for other. Like the Terai Zone is favorable for land use like cultivation and settlement, the Siwalik Zone may be favorable for quarry site for gravel and stone. Considering these diversity even the design specification for hill and terai (plain) is different for infrastructures such as road and irrigation. Structures present in the rocks are also very important for locating construction site for the proposed structure. Geological Structures that are commonly found in Nepalese Himalaya are:

      ·         Folds

      ·         Active Faults and Thrusts

      ·         Joint, Cracks and Fractures

      ·         Orientation and characteristics of the Bedding and Foliation Plane

Almost all of these structures are unfavorable for construction of infrastructure although orientations of some of them are favorable. Folds are sometime regional and sometime local in range of scale. Local folds are more risk than regional ones so care should be adopted when construction has to be done on them. Active faults and thrusts should be avoided while finding the location for construction of structure as they have low bearing strength and rocks underneath them are highly crushed and fractured. Joints cracks and fractures also present problem during construction. They pose problem of stability and also of seepage during construction of dams and reservoirs, so should be avoided as far as possible or should be treated when option of avoiding is not available. Orientation and characteristics of bedding plane and foliation plane plays major role in the hill slope stability and during alignment of tunnels. It is one of the major factors that govern the alignment of the tunnel. These planes are sometimes considered favorable and sometimes unfavorable due to their orientation.

Geosynthetics

Overview of Geosynthetics

1.1 Introduction
1.2 Historical Development
1.3 Types of Geosynthetics

1.1 Introduction

The application of geosynthetics in different civil engineering constructions like road construction, hydraulic construction, playgrounds, land fill and even in building construction is gradually increasing to solve different geotechnical problems as shown in Figure 1.1.




















Figure 1.1: Application of geosynthetics in civil engineering works

1.2 Historical Development

The application of different natural materials for the reinforcement of soft soil like tree trunks, branches, straw, grass etc has been started from prehistoric time. This technology was also used in the construction of Great Wall of China (see Figure 1.2). This technology is still using to stabilize soft soils.

Figure 1.2: Soil reinforcement technology used in Great Wall of China.

The major achievement in geotechnical engineering was taken place when the natural reinforcing materials could be replaced by similar quality and cost effective artificial synthetic material. The following graphs show the boom of market of geosynthetics immediately after its development.

Figure 1.3: Estimated geosynthetics market in North America

1.3 Types and functions of Geosynthetics

Geosynthetics are the flat synthetics structures developed with different properties as per the requirement of different geotechnical works. Basically there are five types of Geosynthetics:
a) Geotextiles b) Geomembranes c) Georids

Figure 1.4: Types of Geosynthetics

d) Geonets e) Geocomposites
a) Geotextiles are basically textiles in traditional sense made from synthetic fibers. So this material is flexible, porous in nature and bio-undegradable. The main point is they are porous to water flow across their manufactured plane and also within their plane in wide variety. There are at least 80 specific application areas for geotextiles that have been developed to fulfill following major functions:
1. Separation
2. Reinforcement
3. Filtration
4. Drainage
5. Moisture barrier (when impregnated)
b) Geomembranes: This is an impervious thin sheet of rubber or plastic material used primarily for linings and covers of liquid or solid storage facilities. This is the second largest group of geosynthetics. The primary function of geomembranes is always as a liquid or vapour barrier. At least for 30 individual applications have been developed in civil engineering works.
c) Geogrids: These are plastic formed into a very open, grid like configuration with large apertures.
Often these are stretched into one or two directions for improved physical properties. By themselves, there are at least 25 application areas of geogrids, and they function in two ways: separation and reinforcement.
d) Geonets: Geonets are usually formed by continuous extrusion of polymeric ribs at acute angles to one another. When the ribs are opened, relatively large apertures are formed in a netlike configuration. The main function of this material is drainage in along the manufacturing direction.
e) Geocomposites: There are varieties of combinations of geotextiles and geogrids, geotextiles and geonets, geogrids and geomembrannes etc according to the special functions to be fulfilled in the site.

Functions of Geosynthetics: The primary and secondary functions of geosynthetics are presented in

Table 1.1.

Table 1.1: Functions of geosynthetics

Functions	Separation	Filtration	Drainage	Reinforcement	Protection	Sealing
Geotextiles	P	P	S	S	P	S
Geomembrannes	S			S		P
Geogrids				P
Geonets			P		S
Geocomposites			P		S	S
P-Primary S-Secondary

Geosynthetics Lecture Notes by S.P. Joshi (IOE, Nepal)

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