Geotechnical Fundamentals PDF

GEOTECHNICAL FUNDAMENTALS UNIT 1: Soil and Rock of the Earth 1.1 Introduction 1.2 Definitions of Key Terms 1.3 Focus Questions 1.4 Soil Formation 1.5 Deposition 1.6 Soil Profiles and Horizons 1.7 Mass-Volume Relationship 1.8 Q...

GEOTECHNICAL FUNDAMENTALS UNIT 1: Soil and Rock of the Earth 1.1 Introduction 1.2 Definitions of Key Terms 1.3 Focus Questions 1.4 Soil Formation 1.5 Deposition 1.6 Soil Profiles and Horizons 1.7 Mass-Volume Relationship 1.8 Questions 1.9 Web Pages Soil and Rock of the Earth 1 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS 1.1.1 Introduction Rocks are igneous, sedimentary, or me tamorphic in origin. Rock properties are dependent upon the minerals that make up the rock, formation process, and weathering condition. Rocks are generally strongest when newly formed, and gradually become weaker and softer when exposed to weathering forces. All rock deposits contain joints, faults, and other discontinuities (eg. cleavages, bedding, and laminations) that significantly affect the behavior and properties of the rock mass. Soils are formed by physical and chemical weathering of rocks. The weathering processes occur either in-situ, leading to residual soils, or involve transport processes; by air (wind), ice, and water, followed by deposition in a range of environments (e.g. Aeolian, lacustrine, marine, alluvial, glacial). Soil properties reflect the materials’ origin, its mode of transportation, its depositional environment, and its subsequent history. 1.2.1 Definition of Key *Definitions printed from: Physical Geography Glossary of Terms: http://www.physicalgeography.net/glossary.html Rocks formed by solidification of molten magma either beneath *Igneous rock (intrusive igneous rock) or at (extrusive igneous rocks) the Earth's surface. Rocks formed from the re-crystallization of igneous, sedimentary, *Metamorphic rock: or other metamorphic rocks through pressure increase, temperature rise, or chemical alteration. Rocks formed by the deposition, alteration and/or compression, *Sedimentary rock: and lithification of weathered rock debris, chemical precipitates, or organic sediments. *Parent Material: The mineral material from which a soil forms. Breakdown of rock and minerals into small-sized particles through *Physical Weathering: mechanical stress. Breakdown of rock and minerals into small-sized particles through *Chemical Weathering: chemical decomposition. Transported Soil: Soil transported from their place of origin. Residual Soil: Soil developed directly from the weathering of the bedrock below Boulders: Large fragment of rock that has a diameter greater than 256 mm. Sand: Mineral particle with a diameter between 0.075 & 4.75 mm. Silt: Mineral particle with a diameter between 0.002 & 0.075 mm. Clay: Mineral particle with a diameter less than 0.002 mm. A vertical section of the soil through all its horizons and extending into Soil Profile: the parent material. Soil and Rock of the Earth 2 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS A layer of soil differing in properties and characteristics from the Soil Horizon: adjacent layers below or above. Water Content: The ratio of mass of water to the mass of solids Wet Unit Weight: The weight of soil solids and water per unit volume Dry Unit Weight: The weight of soil solids per unit volume. Void Ratio: The ratio of volume of void space to volume of soil solids. Porosity: The ratio of the volume of voids to the total volume = Vv / Vt Degree Of Saturation: The ratio of volume of water to volume of void space. = Vw / Vv The process, generally compaction or/and cementation, of *Lithification: converting sediments into sedimentary rock. See the following for further information: Physical Geography Glossary of Terms: http://www.physicalgeography.net/glossary.html 1.3.1 Focus Questions 1. What are the differences between igneous, sedimentary and metamorphic rock? 2. Why are there different soil types? 3. What affects the properties of soil? 4. What are the two main weathering processes? 5. What is the difference between transported and residual soil. 6. What are the main transportation agents of soil? 7. What does the subsurface environment look like? 8. What are the physical properties of soil? 9. How are physical properties calculated? Soil and Rock of the Earth 3 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS 1.4.1 Definition of Soil & Rock Soil, in the engineering sense, is defined as all fragmented minerals at or near the earth's surface plus the air, water, organic matter, and other substances of unconsolidated sediments and deposits of solid particles that have resulted from the disintegration of rock. It ranges from soft spongy peat through soft clays, loams, and silts to coarse-grained sands and gravels, stiff clays and shale. In engineering, our primary concern is strength as opposed to the interests of other professions. Rock in the engineering sense is natural aggregate of minerals connected by strong bonding or attractive force, or a natural aggregate of minerals that cannot be readily broken by hand and will not disintegrate on its first drying and wetting cycle. Blocks of rock are separated by discontinuities such as bedding planes, joints, faults, and shears. These naturally formed surfaces are weaknesses, which reduce the strength of large masses of rock. It is usual, therefore, to distinguish the properties of the intact rock from the properties of the rock mass that includes the effect of the rock discontinuities. 1.4.2 GEOLOGICAL CLASSIFICATION OF ROCK Rocks are classified with respect to their geological origin. The main classifications are: 1.4.2.1 Igneous Rocks Igneous rocks are formed by the solidification of molten materials, either by intrusion at depths within the earth crust or by extrusion at the earth's surface. The mineral composition of igneous rocks is mainly silicates, from simple quartz (SiO2) to the complex pyroxene. The igneous rock properties and mineral sizes depend on the magma’s elementary composition, its temperature, its exerting pressure, and i t s rate of cooling. Fast cooling rates of magma lead to smaller mineral crystals and a fine interlocking texture and slow cooling rates lead to larger crystals and a coarser texture. Many chemical combinations in igneous rocks are unstable in the environment existing at the earth's surface. Upon exposure to air, water, chemicals in solution, freezing temperatures, varying temperatures, and erosive factors, the rock minerals break down to form the various soil types existing today. Rocks, whose principal mineral is quartz or orthoclase (potassium feldspar) with high silica content, decompose to predominantly sandy or gravely soil with little clay. These rocks are classified as acidic. Granites, syenite, and rhyolite are examples of this type of rock. Rocks containing minerals such as iron, magnesium, calcium, or sodium, but little silica, decompose to form silt and clay soils and are classified as basic rocks. Some examples are gabbros, diabases, and basalt. Soil and Rock of the Earth 4 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS Generally, the acidic rocks are light-colored, while the basic rocks are very dark. Intermediate colors reflect an intermediate chemical composition. Rock types considered intermediate (between acidic and basic) includes trachyte, diorite, and andesite. Diorite and andesite easily break down into the fine-textured soils. The clay portion of fine-textured soil is the result of primary rock minerals decomposing to form secondary minerals. Clays are not small fragments of the original minerals that existed in the parent rock. Because of this change, the properties and behavior of clay soils are different from the gravel, sand, and silt soils, which are still composed of the primary rock minerals. 1.4.2.2 Sedimentary Rock Sedimentary rocks such as sandstones, limestone, and shale are formed by lithification of sedimentary soils. Depending on the mineral composition, sedimentary rock can be classified into: a. Calcareous: predominant mineral is calcite (CaCO3); examples are limestone (CaCO3) and dolomite CaMg (CO2). b. Siliceous: predominant mineral is quartz (SiO2); examples are sandstone and quartzite. c. Argillaceous: predominantly clay minerals; examples are shale and mudstone. Shales are formed predominantly from deposited clay and silt particles. The degree of hardness varies, depending on the type of mineral, the bonding that developed, and the presence of foreign materials. Limestone is predominantly crystalline calcium carbonate (calcite) formed under water. This rock material forms because of chemicals precipitating from solution and from the remains of marine organisms and action of plant life. Sandstone is predominantly quartz cemented mostly with silica, but also with calcium carbonate or iron compounds. 1.4.2.3 Metamorphic Rock Metamorphic rocks were originally igneous, sedimentary, or metamorphic rocks altered physically, chemically, or mineralogically by the application of intense heat and/or pressure and plastic flow at some time in their geological history. Plastic flow for rock refers to the slow viscous movement and rearrangement within the rock mass as it changes and adjusts to the pressures created by external forces. Thermal metamorphosis of sedimentary rock usually produces harder and tougher materials; limestone crystallizes into marble and sandstones into quartzite; shale is transformed into slate and at higher pressures, slate is transformed into schist. Metamorphosis due to pressure results in laminated or banded bedrock (foliated rock). Soil and Rock of the Earth 5 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS 1.4.2 FORMATION OF SOILS 1.4.2.1 Soil Forming Factors The five soil forming factors are: 1. Parent material: The primary material from which the soil is formed. T he soils’ parent material could be bedrock, organic material, an old soil surface, or a deposit from water, wind, glaciers, volcanoes, or material moving down a slope. 2. Climate: Weathering forces such as heat, rain, ice, snow, wind, sunshine, and other environmental forces, break down parent material and affect how fast or slow soil formation processes go. 3. Organisms: All plants and animals living in or on the soil (including micro-organisms and humans). The amount of water and nutrients that plants need affects the way soil forms. The way humans use soils affects soil formation. Also, animals living in the soil affect de- composition of waste materials and how soil materials will be moved around in the soil profile. On the soil surface remains of dead plants and animals are worked by microorganisms and eventually become organic matter that is incorporated into the soil and enriches the soil. 4. Topography: The location of a soil on a landscape can affect how the climatic processes impact it. Soils at the bottom of a hill will get more water than soils on the slopes, and soils on the slopes that directly face the sun will be drier than soils on slopes that do not. Mineral accumulations, plant nutrients, type of vegetation, vegetation growth, erosion, and water drainage are dependent on topographic relief. 5. Time: All of the above factors assert themselves over time, often hundreds or thousands of years. Soil profiles continually change from weakly developed to well-developed over time. 1.4.2.2 Residual Soils Residual soils have formed from the weathering of rock or the accumulation of organic material that remains at the location of their origin. The weathering process is attributed to mechanical or chemical weathering. When various weathering agents attack newly exposed rock, soil forms from the weathered rock. Parent Material Residual Product Granite Sand & Clay Basalt Clay Shale Silt & Clay Sandstone Sand Limestone Caverns & Residual Clay Soil Changes Due To Weathering Processes Soil and Rock of the Earth 6 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS 1.4.2.3 Weathering Weathering is the physical disintegration and chemical decomposition of rocks in response to environmental conditions at or near the earth's surface. Mechanical weathering is the process by which rocks break down by physical forces such as wind, rain, running water, ice, and frost. This process includes: 1. Thermal expansion and contraction due to daily and seasonal changes in temperature. 2. Frost action due to water present within the fissures and imperfections in rock masses. 3. Exfoliation is the process of peeling off the outer layers of coarse-grained rock. When water enters cracks and chemically reacts with feldspar, a portion changes to clay. Since clay occupies more space, it exerts pressure and causes the outer layer to peel off. 4. Impact between rocks such as rock slides, suspended solids in rivers, and glacier movement. 5. Rock expansion occurs when rocks, formed at a greater pressure than atmospheric pressure, are subjected to a lower pressure. 6. Plant, animal, and human activities. 7. Volcanic ash. 8. Tectonic forces (earthquakes). Chemical weathering is the decomposition of rock due to chemical reactions in the rock material that occur from exposure to the atmosphere: temperature change, water, or other fluids. Climate, topography, drainage, and vegetation affect the rate of chemical weathering. Examples of chemical weathering are: 1. Oxidation: some rocks are rich in iron and rust will form in the presence of water and air; this process decomposes the rock. 2. Reduction: a chemical reaction takes place without oxygen; this process is influenced by the presence of anaerobic bacteria. 3. Hydrolysis: minerals take up OH-ions, usually from water, into their structure and decompose into soil particles. 4. Carbonation: under high pressures and temperatures, carbons can be modified into coals, petroleum or gas. 5. Acid Rain: when carbon dioxide dissolves in water, a weak acid is formed (carbonic acid); the acid can dissolve minerals and cause rock decomposition. Soil and Rock of the Earth 7 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS 1.4.3 TRANSPORTED SOILS Transported soils are materials moved from their place of origin and deposited elsewhere. Transportation may have resulted from the effects of gravity, wind, water, glaciers, or human activity. Often soil particles are segregated according to size by, or during, transportation. The main transportation agents are: 1. Gravity and Winds: Gravity can only transport aggregate particles limited distances, such as down a hill; winds whip-up and carry soil in dust storms and sandstorms and deposit them elsewhere. 2. Glaciers: Glaciers move slowly down slope carrying debris from neighboring rock walls and material from the ground over which they pass. They are the most important eroding and transporting agents in the northern latitudes and mountainous terrain. 3. Sea/Lake Waves and Current: Waves can move sand and gravel and be a significant erosion force on a shoreline. 4. Rivers and Streams: Rivers and streams are the most important agents because of their widespread occurrence. Fast flowing rivers and streams cut downward making themselves deeper and longer, the material is transported downstream: the distance depends on the energy available to carry the sediment. 5. Mass Wasting Processes: The movement of soil is the direct result of gravity acting on minor and major instabilities. Examples include rain-wash and sheet outwash effects, freeze-thaw, creep, landslides, flow sides, and rock falls. 1.5.0 DEPOSITION 1.5.1 River And Stream Deposits Flowing bodies of water can move volumes of soil by carrying the particles in suspension or by rolling them along the river bottom. The maximum size of a particle that a given water current can carry is called its "competence". The competence of a given river or stream depends on its velocity. Soils carried and deposited by rivers are classified as alluvial deposits. 1.5.2 Ice Borne Deposits In the mountainous regions, ice (glacier) is the major erosion agent. The principal deposit of ice is till, which consists of unsorted mixtures of clay, silt, sand, gravel, and boulder. It is usually hard and dense due to the high overburden pressure of ice that it was subjected to during its geological life. If the melted water is dammed by high topography or obstructed by drainage channels, a very large inland lake may be formed (e.g. Lake Agassiz). Large deltas or fluvio-glacial gravel, sand, and silt form where rivers enter the lakes. Finer silt and clay are deposited in open water as glacio- lacustrine deposits (e.g. the Agassiz clay of Winnipeg basin). The following are terms one should be familiar with: Soil and Rock of the Earth 8 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS 1. Glacial Deposits – are collectively called "glacial drift" of which the most abundant kind is "glacial till," a non-stratified mixture of all particle sizes. 2. Moraine – an accumulation of unconsolidated material deposited by glaciers. 3. Ground Moraine – unconsolidated material deposited directly beneath the base of a glacier. 4. End Moraine – an accumulation of unconsolidated material deposited at the lower end of a glacier. 5. Terminal Moraine – the end moraine marking the farthest advance of a glacier. Others farther back are called recessional moraines. 6. Stratified Drift – created mainly by "outwash" deposited by glacial melt water streams beyond the existing glacier margin. 7. Eskers – form as long, sinuous sand-gravel ridges, probably beds of sub glacial streams near the ice margin. Refer to the following link for more information on geology: Seafriends - Soil: Geology: Part 1 http://www.seafriends.org.nz/enviro/soil/geosoil.htm 1.5.3 Wind Borne Deposits (Aeolian Deposits) 1.5.3.1 Loess Widespread dust storms arising from winds over the glacial outwash left thick deposits of windblown silt called "loess." Loess has low density and high permeability. If it becomes saturated, its strength decreases sufficiently to cause collapse of its structure and subsequently consolidates under its own weight. Saturated loess is very weak and is frequently the cause of foundation problems and landslides. Loess has a calcium carbonate content that acts as a binding agent, which, though weak, allows loess to form vertical or even overhanging walls on the river or stream banks. 1.5.3.2 Sand Dunes Unlike silt, which is carried in suspension by the wind, sand grains settle rapidly enough that they bounce along the ground. Because of this transport by "saltation," sand dunes gradually build out from a sand source and submerge the older landscape. Large dunes have a "slip face" on the leeward side, the primary area of sand deposition. Sand here is very loose and continually adjusts to the angle of repose (30° -> 35°). Dunes migrate downwind. An Egyptian formula gives an average rate of advance of about R = 180/H, where H is the dune height in metres and R is in metres per year and does not exceed a maximum of about 20 metres per year. Soil and Rock of the Earth 9 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS 1.6.0 SOIL PROFILES AND HORIZONS Soil is a three-dimensional system, it has a two dimensional surface area and a third dimension called the depth. There is limitation in all three dimensions. The transition of soil types in both horizontal and vertical directions may be gradual or abrupt depending on the geology and the soil formation factors. Soil formation may require hundreds of years, as the process is very gradual. The degree of rock weathering or soil formation varies with depth. With time, soils generally become deeper and develop distinct layers or horizons. The soil profile in mineral soils has three horizon types, from the surface downwards called A, B and C. Soil horizons are typically distinguished by color differences, but closer study also shows differences in chemical and physical properties. A soil profile is a vertical section of the soil from the surface through all of its layers (horizons) into the parent rock. Because of different degrees of weathering, soil horizons appear as layers in a soil profile. A soil profile consists of four general horizons. Fig. 1.1 Typical Soil Profile Horizon A is the closest to the surface and contains organic matter (topsoil). The soils in Horizon A are usually black or brown in color. Due to water percolation, small clay particles and soluble minerals are washed-out from Horizon A into deeper horizons; therefore, Horizon A is the zone of maximum leaching. Horizon A is very compressible, elastic, and unstable. Horizon A is a poor foundation layer. Horizon B is located beneath Horizon A and is defined as the subsoil by pedologists (soil scientists). I t isenriched with small clay particles, oxides, and soluble carbonate compounds from Horizon A. The abundant clay in Horizon B makes it hard when dry and sticky or "gummy" when wet. The iron oxides in Horizon B make it brown or yellow in colour. Horizon B is a relatively stable stratum. Horizon C is under Horizon B and is weathered parent material that has been broken from bedrock (parent rock). Horizon D is the massive, undisturbed bedrock (parent material). Soil and Rock of the Earth 10 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS 1.7.0 Mass-Volume Relationships Soil is a three-phase system. Solid, liquid and gas are present in soil. Soil deposits comprise of accumulated solid particles of soil or other materials plus the void spaces that exist between the particles. The void spaces are filled partially or completely with water or other liquid. Void spaces, which are not occupied by fluid, are filled with air or other gas. Engineering properties of a soil deposit, such as strength and compressibility, are related directly to, or at least affected by, basic factors such as how much volume or weight of a bulk soil are solid particles or water or air. Information such as soil density (mass per unit volume) water content, void ratio, degree of saturation etc. is used in calculations to determine the bearing capacity (strength)of soil used in design of a foundation, to estimate foundation settlement, and to find the stability of earth slopes. In other words, such information helps to define the condition of a soil deposit for its suitability as a foundation or construction material. Consequently, an understanding of the terminology and definitions relating to soil composition is fundamental to the study of soil mechanics. Bulk soil exists in nature as a random accumulation of soil particles, water and air space. For analysis it is convenient to represent the soil mass by a phase diagram, See Figure 1.2. Soil Solids Voids Water  Chemically inert  Space between  Absorbed water particles soil particles in soil  Vary widely in size, mineral  Could be filled  Water filling the composition, shape with air, fluid or void spaces  Solid portion of a soil mass: vapors called the soil skeleton  Pattern of arrangement is Soil Solids Air Void Spaces: filled with either water or air Water Figure 1.2 Solids Soil and Rock of the Earth 11 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS Using the phase diagram, the interrelationships of weight and mass to the volume being analyzed are shown as: Volume Mass Va AIR Ma Vv Vt Vw WATER Mw Mt Vs SOLIDS Ms Figure 1.3 Relationship between mass/weight and volume 1.7.1 Basic Relationships The following relationships are shown in Figure 1.3: 1) TOTAL WEIGHT (Wt) = WT. OF SOLIDS (Ws) + WT. OF WATER (Ww) + WT. OF AIR (=0) 2) TOTAL MASS (Mt) = MASS OF SOLIDS (Ms) + MASS OF WATER (Mw) 3) TOTAL VOLUME (Vt) = VOL. OF SOIL SOLIDS (Vs) + VOL. OF WATER (Vw) + VOL. OF AIR (Va) 4) TOTAL VOLUME (Vt) = VOL. OF SOIL SOLIDS (Vs) + VOL. OF VOIDS (Vv) The following relationships are used for solving problems: The relationship between weight and volume: Ws = VsGsϒw The relationship between mass and volume: Ms = VsGsρw where: Ws = weight of soil Ms = mass of soil Vs = volume of soil Gs = specific gravity of soil solids ϒw = unit weight of water, (9.81 kN/m3) ρw = density of water, (1000 kg/m3, 1 gm/cm3) Soil and Rock of the Earth 12 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS The specific gravity of commonly occurring rock and soil are between 2.30 and 3.1. Typical values of Specific Gravity of Soil Solids (Gs) are as follows: SOIL TYPE Gs Sand 2.65 - 2.67 Silty sand 2.67 - 2.70 Inorganic Clay 2.70 - 2.80 Soil with Iron or Mica 2.75 - 3.00 Organic Soil 1.0 - 2.60 Table 1.1 Basic Soil Property Relationships Wet Unit Weight: ϒwet = Wt / Vt (kN/m3) Dry Unit Weight: ϒdry = Ws / Vt (kN/m3) ϒdry = ϒwet / (1+w/100) (kN/m3) Wet Density: ρ wet = Mt / Vt (kg/m³, g/cm3) Dry Density: ρ dry = Ms / Vt (kg/m³, g/cm3) ρ dry = ρwet / (1 + w/100)(kg/m³, g/cm3) Water content: w, (%) = (Ww / Ws) 100% or w% = (Mw / Ms) 100% Where: w, (%) = water content, Ww = weight of water, Ws = weight of dry soil, Wt = total or wet weight, Mw = mass of water, Ms = mass of dry solids, Mt = total or wet mass Weight of Dry Soil: Ws = Wtwet / (1+ w/100) Mass of Dry Soil: Ms = Mwet / (1+ w/100) Void Ratio: e = Vv / Vs Porosity: n, (%) = (Vv / Vt) 100% Relationship between void ratio and porosity: n, (%) = {e / (1+e)} 100% Degree of Saturation: Sr, (%) = (Vw / Vv) 100% Soil and Rock of the Earth 13 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS Additional Relationships Vs = Vt / (1+e) ϒ dry = Gs * ϒ w / (1+e) ρ dry = Gs * ρw / (1+e) ϒ wet = {(Gs + Se) / (1+e)} ϒw, where “S” is in decimal notation ρ wet = {(Gs + Se) / (1+e)} ρw, where “S” is in decimal notation Se = wGs where “S” and “w” are in percent Gs = Ms / (Vs*ρw) For a fully-saturated soil, the unit weight & density become: ϒ Sat = {(Gs + e) / (1+e)} ϒw ρ Sat = {(Gs + e) / (1+e)} ρw For a submerged soil, the submerged (buoyant) unit weight is: ϒ Sub = {(Gs - 1) / (1+e)} ϒw Example 1: A gravel sample is taken from a stockpile: total stockpile mass=200,000kg.The data from the moisture content test is Wet Mass = 424g Dry Mass = 400g (after oven drying) QUESTION How much water must be added to the stockpile to bring the moisture content to 15%? STRATEGY Write down what is given and use the appropriate equations to find the unknowns. You are able to find the moisture content and mass of water for the present condition of the stockpile. You have the desired moisture content that allows you to calculate the mass of water at the desired moisture content. The difference between the two water masses is the answer. Step 1: Determine mass of water in sample. Total Mass (Mt) = Mass of Solids (Ms) + Mass of Mass of Water (Mw) 424g = 400g + Mw 424g - 400g = Mw 24g = Mw Mass of Water = 24g Soil and Rock of the Earth 14 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS Step 2: Determine moisture content of sample w % = {Mw / Ms} x 100 w%= {24g / 400g} x 100 w % = 6% Original Moisture Content = 6.0% Step 3: Determine mass of water in stockpile. If 424 g of wet gravel contains 24 g of water, then how much water does 200,000 kg of wet gravel contain? Using a direct proportion: (24g / 424g) = (Mass of water in stockpile / 200,000 kg) Mass of water in stockpile = 11,321 kg Step 4: Determine mass of solids in stockpile If the 200000kg stockpile has 12000kg of water then the mass of solids in the stockpile is: TOTAL MASS (Mt) = (Ms) + MASS OF WATER (Mw) 200,000kg = (Ms) + 11321kg 200000kg - 11321kg = (Ms) 188679kg = (Ms) Mass of solids in stockpile= 188,679 kg OR Ms = Mt / 1 + w = 200000kg / 1.06 = 188,679 kg Step 5: Determine mass of water in stockpile at 15% moisture content w% = {Mw / Ms} x 100 15% = {Mw / Ms } x100 15% = {Mw /188,679kg} x 100 0.15 = Mw / 188,679kg (divided both sides by 100) Mw = 0.15 x 188,679kg Mw = 28,302 kg Step 6: Find mass of water required to bring the moisture content of the stockpile to 15%. 1. Original mass of water in stockpile = 11,321kg (Step 3) 2. Mass of water required in the stockpile for a moisture content of 15% = 28,302kg Answer: Subtracting 1 from 2 gives you amount of water to be added = 16,981 kg OR Mw = {(15%-6%)/100} Ms = (0.09) 188679 = 16,981 kg Soil and Rock of the Earth 15 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS Example 2: A soil has been compacted in an embankment with a bulk density of 2000 kg/m3 at a water content of 10%. The value of Gs is 2.65. QUESTION Calculate the dry density, void ratio, porosity, and degree of saturation. STRATEGY Write down what is given and use the appropriate equations to find the unknowns. You are able to find the dry density. Calculate the associated volumes and masses then use the calculated values in the appropriate equations. Step 1: Draw and label the mass-volume diagram VOLUME, m3 MASS, kg AIR WATER 1.0 2000 SOLIDS Hint: Label the volumes and masses on the diagram when they are calculated: this helps to visualize what was calculated. Step 2: Calculate the dry density. We can calculate the mass of soil solids Ms = Mt / (1 + w% / 100%) Ms= 2000 kg/m3 / (1 + 10 \100) Ms= 1818 kg 3 Note: Since the volume is 1m3, Dry Density (ρdry) = 1818 kg/m Soil and Rock of the Earth 16 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS Step 3: Calculate the void ratio. We have: e = Vv / Vs: we do not know Vv or Vs, so we must explore some way to find them We know: o TOTAL VOLUME (Vt) = VOL. OF SOIL SOLIDS (Vs) + VOL. OF VOIDS (Vv) = 1 m3 o Therefore; we need to determine either Vs or Vv o We have: Gs = Ms / Vs (ρw); where the only unknown is Vs.  2.65 = 1818kg / Vs (1000kg/m3)  Vs = 1818 kg / 2650 kg/m3  Vs = 0.68 m3 Using Total Volume, Vt = Vol. of Soil Solids (Vs) + Vol. of Voids (Vv) 1m3 = 0.68m3 + Vv Vv = 0.32 m3 Using e = Vv / Vs e = 0.32 m3 / 0.68 m3 e = 0.471 Step 4: Calculate the Porosity. n, % = (Vv / Vt) x 100% n, % =( 0.32 m3 / 1 m3 ) x 100 n = 32.0 % Step 5: Calculate the Degree of Saturation Sr % = (Vw / Vv) x 100% We must determine Vw as Vv = 0.32 m3 Mass of Water = Wet Mass – Dry Mass = 2000kg – 1818 kg = 182 kg Vw = Mass of water / Density of water (ρw) 3 = 182 kg / 1000kg/m 3 = 0.182 m 3 therefore, Sr = (0.182 m3 / 0.32m X 100 = 56.9 % Soil and Rock of the Earth 17 Revised: 2020-09-29  GEOTECHNICAL FUNDAMENTALS 1.8.0 Questions 1. Describe the following environments: Aeolian, lacustrine, marine, alluvial, and glacial. 2. Name the three main classes of rock and describe how they were formed. 3. Provide comments on the hardness, soundness, and durability associated with the three main types of rock. 4. Describe the two processes that transform soil sediments into sedimentary rock. 5. What types of processes occur to cause metamorphosis of rocks? 6. Why are sand and gravel deposits found along old river and stream locations? 7. Describe the main types of weathering and give two examples of each. 8. What are loess soils, and what is the potential danger associated with loess? 9. In a glacially effected area, what types of glacial formations represent possible sources of sand and gravel for the construction industry? 10. What is the potential danger to stability in areas where the land is formed from marine clay? 11. The mass of a saturated soil sample is 530 gm. The dry mass after oven-drying is 410g. Determine the a) water content b) void ratio c) saturated unit weight d) porosity. 12. A soil sample has a bulk unit weight of 20.0 kN / m3 at a water content of 12%. Determine the a) void ratio b) dry unit weight c) degree of saturation. 13. A wet soil sample has a volume of 500cm3 and has a mass of 950 gm. After oven drying, the mass is 900 g is 2.55. Determine the a) water content b) void ratio c) degree of saturation d) porosity. 14. The void ratio of a soil sample is 0.82. Determine the bulk and dry unit weights for the following degrees of saturation: a) 75% b) 85% c) 95% 1.9.0 Web Resources: Physical Geography Glossary of Terms: http://www.physicalgeography.net/glossary.html USGA General Interest Publications Web Page http://pubs.usgs.gov/gip/deserts/contents/ Seafriends - Soil: Geology: Part 1 http://www.seafriends.org.nz/enviro/soil/geosoil.htm Soil and Rock of the Earth 18 Revised: 2020-09-29