04/10/2021 CVE3621 Geotechnical Engineering 1 Year 3, Semester 1 Lecture 1 The nature of ground materials Christian Schembri BE&A(Hons), MSc(Lond) DIC, Perit christian.schembri@um.edu.mt CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 1 Fundamental to geotechnical engineering… We require an understanding of what ground materials are made of, and how these elements interact. Rock Mechanics Soil Mechanics We may also need to understand how ground materials can be used by man to create new building elements, e.g. fills, concrete CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 2 1 04/10/2021 Why do we need to understand ground materials? We can choose to build using steel or we can choose concrete, or both We can go for masonry and timber In structural engineering we have a choice For a given site, we cannot choose the ground materials – they are already there. We have no choice... In geotechnical engineering, we need methods of understanding these materials CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 3 Material properties in the construction industry • Steel – easily understood • Concrete – easily simplified • Intact rock – similar to concrete but subject to natural variations • Sand / Compacted fill – complex • Clay – very complex • Fractured rock – a complete mess! CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 4 2 04/10/2021 Why are ground materials complex to understand? Not always homogenous Rarely isotropic Often exhibit non-linear behaviour They consist of solid particles, water and air all together. 5 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri The challenge CHILE Continuous, Homogenous, Isotropic, Linearly Elastic Versus DIANE Discontinuous, Inhomogenous, Anisotropic, Non-Elastic CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 6 3 04/10/2021 The three phases Solid particles • • • • • • Often incompressible, They can be crushed May be rounded or angular They vary in size from boulders to extremely small (clay) May be cemented together May displace each other when loaded CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 7 The three phases Water • • • • • Almost incompressible Can take compression, tension Unable to resist shear Can be absorbed or adsorbed Can create large capillary forces that hold solid particles together • May force particles apart • May transport particles • May dissolve air into it CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 8 4 04/10/2021 The three phases Air • Highly compressible • Can be absorbed into pores • Can flow freely between solid particles or can be trapped between water meniscii • Can dissolve into water and then be released when pressures change 9 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Engineering properties In most cases, these will depend on the relative proportion of solids, water and air Bulk density Strength Compressibility Dilation Dry density Bulk Unit weight Saturated density moisture content Submerged density voids ratio Deviatoric strain Unit weight Undrained strength Specific gravity volumetric change CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 10 5 04/10/2021 Engineering properties • As we engineer soils, we need to keep in mind that the proportions of solids, water and air will be different from site to site and possibly even within the same site. • The type of solids will be different • The size of the solids will be different • The range of sizes of solids and their respective proportions will be different, and therefore so will the voids in between • The amount of water and air may change with time • The amount of water and air will change due to our interventions (projects), and the particles may be rearranged • Water and air may be prevented from leaving the solid skeleton (e.g. in the undrained state) CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 11 A common set of definitions • As we investigate and we engineer soils, we need a common set of descriptors to monitor the respective quantities of solids, water and air, and how these change. • This is achieved by “phase relationships” Phase relationships are used in laboratory testing, as we attempt to understand what constitutes a soil and how it behaves. Some of the descriptors are also referred to in geotechnical calculations, and can be assessed via outputs of, for example, finite element software CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 12 6 04/10/2021 Phase relationships To compute the masses (or weights) and volumes of the three different phases. Notation M = mass or weight V = volume s = soil grains w = water a = air v = voids t = total Vv Va air Vw water Ma=0 Mw Vt Vs soil Mt Ms Phase Diagram 13 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Definitions Water content (w) is a measure of the water present in the soil. w MW MS Vv X 100% Expressed as percentage. Va air Vw water Ma=0 Mw Vt Vs soil Mt Ms Range = 0 – 100+%. Phase Diagram CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 14 7 04/10/2021 Definitions Void ratio (e) is a measure of the void volume. Vv V e V VS Va air Vw water Ma=0 Mw Vt Void ratio is a very important measure, and is used to describe deformation, (e.g. settlement) Vs soil Mt Ms Phase Diagram 15 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Definitions Porosity (n) is also a measure of the void volume, expressed as a percentage. V n V VT Vv X 100% Theoretical range: 0 – 100% Va air Vw water Ma=0 Mw Vt Vs soil Mt Ms Phase Diagram CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 16 8 04/10/2021 Definitions Degree of saturation (S) is the percentage of the void volume filled by water. S VW VV X 100% Range: 0 – 100% Dry Vv Va air Vw water Ma=0 Mw Vt soil Vs Saturated Mt Ms The degree of saturation gives important information regarding the applicability of the principle of effective stress 17 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri A Simple Example In this illustration, e=1 Vv n = 50% S = 50% Va air Vw water Ma=0 Mw Vt Vs soil Mt Ms Phase Diagram CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 18 9 04/10/2021 Definitions Bulk density (m) is the density of the soil in the current state. M m T VT Units: t/m3, g/ml, Vv kg/m3 Va air Vw water Ma=0 Mw Vt Vs soil Mt Ms Phase Diagram 19 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Definitions Dry density (d) is the density of the soil in dry state. Saturated density (sat) is the density of the soil when the voids are filled with water. Submerged density (’) is the effective density of the soil when it is submerged. ’ = sat - w CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 20 10 04/10/2021 Definitions Dry density (d) is the density of the soil in dry state. M d S VT Units: t/m3, g/ml, Vv kg/m3 Va air Vw water Ma=0 Mw Vt Vs soil Mt Ms 21 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Definitions Bulk, saturated, dry and submerged unit weights () are defined in a similar manner. Here, use weight (kN) instead of mass (kg). = g N/m3 kg/m3 Often expressed as kN/m3 to keep the numbers small CVE 3621 - Geotechnical Engineering 1 - Christian Schembri m/s2 In the relationship above, g is not ‘grams’ but the acceleration due to gravity 22 11 04/10/2021 Definitions Unit weight of fresh water γw = 9.81 kN/m3 • Unit weight of sea water γw = 10.00 kN/m3 23 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Specific Gravity Gs • The RATIO of the weight or mass of a volume of the material to the weight or mass of an equal volume of water Gs WS Ms V s s s Vs w Vs w Vs w w Particle density d MS Vs Specific gravity of the soil grains (Gs) typically varies between 2.6 and 2.8 Mg/m3 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 24 12 04/10/2021 Phase Relations From the previous definitions, M Se w W M S GS n air e Se VV e VT 1 e 1 water Sew soil G s w Phase Diagram 25 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Phase Relations m sat M T GS Se W VT 1 e M G e T S W VT 1 e M G d S S W VT 1 e air e Se 1 water Sew soil G s w Phase Diagram CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 26 13 04/10/2021 Try not to memorise the equations. Understand the definitions, and develop the relations from the phase diagram with VS = 1; • • • • • Assume GS (2.6-2.8) when not given, otherwise measure it; Do not confuse densities with unit weights; Do not confuse bulk density with all the other densities Think carefully about which unit weight is applicable… Soil grains are assumed incompressible. Their mass and volume remain the same at any void ratio. 27 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri A Suggestion.. If you can remember one thing in phase relations, that should be .. air e Se water Sew 1 soil Gs w CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 28 14 04/10/2021 Solid Particles We need to consider • The type of material making up the particles, • The smallest and the largest • The distribution of sizes in between • Roundness or angularity of the particles. Topsoil Stone Gravel Sand Recycled 29 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Range of sizes encountered during our work Sub-microscopic (clay particles) Block-sized (in between rock fractures) CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 30 15 04/10/2021 Particle sizes • Boulder • Cobble • Gravel – Coarse – Medium – Fine • Sand Limit of sieve analysis, limit of visibility of naked eye – Coarse – Medium – Fine • Silt • Clay Limit of hydrometer/ sedimentation analysis, limit of normal microscope 10-6mm: limit of electron microscope 31 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Sand and clay The main difference between sand and clay is the size of the particles. Clay particles are extremely small Sand Sand Sand Sand CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Clay particles - enlarged 32 16 04/10/2021 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 33 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 34 17 04/10/2021 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 35 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 36 18 04/10/2021 Clay at close range •Clay is made up of a large number of plate-like particles that are very small indeed. They are not visible using a normal microscope, but can be seen under an electron microscope •Clay particles are so small that water molecules are adsorbed to their surfaces 37 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Why is particle size important? ...surface area If soil particles are simplified to cubes: Length of cube side (cm) Number of particles Total volume (cm3) Total surface area (cm2) Surface area /volume (cm-1) 1 (gravel) 1 1 6 6 1μ = 10-4 (clays) 1012 1 60,000 60,000 1mμ = 10-7 1021 1 60,000,000 60,000,000 Clay constituents CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 38 19 04/10/2021 Surface area per unit mass (1g) 0.1mm sand → 0.03 m2/g → surface area of an small envelope (water content: 1.5x10-4%) Kaolinite → 10 m2/g → surface area of a single bedroom (water content: 0.5%) Illite → 100 m2/g → surface area of an apartment (water content: 5%) Montmorillonite → 1000 m2/g → 6g will cover a football pitch! (water content: 50%) Kaolinite, illite and montmorillonite are the constituents of Maltese Blue Clay Water contents are based on a water film of (5 x 10-10m) thickness CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 39 Ways of measuring particle size Sieve analysis • Place the soil into the top sieve • Measure the weight of material retained on each sieve • Express amount going through each sieve as a percentage of the total weight • Plot on a graph have logarithmic xaxis This method is suitable for particles between 0.063mm and 75mm CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 40 20 04/10/2021 Ways of measuring particle size Sedimentation Method based on Stokes’ law, which governs the velocity at which spherical particles settle in suspension • Mix soil with hydrogen peroxide to remove organic material • Place the soil in suspension (distilled water +deflocculating agent) into a measuring cylinder • Measure time & specific gravity by hydrometer at different levels. • Plot on a graph having logarithmic xaxis This method is suitable for particles less than 0.063mm CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 41 Typical grading curves CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 42 21 04/10/2021 Grading • Well graded: having no excess of particles in any size range, thus creating a matrix in which voids are minimized • Poorly graded: many particles having the same size or within narrow limits • Gap graded / step graded: having large particles and small particles but with a relatively low proportion of intermediate sizes • Grading envelope: specified range of sizes and their relative proportion, allowed in a soil • D10 size: the size of particles such that 10% of the particles are smaller than that size CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 43 22 CVE3621 Geotechnical Engineering 1 Year 3, Semester 1 Lecture 2 Soil Water Christian Schembri BE&A(Hons), MSc(Lond) DIC, Perit christian.schembri@um.edu.mt CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 1 Water in the ground • Most problems encountered in geotechnical engineering occur because of the presence of water. • The ease by which water goes through a ground material has a decisive effect on the cost and difficulty of a construction operation, or an intervention in the ground. • The presence and FLOW of water will influence the strength of the ground, and the way the ground responds to our engineering interventions. CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 2 1 Scope of this lecture • To understand fluid flow in a porous medium, such as a soil, • To learn about hydraulic gradient, Darcy’s Law and permeability • To learn about how permeability of a soil can be measured CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 3 Pore spaces • In general, all voids within a soil are interconnected to neighbouring voids. In an assemblage of spheres, isolated voids are an impossibility, regardless of the type of packing. • In gravels, sands and silts, it is hard to imagine isolated voids • In clays, consisting mostly of plate-like particles, a small percentage of isolated voids would seem possible, but electron microscope photographs show that all voids are interconnected. CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 4 2 Static water vs Flow We have seen that pore space within a soil can be filled with air, filled with water, or a combination of both, this depending on its position above or below the water table. If a soil is saturated (i.e. the pore space is full of water), this water may be static, or on the move 5 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri The water table Water pressure depth CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 6 3 Water table and phreatic surface As water infiltrates through pore spaces in the soil, it first passes through the zone of aeration, where the soil is unsaturated. At increasing depths water fills in more spaces, until the zone of saturation is reached. This relatively horizontal plane atop this zone constitutes the water table. The term phreatic surface is where the hydrostatic pressure of groundwater or soil moisture is atmospheric (or pressure head is zero). This surface normally coincides with the water table, but is not necessarily so CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 7 Why water can be on the move…. • Water can flow because of a difference in level • A water table exists at a higher, more distant location • An excavation has been created, and water is no longer restrained • Water can flow because of some applied force It can be squeezed out from beneath a heavy load. (or a foundation) CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 8 4 Flow of water through a soil When we consider the velocity of water through a soil, this is not the velocity of an individual water molecule, which has to go through the irregular and confined conduits existing between particles. We consider the average velocity through a given crosssectional area of soil rather than specific velocities through conduits Velocity of flow v (m/s) = flow rate q (m3/s) /cross-sectional area A(m2) 9 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Energy in a fluid • A moving fluid tends to remain in motion, because it possesses kinetic energy Ek= ½mv2 = ½ρv2 (since density = mass per unit volume) • If a weightless container filled with fluid is moved upwards a distance z, work is done in raising the fluid upwards, giving it gravitational potential energy Eg= mgz (= ρgz for unit volume) • A fluid mass also has potential energy due to the pressure P acting on it (P = N/m2 = Nm/m3 = J/m3) (e.g. atmospheric pressure acts on a body of water) CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 10 5 The Bernoulli equation Total energy per unit VOLUME: Etv= ½ρv2 + ρgz + P Dividing by ρ gives the total energy per unit mass: Etm = ½v2 + gz + P/ρ ◄ this is called the Bernoulli equation Where Etm is the total energy per unit MASS for steady flow of a frictionless, incompressible fluid along a smooth line of flow, the sum of the three components is a constant at a given point (real fluids are not necessarily so) CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 11 The Bernoulli equation in soils Dividing the equation by g, we get an expression in terms of Energy per unit weight (J/N or m). The terms therefore have units of length. (v2/2g) + z + (P/ρg) = constant Fluid velocities in soils are very small, so small such that the v2/2g term in the equation can be neglected completely. The energy in soil water is therefore z + P/ρg, Which is equal to z + u/γw CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 12 6 Head In soil mechanics, Etm/g is termed ‘HEAD’ (h), and consists of two distinct components Total hydrostatic head = elevation head + pressure head h = z + (u/γw) 13 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Example: pressurised vessel hp= u/γ piezometer Where u is the water pressure inside the vessel hp h = hydrostatic head Z hydrostatic head at the middle of the tank = h CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 14 7 Example: 2 piezometers Dh A pB =11m zB = 8m Soil Datum zA = 8m pA =15m Note: a piezometer is a small-diameter well with a very short well screen or section of slotted pipe at the end. It is used to measure the hydraulic head at a point in an aquifer B Dl along flowline Impermeable rock CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 15 Hydraulic gradient Between two points A & B, if hydrostatic head at A > hydrostatic head at B Water will flow from A to B In flowing between A & B, the water experiences a head loss Δh equivalent to the difference in head between the two points The head loss Δh divided by the distance Δl between A & B is the hydraulic gradient, denoted by i i = -Δh/Δl CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 16 8 Henri Darcy (1803-1858) Henri Darcy was a highly capable French engineer who built roads, railways and water supply systems. He had an inquiring mind and was a great hydraulic researcher, and his work became part of the standard curriculum for teaching hydraulics at the time, and remains so to this day In 1856, Darcy was entrusted with the design and construction of the municipal water supply system for his home town of Dijon. The flow of water through sands were initially directed to the design of sand filters for the Dijon water supply. The Darcy apparatus was quite simple. He used a vertical iron pipe to contain the sand, and measured the head loss for various discharges and various sizes of sand. Darcy found that the velocity of flow was directly proportional to the hydraulic gradient, and that the constant of proportionality was different for each type of sand 17 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Darcy’s Law The velocity of flow is directly proportional to the loss of head per unit length (hydraulic gradient), v = -k i The constant of proportionality k is different for different soils, and has the units of velocity (ms-1) This constant of proportionality is termed “permeability” The permeability k of a soil applies only to water (at 20ºC). If thick oil is used, the constant will be different. It is therefore NOT an intrinsic property of a soil. CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 18 9 Some typical values of permeability Gravel >1x10-1 m/s or 1m in 1sec Sand (down to 3.6cm in 1 hr) 1x10-1 m/s to 1x10-5m/s Fine sands, coarse silts (down to 0.36 mm in 1 hour) 1x10-5 m/s to 1x10-7m/s 1x10-7 m/s to 1x10-9m/s Silts (down to 2.5mm in 1 month) <1x 10-9 m/s Clays (or 3cm in a year) Permeability is an important property of a soil, because it determines how quickly water can escape from the soil, and therefore it has an effect on the changes in behaviour of a soil under stress. 19 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Water in the ground Soil Rock CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 20 10 Why is total head important in geotechnics? 21 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Measuring permeability The constant head permeameter From Darcy’s Law: h q=Aki q=Q/t i = h/l A=area of sample filter manometers soil filter l k= Ql/tAh Q in time t Measuring cylinder This method, described in BS 1377 Part 5, is suitable for gravels, sands and fill materials CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 22 11 Measuring permeability The falling head permeameter From Darcy’s Law: Manometer standpipe of area a h1 at t1 k= (al/At) ln(h1/h2) A=area of sample valve h2 at t2 l soil overflow perforated base CVE3621 - Geotechnical Engineering 1 - Christian Schembri t=t2-t1 This method, described in BS 1377 Part 5, is suitable for silts and clays 23 12 CVE 3621 Geotechnical Engineering 1 Year 3, Semester 1 Lecture 3 Soil Water (2) Christian Schembri BE&A(Hons), MSc(Lond) DIC, Perit christian.schembri@um.edu.mt Scope of this lecture • To learn about the water cycle • To learn about soil water flow in two-dimensional situations, and how these can be represented • Introduce very briefly a method used to measure insitu permeability CVE3621 - Geotechnical Engineering 1 - Christian Schembri 2 1 The Hydrologic cycle The ultimate source of ground water is precipitation (in the form of rain, snow, or hail). The precipitation that does not evaporate or immediately flow to rivers, streams, or lakes percolates into the ground, where some of it eventually reaches the water table. The concept of the hydrologic cycle is central to understanding the occurrence of ground water. The hydrologic cycle, as the name implies, is an endless dynamic process of the circulation of water between the oceans, the atmosphere and the land. CVE3621 - Geotechnical Engineering 1 - Christian Schembri 3 Aquifer A geologic unit that can store and transmit water at rates fast enough to supply reasonable amounts of water to wells. The permeability of an aquifer normally exceeds 10-7m/s. Examples include sands, gravels, limestone and sandstone CVE3621 - Geotechnical Engineering 1 - Christian Schembri 4 2 Aquitard A layer of low permeability material that can store ground water and transmit it slowly (Also referred to as a leaky confining layer) CVE3621 - Geotechnical Engineering 1 - Christian Schembri 5 Unconfined aquifer If the upper boundary of the ground water is a water surface at atmospheric pressure, the flow and the aquifer are said to be unconfined An open standpipe piezometer inserted in an unconfined aquifer would be filled with water to the same level as the water table CVE3621 - Geotechnical Engineering 1 - Christian Schembri 6 3 Confined aquifer If the aquifer is saturated throughout and bounded above by a layer with significantly lower permeabilty, the flow and the aquifer are said to be confined An open standpipe piezometer inserted in a confined aquifer would be filled with water to a higher level than the top boundary of the aquifer CVE3621 - Geotechnical Engineering 1 - Christian Schembri 7 Artesian conditions – in confined aquifers CVE3621 - Geotechnical Engineering 1 - Christian Schembri 8 4 Example: confined aquifer m.s.l. 50m u = 6.1x105 N/m2 100m u = 9.0 x105 N/m2 CVE3621 - Geotechnical Engineering 1 - Christian Schembri 9 Water in the ground can be moving CVE3621 - Geotechnical Engineering 1 - Christian Schembri 10 5 Water in the ground can be made to move 11 CVE3621 - Geotechnical Engineering 1 - Christian Schembri Measuring permeability via in-situ tests From Darcy’s Law: • The pumping out test k= q ln(r2/r1) π (h22-h12) q in time t aquifer h1 impermeable stratum CVE3621 - Geotechnical Engineering 1 - Christian Schembri h2 r1 r2 12 6 Flow lines • The path traced by a water particle as it moves through the soil is called a flow line • Flow lines connect points having a difference in head: from high head to low head • Flow lines never experience abrupt changes in direction within the same porous medium – smooth curves are traced as direction changes ✔ CVE3621 - Geotechnical Engineering 1 - Christian Schembri 13 Equipotentials • As water moves along a flow line, it experiences a continuous loss of head • A flow line can therefore be divided into points defining equal head loss • Points of equal head, on different flow lines, can be joined together to give contours of head, or equipotential lines CVE3621 - Geotechnical Engineering 1 - Christian Schembri 14 7 Flow lines and equipotential lines h1 Δh b • The loss in head between two equipotentials, divided by the physical distance between them is equivalent to the hydraulic gradient h2 h3 L • The hydraulic gradient is a maximum along a path normal to the equipotentials • Since flow occurs between two points having the maximum difference in head, it follows that flow lines must be perpendicular to equipotentials 15 CVE3621 - Geotechnical Engineering 1 - Christian Schembri Flow nets • • • • If the difference in head between two points is divided into Nd drops, Nd-1 equipotentials can be drawn between these two points: Δh=h/Nd The total width of soil available for flow to take place can be divided into Nf flow channels, separated by Nf-1 flow lines Δq=q/Nf By Darcy’s law, for unit width of soil: Δq=k(Δh/L).b If the distance between equipotentials is made to be equal to the distance between equipotentials, b=L, therefore b/L=1 CVE3621 - Geotechnical Engineering 1 - Christian Schembri Δh b L If b/L=1 Δq= kΔh q/Nf=kh/Nd Therefore total unit flow per unit width, q=kh(Nf/Nd) 16 8 Rules for drawing a flow net • Flow lines must be perpendicular to equipotentials • Flow lines must be smooth curves or straight • The net formed by the intersection of flowlines and equipotentials should consist of squares, which can be curvilinear • Objects which are impermeable (sheet piles, bases of retaining walls or dams, impermeable strata) are flow lines since water will flow along them not across them • Water surfaces are equipotentials Drawing a flow net which satisfies the above is a trial and error process which is difficult to do correctly in just one attempt – an eraser and a pencil are essential! 17 CVE3621 - Geotechnical Engineering 1 - Christian Schembri Flow net problem – flow around sheet pile wall 4.5m lake Detwatering for foundation construction 1 sand 12 2 8.6m 11 4 1 2 3 10 4 5 9 The difference in head of 4m is 4.0m subdivided into twelve drops, by 11 equipotential lines (Nd=12) Flow around the 6.0m sheet pile is subdivided into 4 channels, by 3 flow lines (Nf=4) 6 7 8 impermeable stratum CVE3621 - Geotechnical Engineering 1 - Christian Schembri 18 9 Flow net problem – flow around sheet pile wall Dewatering for foundation construction lake 3.5 m 1 sand 12 2 11 2 3 4 A 1 10 4 5 9 6 7 8 4.0m Δh = 4/12 = 0.333m At point A, after 3 drops, h = 4.5-(3x0.333) = 3.5m At point A, u=(h-z)γw = [3.5-(-6)]x10 =95 kPa impermeable stratum 19 CVE3621 - Geotechnical Engineering 1 - Christian Schembri Flow net problem – effective stress This flow net indicates a potential recipe for disaster. A quick condition is created at points A to B CVE3621 - Geotechnical Engineering 1 - Christian Schembri 20 10 Draw the flow net Determine the quantity of water flow below the spillway and calculate the uplift force on the spillway 30m 12.5m 10m 15m Sandy gravel k=5x10-5m/s Impermeable CVE3621 - Geotechnical Engineering 1 - Christian Schembri 21 Typical uses of flow nets: Excavations below the water table requiring de-watering. Pumps need to be sized and energy consumption quantified. The pressures acting around the retaining structures can be quantified, and the soils checked for liquefaction potential (piping) - which can lead to loss of strength and catastrophic collapse CVE3621 - Geotechnical Engineering 1 - Christian Schembri 22 11 Typical uses of flow nets: Flownets can be used to determine flow patterns to / from wells CVE3621 - Geotechnical Engineering 1 - Christian Schembri 23 Flow nets in natural settings With some knowledge of ground permeabilities and water levels, flownets in natural situations can be imagined, drawn and verified by investigation CVE3621 - Geotechnical Engineering 1 - Christian Schembri 24 12 Typical uses of flow nets: The design of embankment dams requires careful analysis of how water flows through the different soils making up the dam. These are often designed to have different permeabilities. The strength (and therefore the safety) of such soil heaps depends on the pore pressures within (by the principle of effective stress) CVE3621 - Geotechnical Engineering 1 - Christian Schembri 25 Seepage analysis Modern geotechnical engineering software can carry out complex seepage analyses to determine flow patterns in the ground or around projected structures. Such analyses require a thorough understanding of seepage principles and an awareness of the possibilities and limitations of numerical modelling. Flow nets are very handy to check the output of such computer analyses. Note that it is very easy to get beautiful rainbow-coloured plots which are impressive, but which could also represent complete nonsense. CVE3621 - Geotechnical Engineering 1 - Christian Schembri 26 13 01/11/2021 CVE3621 Geotechnical Engineering 1 Year 3, Semester 1 Lecture 4 Introduction to Rock Engineering Christian Schembri BE&A(Hons), MSc(Lond) DIC, Perit christian.schembri@um.edu.mt CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 1 What is Rock? • • • • A natural material Strength may be highly variable May be fractured and deformed Characteristics depend on the properties of the intact rock and of discontinuities • The main types of rock are: – Sedimentary – Igneous – Metamorphic CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 2 1 01/11/2021 The Rock Cycle source: Fenton (2013) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 3 What is rock engineering? • It is commonly the reverse of structural engineering • In structural engineering we start with nothing and construct, • While in rock engineering we normally start with something and excavate. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 4 2 01/11/2021 Structural vs Geotechnical Engineering Materials Quality of Materials Design Structural Engineering Chosen and specified Controllable Linearly‐elastic (most commonly) Stiffness Moduli Constant Uncertainty Relatively low Geotechnical Engineering Natural Highly variable Elastic to Non‐elastic Variable High Geotechnical engineering design therefore requires a sound knowledge of the properties of the ground CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 5 Burland’s Soil Mechanics Triangle Geotechnical Engineering Structural Engineering CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 6 3 01/11/2021 Fundamentals to keep in mind Geologic Context and Scale • Ask questions like: • From where did this sample come? • What are its origins? • What is its stress history? • What deformation events has it undergone? • So then you can judge how representative it is CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 7 Geologic Context Geologic History, Processes and Tectonics are a good aid in understanding what ground conditions to expect. source: Dart et al. (1993) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 8 4 01/11/2021 Geologic Context source: Schembri (2014) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 9 Geologic Context CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 10 5 01/11/2021 Geologic Context CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 11 Geologic Context CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 12 6 01/11/2021 Geologic Context 13 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Concept of Scale • It is likely that the amount of discontinuities increase with increasing scale therefore strength decreases with increasing scale • What is the scale of the project vis-à-vis the rock scale? CVE 3621 - Geotechnical Engineering 1 – Christian Schembri source: Wyllie and Mah (2004) 14 7 01/11/2021 At same site but at different view scales 3 joint sets Victoria Fault with extensive displacements 1 joint 15 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri CHILE vs DIANE Ideally rock masses are CHILE but because of Rock masses are DIANE Continuous Homogeneous Isotropic Linearly Elastic fractures spatial variations directional variations micro and macro fractures Discontinuous Inhomogeneous Anisotropic Non Elastic The properties of rock depend on the scale we are looking at rock – the chances are that ‘defects’ increase with increasing size CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 16 8 01/11/2021 What Rock Strength? source: Saroglou (2014) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 17 Intact Rock • Intact Rock contains neither joints nor hair cracks. Hence, if it breaks, it breaks across sound rock. • Intact rock strength may be described by: – Uniaxial Compressive Strength (UCS) – Point load strength index CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 18 9 01/11/2021 Uniaxial Compressive Strength (UCS) • UCS : σc = P/Ao • E = σ/εa σc = σu source: ISRM suggested method (1979) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 19 Point Load Strength Index source: ISRM suggested method (1985) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 20 10 01/11/2021 Rock Mass • Rock Mass refers to the in-situ rock, i.e. at a larger scale than considered for the intact rock strength • A rock mass is made up of the rock matrix and discontinuities • The properties of a rock mass depend mainly on the: – Quality of intact rock – Quality of discontinuities – Rock Structure CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 21 Methods of estimating rockmass properties • Laboratory tests on intact rock or on rock with discontinuities (large samples) • Appropriate use of Rock Mass Classification Systems (RQD, Q, RMR, GSI ...) • In situ testing (eg. Pressure monitoring using hydraulic cells, in situ rock deformability) • Back Analysis source: Hudson & Harrison (1997) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 22 11 01/11/2021 Principal Failure Criteria for rockmass • Mohr-Coulomb criterion • Hoek & Brown (1980) criterion is linked with a rock mass classification system – GSI Hoek & Brown is the most widely used criterion for the estimation of rock mass properties Generalized HoekBrown criterion (2002) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 23 Mohr-Coulomb criterion Difficulties with the application of the criterion, however it offers a rapid approximation and is mostly valid for discontinuities CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 24 12 01/11/2021 Hoek-Brown criterion for rock mass Generalized HoekBrown criterion (2002) It is applicable in isotropic conditions that is: • Intact rock • Rockmass with 3 and more joint sets CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 25 Hoek-Brown empirical failure criterion “Since this is one of the few techniques available for estimating the rock mass strength from geological data, the criterion has been widely used in rock mechanics analysis” (Hoek, 1990) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 26 13 01/11/2021 Discontinuity Parameters source: Hudson & Harrison (1997) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 27 Discontinuity Parameters • • • • • • • • • Orientation (Dip direction and dip angle) Number of discontinuity sets Spacing of discontinuities Persistence Surface roughness Joint wall strength Aperture Infill material Groundwater CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 28 14 01/11/2021 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 29 Rock Mass Classification Systems • Due to variability and uncertainties, it is difficult to apply theories fully in practical rock engineering situations • Rock Mass Classification systems aim to compromise and bring together – Engineering theories – Rock properties CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 30 15 01/11/2021 Types of Rock Mass Classifications Qualitative / descriptive (eg. GSI) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 31 Types of Rock Mass Classifications Quantitative (eg. Q, RMR) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 32 16 01/11/2021 Aims of Rock Mass Classifications • Stability assessment – Giving support recommendations (eg. Q system) – Stand-up time (eg. RMR) • Ground support design – Liner thickness, bolt spacing and length (eg. Q system) • Excavation class and support classes • Engineering parameters (only GSI) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 33 A word of caution • No classification is applicable to all possible rock mass conditions – engineering judgment is needed • Describe only “average” conditions The big advantage is that they provide the only means of translating geology into numbers CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 34 17 01/11/2021 Main types of Rock Masses CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 35 Main failure modes of rock mass around tunnels Brittle failure of strong massive rock under high in situ stress levels Formation of a “plastic” zone by shear failure of weak rock under high stresses relative to the strength of the rock mass Gravitational falling or sliding of blocks or wedges defined by intersecting structural features CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 36 18 01/11/2021 Tunnel instability – Rock mass rating, ratio σ1max/σc CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 37 Structurally Controlled Instabilities CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 38 19 01/11/2021 Types of rock slope failures CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 39 20 08/11/2021 CVE3621 Geotechnical Engineering 1 Year 3, Semester 1 Lecture 5 Intact Rock Christian Schembri BE&A(Hons), MSc(Lond) DIC, Perit christian.schembri@um.edu.mt CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 1 Lecture Contents 1. Main properties of Intact Rock 2. Complete stress-strain curve 3. Uniaxial compressive strength 1. Effects of UCS testing configurations 2. Deformability & failure 3. Modes of failure 4. Indirect determination of strength 5. Triaxial testing of intact rock 6. Failure criteria for isotropic rock CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 2 1 08/11/2021 Properties of intact rock • What properties of rock do we need to know? • Why do we need to study them? • What are the methods available to study these properties and the considerations to take? • In which situations are the properties of the intact rock mostly required? • Not easy: – to decide which properties are important, – to determine with confidence, – to apply CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 3 Strength & Deformability of Intact rock • The most used parameters in Rock Engineering works including but not limited to underground excavations, slope cuts and foundations of structures: – Uniaxial Compressive Strength (UCS), σci – Tangent Modulus of Elasticity, Et • These parameters are an aid in conducting engineering assessments of expected mechanisms of excavation and support requirements but form only a part of such assessment • UCS is also widely used in rock mass classification systems CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 4 2 08/11/2021 Comparing in-situ stress with properties of rock such as intact rock strength CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 5 In-situ stress state source: Hudson & Harrison (1997) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 6 3 08/11/2021 In-situ stress measurement • It is not a simple task with test methods which are not easily available • At times using indirect methods or methods that change in-situ stresses • A test method would involve the application of stress on a particular plane which probably would not be a principal plane • In-situ stresses are relieved by the development of cracks/failure in some parts of the rock, therefore stresses would then be distributed to other locations, this will have an affect on any in-situ stress measurement. Ex: drilling a borehole would create a new stress field around its walls 7 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri In-situ stress measurement flatjack method hydraulic flat jack method source: Hudson & Harrison (1997) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 8 4 08/11/2021 Our focus today… • Properties of the intact rock • Simpler to prepare samples in the laboratory and measure these properties • However some difficulties are involved in conserving the natural moisture content, geometrical properties required (diameter, diameter to height ratio, flatness, straightness, perpendicularity), representativeness • Our aim is to familiarise ourselves with the main test methods available within the context of the engineering behaviour of rock 9 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Uniaxial Compression Test ISRM suggested method (1979) During uniaxial compression we may measure the axial and radial deformation Compressive strength, σci = P/Ao (MPa) Young’s modulus, E = σ/ε (GPa) Poisson’s ratio, v = ‐ εr/εa (%) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 10 5 08/11/2021 Young’s Modulus (E) Secant, Es slope of straight line joining the origin to a point on the curve at some fixed % of the peak strength. Tangent, Et slope of the curve at fixed %, usually at 50% of the peak strength. Initial, slope of the curve in the initial portion of loading curve. 11 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Indirect determination of Ei Modular Ratio, MR = Ei / σci (Deere, 1968) • For high MR (>500) one expects brittle behaviour • For low MR (<200) one expects ductile behaviour CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 12 6 08/11/2021 Brittle and ductile behaviour Brittle deformation : process of sudden loss of strength across a plane following little or no permanent (plastic) deformation Ductile deformation : occurs when the rock can sustain further permanent deformation without losing load bearing capacity Yield : Departure from elastic behaviour, i.e. When some of the deformation becomes irrecoverable CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 13 Stiffness and Behaviour at Loading source: Saroglou (2014) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 14 7 08/11/2021 Size and shape effects on strength Size effect : the compressive strength and brittleness reduce for larger specimens due to greater number of microcracks Shape effect : the compressive strength and ductility increase as the aspect ratio (D/L ratio) increases due to the specimen end stress effects of steel platens Elastic Modulus : is not affected much as the relation between overall stress and strain is an average response for many individual aspects of the microstructure source: Hudson & Harrison (1997) 15 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Strength Correction with specimen diameter σc50 = σc / (50/d)0.18 Where σc50 = UCS for specimen with dia. 50mm σc = UCS for specimen with dia. d d = specimen diameter (mm) from Hoek & Brown (1980) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 16 8 08/11/2021 Complete Stress-Strain Curve The complete stress-strain curve was discovered in 1966, providing information on the behaviour of rocks after their peak strength has been reached. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 17 Stress or Strain controlled? • The aim of applying a strain-rate rather than a stress-rate is to obtain the portion of the stress-strain curve at the post-peak region more reliably and hence obtaining a complete stress-strain curve • A stress-controlled test would very likely give us the portion of the curve up to the peak strength – In stress controlled, failure would be violent and explosive – This section of the curve is usually all that is needed for concrete, as the peak strength is defined as failure for concrete. Concrete does not have a post-peak curve, it breaks completely. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 18 9 08/11/2021 Definitions • Peak strength : maximum stress that the intact rock can sustain (UCS or σci) • Residual strength : minimum strength of rock generally after considerable post peak deformation • Pre-peak part of the graph is normally referred to as the elastic range while the post-peak part is normally referred to as the plastic range, however only till about 50% of UCS we have close to elastic-behaviour CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 19 Are we interested in the Complete Stress-Strain curve? • In most local situations, NO • We may be interested: – for research purposes, – for large-scale structures such as large dams or large span bridges, – for deep tunnels where high in-situ stresses are not avoidable CVE 3621 - Geotechnical Engineering 1 - Adrian Mifsud 20 10 08/11/2021 Practical Example – Tunneling • The complete stress-strain curve may be important for underground structures where a section of the rock may be in its post-peak state. A stress-state change due to a tunnel excavation is shown. At tunnel face (assuming no support) σ3 = 0 after excavation. 21 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Practical Example – Tunneling Ideally one would have a situation where the excavated portion only would be in the post-peak region CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 22 11 08/11/2021 Practical Example – Tunneling • The development or otherwise of a plastic zone around a tunnel depends on: – the ground stresses • higher ground stresses increase chances of having a plastic zone – rock mass strength • lower strength increases chances of having a plastic zone – internal tunnel support • this would act as a confining pressure which would increase the strength of the rock mass CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 23 Tunnelling – Methods of support Forepoles and lattice girders CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 24 12 08/11/2021 Tunnelling – Methods of support Tunnel Boring Machine & Precast concrete arches CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 25 Rock Classification according to strength (ISRM 1981) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 26 13 08/11/2021 Modes of failure σ1 Vertical cracks σ3 =0 σ3 =0 σ1 In uniaxial compression testing it is not uncommon to get vertical cracks (perpendicular to minor axis) Consequently a small confining pressure has significant effect on inhibiting the development of these cracks, with the crack formation gradually changing to shearing as the confining pressure is increased CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 27 Modes of failure in UCS testing Shear failure Cataclasis Axial Cleavage Cataclasis refers to internal crumbling by the formation of a conjugate system of fractures Axial cleavage occurs along the loading direction CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 28 14 08/11/2021 Triaxial Compression In triaxial compression σ2 = σ3 σ1 : major principal stress (axial) σ3 : minor principal stress (confining) The shear failure plane occurs at an angle less than 45o (usually 20o-30o) to the major loading axis 29 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Triaxial Compression – Brittle Ductile Transition ductile brittle CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Another effect of an increasing confining pressure is the transition from brittle to ductile behaviour Below the transition line the material strain softens and above it the material strain hardens 30 15 08/11/2021 Failure modes • In civil engineering, it is important to consider the possible failure modes before trying to plug in values in equations which may not be applicable. • How can a rock slope fail? • How can a foundation fail? • To identify the possible failure modes is much more worthwhile than inputting numbers to estimate bearing capacity blindly. Bearing capacity is one type of failure, which itself may take several forms. Other types of failure may include slope instabilities, punching through weaker strata or into cavities, excessive settlements, … CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Collapse of a structure CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 31 • The lowest UCS results for this site were 6MPa, generally >8MPa with the rock mass being generally massive. • When the thick wall was analysed: – an assumed uniform stress block under the wall resulted in <1MPa imposed stress – Analysing the arch resulted in concentrated stresses at foundation level <2.5MPa (relatively high) • More than comparing estimated bearing capacity values to imposed actions we need to think about: – How were our values derived? In what ways is our model representative of reality? – What are the assumptions of our calculations? – What may go wrong? 32 16 08/11/2021 Indirect determination of strength • To get a rough estimate of strength values with use of simple and cheap methods – Schmidt hardness test (Schmidt type L) – Point load test – Ultrasonic test • One should be very cautious when using indirect measurements of strength in design and preferably should not rely on such values CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 33 Schmidt Hammer (type L) ISRM (1978) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 34 17 08/11/2021 A small aside – from Michie et al. (2014) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 35 A small aside – from Michie et al. (2014) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 36 18 08/11/2021 Point Load (PL) test De2 = D2 De2 = 4DW / π Is = P / De2 F = (De / 50)0.45 Is(50) = FIs σc = k.Is(50) (diametral) (other shapes) (uncorrected PL) (size correction factor) (corrected PL to 50mm dia. core) (correlation with UCS) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri ISRM (1985) 37 Correlation of point load strength with UCS strength • On average UCS is 20 to 25 times the point load strength (Is(50)) • It can vary between 10 and 50 especially for anisotropic rocks • 100% errors are possible CVE 3621 - Geotechnical Engineering 1 – Christian Schembri ISRM (1985) 38 19 08/11/2021 Ultrasonic test Linear correlation of wave velocity with uniaxial compressive strength in the form of, VP = a +bσc VP,S = L / tP,S CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 39 Strength Criteria for Rock • Mohr-Coulomb failure criterion • Hoek-Brown criterion CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 40 20 08/11/2021 Mohr-Coulomb criterion 41 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Hoek-Brown criterion for intact rock Hoek-Brown criterion (2002) – Empirical for larger m for smaller m CVE 3621 - Geotechnical Engineering 1 – Christian Schembri This criterion was obtained by fitting curves to experimental triaxial data. It can be determined statistically by triaxial tests for σ3 in the range 0 < σ3 < 0.5 σci 42 21 08/11/2021 Generalized Hoek-Brown criterion (2002) m – relates to degree of ‘particle interlocking’, for intact rock it is high and reduces as brokenness increases s – relates to the degree of fracturing. It is equal to 1 for intact rock and tends to zero as strength reduces from peak to residual a = 0.5 for intact rock CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 43 Hoek-Brown criterion for rock mass Rock mass strength can be determined if the following are known: • Uniaxial compressive strength of intact rock, σci • Parameter, mi • Geological Strength Index, GSI • Disturbance factor, D (varies from 0 to 1) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 44 22 08/11/2021 Tutorial • In order to calculate the strength and deformation properties of the intact rock, samples were tested in the laboratory. • The following laboratory tests were executed: – Determination of rock density – Point load tests – UCS tests with measurement of deformation modulus, Ei • The results are presented in the next slides and can be considered as representative for the intact rock. 45 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Density (kN/m3) Is50 (MPa) UCS σc50 (MPa) Ei (GPa) Density (kN/m3) Is50 (MPa) UCS σc50 (MPa) 27.1 39.0 83 27.5 80.8 27.4 55.6 78 27.5 31.4 27.1 2.2 49 92 27.3 69.9 27.3 2.5 62 80 26.4 109.8 27.0 3.1 73 69 26.4 64.2 27.4 3.8 82 95 27.8 47.8 26.7 1.6 46 68 27.3 52.6 26.5 2.3 67 85 25.1 45.9 27.6 45.9 27.4 103.7 27.5 82.3 27.0 60.8 27.4 71.3 27.4 54.7 27.5 49.9 27.7 75.2 27.2 35.9 27.6 27.2 27.3 21.0 27.3 80.1 27.2 63.2 27.2 33.9 26.4 22.5 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Ei (GPa) 46 23 08/11/2021 Question A 1. Calculate the mean values of the following properties for the intact limestone. – Density – Point load strength – Uniaxial compressive strength – Deformation modulus 2. Define the relationship between point load strength and uniaxial compressive strength. 3. Define the value of MR (Ei/σci) and compare with literature findings. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 47 Question B 1. Apply the Hoek & Brown failure criterion for the intact limestone for a range of confining stress between 0 and σci/2. Plot the failure envelope in a σ3 – σ1 graph. Note: Assume mi = 10 for limestone CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 48 24 15/11/2021 CVE3621 Geotechnical Engineering 1 Year 3, Semester 1 Lecture 6 Discontinuities and Rock Mass Classifications Christian Schembri BE&A(Hons), MSc(Lond) DIC, Perit christian.schembri@um.edu.mt CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 1 Lecture Contents 1. 2. 3. 4. 5. Discontinuity parameters Definition of rock mass Rock Quality Designation, RQD Rock mass classifications Stand-up time or primary support design using rock mass classifications CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 2 1 15/11/2021 Recall: Discontinuity Parameters source: Hudson & Harrison (1997) • Rocks do not behave according to their intact properties primarily due to discontinuities. • We need to know the distribution and frequency of discontinuities. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 3 Discontinuity orientations • Orientations of discontinuities are described by: – Dip angle – Dip direction • Discontinuities are almost never completely random, but arranged in a number of orientations forming joint sets • Joint orientations depend on the stress field causing them CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 4 2 15/11/2021 Discontinuity orientations • Described by: – Dip angle – Dip direction 5 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri What is rock mass? Rock mass = Intact rock + Discontinuities Discontinuity sets Intact Rock Discontinuities Surface Outcrop Intact Rock Borehole data CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 6 3 15/11/2021 Rock Quality Designation (RQD), (Deere, D.U. and Deere, D.W. 1963) from borehole data Or from scanline data CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 7 Rock Quality Designation (RQD) • Prior to RQD, rock quality information was only available from geologists’ descriptions and total core recovery (%) • RQD is a modified total core recovery • In 1970s it formed a basic element of several classification systems • Main advantages: – An exploratory tool, – Red-flags damaged rock zones, – Simplicity and reproducibility, – Provides an opportunity for comparing rock mass CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 8 4 15/11/2021 Total Core Recovery (TCR) Solid Core Recovery (SCR) Rock Quality Designation (RQD) CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 9 Project Decisions based on RQD • An analysis of the RQD may lead to: – Relocation of structures or excavations (ex. tunnels), – Change in the choice of foundation level, – Identification of zones of weakness which may require a careful approach, – Additional investigation. • The use of RQD cannot be separated from keen geological observation. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 10 5 15/11/2021 n 89, L = 14m λ (m-1) = n/L = 89/14 =6.36 fractures/m xavg. (m) = L/n =14/89 =0.16m Difficulty to identify natural from drilling fractures and to count 11 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Fractures – Probability Density Function Discrete distribution n RQD = 100 Σ (xi) /L % i=1 Continuous distribution If we integrate for x=0.1m to infinity we will derive the below equation for the RQD considering only intact pieces larger than 100mm RQD = 100 e-0.1λ (0.1λ+1) % In any given length there are many closely spaced fractures and only a few long intervals without fractures. Such a distribution satisfies a probability density function as shown. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 12 6 15/11/2021 Possible bias of RQD data C A D B Would the RQD value differ if we drill in the direction CD instead of AB? CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 13 Possible bias of RQD data Bias to the length of coring run Assume a 300mm highly fractured zone: Coring run RQD 3m 1 – (0.3/3) = 90% 1.5m 1 – (0.3/1.5) = 80% 0.5 1 – (0.3/0.5) = 40% RQD can be re-calculated to “artificial run lengths” such as to standardise to the same “length of coring”. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 14 7 15/11/2021 Rock Mass Classification Systems • Experience shows that there is a link between the quality of a rock mass and its engineering behaviour • By defining a rock classification scheme based on rock quality, quantified by a few, easily assessed parameters, and correlating that rock classification with engineering behaviour, the response of rock mass system to an engineering intervention can be estimated. 15 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Rock Mass Classification Systems An aid in assessing the discontinuities in a rock mass apart from other aspects. source: Hudson & Harrison (1997) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 16 8 15/11/2021 Rock Mass Classification Systems 1. Rock Mass Rating, RMR (Bieniawski, 1989) 2. Q-system (Barton et al., 1974) 3. Geological Strength Index, GSI (Hoek, 1998) • These were generally developed from tunnelling experience in hard and discontinuous rocks • Various modifications have been attempted to use the Rock Mass Classification systems for other applications CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 17 Critique of Rock Mass Classification Systems 1. No classification is applicable to all possible rock mass conditions (biased to data used) – therefore expertise is needed 2. Often accuracy is insufficient to obtain values for rock mass parameters 3. Describe only “average” conditions The big advantage is that they provide the only means of translating geology into numbers CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 18 9 15/11/2021 Critique of Rock Mass Classification Systems • The application of such classification systems to rock masses made up of weak and/or complex rocks is complicated by the following factors: 1. Difficult or even impossible to evaluate the classification parameters, 2. Theoretically applicable but practically unreliable since the output results are not fully representative of the rock mass (ex. for marls); 3. Alterability of the rock is not adequately taken into account CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 19 Example of a weak formation • What about the spacing of the discontinuities and their condition? • A low strength would only affect one of the scores in the RMR score. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 20 10 15/11/2021 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 21 Rock Mass Rating, RMR Parameters used in this classification relate to geometry and mechanical condition of the rock: 1. Uniaxial compressive strength of intact rock 2. Rock Quality Designation, RQD 3. Discontinuity spacing 4. Condition of discontinuity surfaces 5. Groundwater conditions 6. Orientation of discontinuities relative to the engineered structure CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 22 11 15/11/2021 Rock Mass Rating, RMR What does the RMR not take into account? • The depth – stress level; • Weak rock masses due to difficulty to evaluate the classification parameters, achievement of true representativeness of the rock mass due to not penalising the rock for all other parameters apart from UCS. All together this gives a high score, as in our previous example of marl. 23 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Tutorial – General Data Parameter Value Persistence 1‐3m Groundwater None Discontinuity type Bedding Joints (2 sets) • • • • Notes Based on field observations No signs of groundwater table were encountered in boreholes. Dip angle 20o‐45o 60o‐90o Consider the UCS obtained from the previous lecture of approximately 58 MPa Strike perpendicular to tunnel axis, drive with dip Assume circular tunnel opening with diameter of 10m No fracture zones CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 24 12 15/11/2021 Tutorial – Borehole Data Depth Formation and description RQD Spacing of Discontinuities Aperture Joint surfaces Infill 0.0 ‐ 12.8m Limestone, moderately fractured 60 – 80% 200 – 600mm and 0.6‐2.0m 1‐5mm Rough and slightly weathered Hard 12.8 – 26.0m Grey limestone, 80 – fresh and locally 90% slightly weathered, slightly to moderately fractured, intersected by 2 joint sets and bedding. Karstic void from 14.5‐14.9m > 2.0m 1‐5mm Slightly weathered Hard Question : Define the primary support design considerations according to RMR and Q systems for each section along the tunnel. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 25 Rock Mass Rating, RMR CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 26 13 15/11/2021 Rock Mass Rating, RMR CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 27 Rock Mass Rating, RMR RMR = Σ(classification parameters) + discontinuity orientation adjustment • Estimation of shear strength parameters (cohesion, friction angle) from RMR is only indicative. • RMR is linked with GSI (GSI = RMR – 5) – be careful!! • Beware of the limitations when using RMR, ex. post-orogenitic geological formations (as marl) with joints CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 28 14 15/11/2021 Tutorial These refer to a rock class II. If we assume a tunnel diameter of 10m we can get an indication of a stand-up time from the graph on the next slide CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 29 Relationship between RMR and stand-up time CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 30 15 15/11/2021 Empirical selection of temporary support measures (Bieniawski, 1989) For 10m wide tunnels – regardless of depth CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 31 Food for thought – data representativeness How would you extrapolate data from investigation boreholes to other rock volumes not investigated? Would you adopt the above approach of dividing the section between boreholes? CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 32 16 15/11/2021 Food for thought – data representativeness The approach of dividing the section between boreholes would be meaningless in most of the cases. A geologic profile would provide the basis on how to divide the section along the tunnel and still this does not provide all the answers!! CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 33 Q-system (Barton et al., 1974) 6 parameters are used in this classification: 1. Rock Quality Designation, RQD 2. Number of discontinuity sets (Jn) 3. Roughness (Jr) of the ‘most unfavourable’ discontinuity 4. Degree of alteration or filling (Ja) along the weakest discontinuity 5. Water inflow (Jw) 6. Stress condition (SRF) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 34 17 15/11/2021 Q-system Q = RQD . Jn Jr Ja . Jw SRF Thus the rock quality index Q is a function of 3 parameters: • Block size (RQD/Jn) • Inter-block shear strength (Jr/Ja) • Active stress (Jw/SRF) Does not consider orientation of discontinuities CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 35 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 36 18 15/11/2021 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 37 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 38 19 15/11/2021 Selection of temporary support measures based on Q-system CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 39 Tutorial If we consider a tunnel diameter of 10m, the support requirements suggested by this system would include bolts of 3m length spaced at 2.2m in both directions and unreinforced shotcrete with thickness of 4 to 10 cm. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 40 20 15/11/2021 Selection of temporary support measures based on Q-system CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 41 Discussion on RMR and Q • Stress is not included in the RMR system • Intact strength of rock is not included in the Q-system • Measured values of discontinuity frequency and RQD depend on the direction of measurement – this is not accounted for in neither RMR nor Q • Similarly, because Erm depends on the discontinuity stiffnesses to a large extent, the modulus is also anisotropic, yet the predictions of E only provide a single (i.e. isotropic) value • Site conditions some times not taken into account – e.g. in situ stress and proximity of the tunnel to the ground surface (RMR does not take into consideration) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 42 21 15/11/2021 In the previous lecture… We obtained the Hoek-Brown failure envelope for the intact limestone. The GSI rock mass classification system may be combined with the Hoek-Brown criterion to obtain the failure envelope for the rock mass. N.B. The data set presented in the Tutorial of Lecture 5 is not a local data set. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 43 Hoek-Brown Criterion • Introduced to provide input data for the analyses required for the design of underground excavations in hard rock. 1. Start from the properties of intact rock 2. Then introduced reduction factors to reduce these properties based on the discontinuity characteristics in a rock mass. • Various authors sought to link geological observations by means of one of the available rock mass classification systems. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 44 22 15/11/2021 45 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Hoek-Brown criterion for rock mass Generalized HoekBrown criterion (2002) σ1 : major principal stress at failure σ3 : minor principal stress at failure σci : uniaxial compressive strength of intact rock mb : reduced value of mi parameter a, s : constants The reduction of intact rock strength to rock mass strength through mb, a, s CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 46 23 15/11/2021 Hoek-Brown criterion for rock mass Rock mass strength can be determined if the following are known: • Uniaxial compressive strength of intact rock, σci • Parameter, mi • Geological Strength Index, GSI • Disturbance factor, D CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 47 What are we trying to achieve? ‘‘The geotechnical engineer should apply theory and experimentation but temper them by putting them into the context of the uncertainty of nature. Judgement enters through engineering geology’’. Karl Terzaghi CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 48 24 15/11/2021 Helpful References • Hudson, J.A. & Harisson, J.P. (2000) Engineering Rock Mechanics, an introduction to the principles. Elsevier Science Ltd. • Goodman, R.E. (1989) Introduction to Rock Mechanics. Second Edition. John Wiley & Sons. • Hoek, E. (2006) Practical Rock Engineering. (freely available from https://www.rocscience.com/documents/hoek/corner/Pra ctical-Rock-Engineering-Full-Text.pdf) • Wyllie, D.C. & Mah, C.W. (2004) Rock Slope Engineering. Civil and Mining. Fourth Edition. London and New York, Spon Press, Taylor & Francis Group. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 49 25 22/11/2021 CVE3621 Geotechnical Engineering 1 Year 3, Semester 1 Lecture 7 Structural Instabilities applied in slopes (1) Christian Schembri BE&A(Hons), MSc(Lond) DIC, Perit christian.schembri@um.edu.mt CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 1 Lecture Contents 1. Definitions 2. The need to represent discontinuity data 3. Method to represent discontinuity data • Equal angle lower hemispherical stereonet (Wolff net) 4. Kinematic feasibility of slope instabilities from discontinuity data CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 2 1 22/11/2021 Recall : Rock failure modes • In rock engineering we encounter 2 main failure modes. Stress Controlled (failure occurs due to high in-situ stress in comparison with rock strength) Structural Controlled (failure occurs along discontinuities) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 3 Today’s focus… Introducing methods that can be used to identify kinematic feasible structural failures as applied in slopes CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 4 2 22/11/2021 A reminder – Discontinuity terms • Dip angle – Gives the steepest angle of descent of a geologic feature to a horizontal plane (described by angles in the range 0°-90°). • Strike – The strike line of a planar feature, is a line representing the intersection of that feature with a horizontal plane. Its direction is given as a bearing with respect to the North (ex. N065o). • Dip direction – This refers to the azimuth of the direction of the dip as projected to the horizontal (which is at 90° to the strike angle). 5 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Dip and dip direction measurements Brunton compass CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 6 3 22/11/2021 Stereographic projections • The stereographic projection is a particular mapping technique that projects a sphere onto a plane. • Therefore it provides a method of representing 3-D data in 2-D space • Various methods exist. Projections may be: – lower or upper hemispherical, polar; – equal area (shows regions on the earth's surface that are of equal area as equal) or equal angle (preserves angles but not distances and areas) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 7 Stereographic projection • In geology, the southern/lower hemisphere is generally used (because the geological features in question lie below the Earth's surface). In this context the stereographic projection is often referred to as the equal-angle lowerhemispherical projection. • The equal-area lower-hemisphere projection is also sometimes used. • We will use the equal-angle lower hemispherical projection (referred to also as Wulff net or stereonet). CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 8 4 22/11/2021 Stereographic projection CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 9 Tutorial – Discontinuity representation A site investigation of rock-cut faces along a road in a mountainous region included the collection of discontinuity data. It was revealed that the main discontinuity planes follow these orientations : – 40/110 (Major plane 1) – 60/120 (Major plane 2) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 10 5 22/11/2021 Tutorial – Discontinuity representation 1. Fill-in and complete the following table : Discontinuity Set Dip Dip Direction Strike 1 2 2. Plot the planes of these discontinuity sets on an equal-angle lower hemispherical stereograph. Annotate your plots. 3. Indicate the poles of these planes on the same stereonet. (The pole refers to the normal of a plane. It can be represented numerically by plunge and trend). CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 11 Slope Instabilities Continuum (CHILE) vs Discontinuum (DIANE) (from Hudson and Harrison) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 12 6 22/11/2021 Main types of slope instabilities Curvilinear slip Planar sliding Wedge sliding Toppling failure CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 13 Curvilinear slip surfaces CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 14 7 22/11/2021 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 15 Toppling failure potential Sliding failure potential CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 16 8 22/11/2021 How do we analyse slope instabilities of a discontinuum? • Kinematic Analysis – preliminary assessment • 'Kinematics' refers to the study of movement, without reference to the forces that produce it. – For some geometries of slope and discontinuities, movement is possible (i.e. the system is kinematically feasible). – For other geometries, movement is not possible (i.e. the system is kinematically infeasible). CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 17 How do we analyse slope instabilities of a discontinuum? • We have seen the 4 main types of slope instabilities • Discontinuity data (orientation) can be plotted on a stereograph • We normally carry out kinematic analysis for slopes having a possible failure plane (discontinuum). • However it is not possible to kinematically analyse curvilinear failures since a trend of discontinuities would not be identified • Stability analysis would be the next step. This analysis involves the resolution of actions and the resistances along possible failure planes. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 18 9 22/11/2021 Kinematic Analysis – Planar Failure Geometry of slope exhibiting planar failure CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 19 Kinematic Analysis – Planar Failure For plane instability to occur the following 4 criteria should be satisfied: 1. The dip of the slope must exceed the dip of the potential slip plane (ψf > ψp) 2. The dip of the potential slip plane must be such that the strength of the plane is reached (In the case of a friction-only plane this means ψp > φ) 3. The potential slip plane must daylight on the slope plane 4. The dip direction of the sliding plane should lie within approximately +/-20o of the dip direction of the slope face. (empirical) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 20 10 22/11/2021 Kinematic Analysis – Planar Failure 20o 20o 40/110 Slide plane Φ=35o ψp ψf 20o 20o 60/120 Slope face 21 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Kinematic Analysis – Planar Failure • Instability overlay for planar failure for use with poles • Poles located within the envelope indicate a planar failure potential In this particular example: Φ = 30o Ψf = 75o (slope dip) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 22 11 22/11/2021 Field Trip at Ghajn Tuffieha – Friday 26th November at 12:00pm Meeting place @ 12:00 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri To bring with you: 1. Camera 2. Notebook 3. Pencils/Biros to take notes and sketch 4. Handout to be delivered 5. A good brain and eyes to make observations of ground features 23 12 29/11/2021 CVE3621 Geotechnical Engineering 1 Year 3, Semester 1 Lecture 8 Structural Instabilities applied in slopes (2) Christian Schembri BE&A(Hons), MSc(Lond) DIC, Perit christian.schembri@um.edu.mt CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 1 Main types of slope instabilities Curvilinear slip Planar sliding Wedge sliding Toppling failure CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 2 1 29/11/2021 Kinematic Analysis – Wedge Failure Geometry of slope exhibiting wedge failure CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 3 Kinematic Analysis – Wedge Failure For wedge instability to occur the following 3 criteria should be satisfied: 1. The dip of the slope must exceed the dip of the line of intersection of the two discontinuity planes associated with the potentially unstable wedge (ψfi > ψi) 2. The dip of the line of intersection must be such that the strengths of the two planes are reached (In the case of friction-only planes possessing the same angle of friction this means ψi > φ) 3. The line of intersection must daylight on the slope plane. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 4 2 29/11/2021 Kinematic Analysis – Wedge Failure Stereoplot depicting wedge failure Stereoplot showing the range of orientations of the line of intersection that form a wedge failure CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 5 More terms • Plunge – Gives the steepest angle of descent of a linear feature to a horizontal plane (described by angles in the range 0°-90°). • Trend – Refers to the direction of a linear feature in the horizontal plane. Its direction is given as a bearing with respect to the North (ex. N065o). CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 6 3 29/11/2021 Kinematic Analysis – Wedge Failure • Instability overlay for wedge failure for use with intersections • Intersections located within the envelope indicate a wedge failure potential In this particular example: Φ = 30o Ψfi = 75o (slope dip) CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 7 Tutorial 2 – Kinematic Analysis 1. On a stereographic projection plot the following fault planes: – Fault 1 with a dip of 20o and a dip direction of N320o – Fault 2 with the orientation of 45o/210o 2. Plot the line of intersection and read off the trend and plunge of this line. 3. Assume a vertical cut is made with the normal to the excavation face trending at N260o. Plot this excavated face on the same stereoplot. 4. Assume φ to be equal to 25o. Plot the planar and wedge instability overlays and determine whether these failures are kinematically feasible in this case. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 8 4 29/11/2021 Tutorial 3 – Kinematic Analysis A quarry is to be opened in a rock mass which contains 4 fracture sets with dip directions and dip angles as follows: Joint Set 1 2 3 4 Dip /Dip direction 64/292 37/151 76/052 16/020 The rock mass can be considered dry and the angle of friction for all fractures is 30o. Consider the primary potential modes of instability (consider plane and wedge failures only for now) at 15o intervals of dip direction (i.e. 0o, 15o, 30o, ... , 345o, 360o) and use kinematic feasibility techniques to prepare a table showing the steepest safe slope and the respective critical failure mode at each azimuth. Now assume that the friction angle is not known (i.e take as equal to 0o) and prepare a similar table as in the first part. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 9 5 06/12/2021 CVE3621 Geotechnical Engineering 1 Year 3, Semester 1 Lecture 9 Structural Instabilities applied in slopes (3) Christian Schembri BE&A(Hons), MSc(Lond) DIC, Perit christian.schembri@um.edu.mt 1 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Toppling failure – 2 main types Direct block toppling of columns of rock CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Flexural toppling of slabs of rock 2 1 06/12/2021 Kinematic Analysis – Direct block toppling Failure For direct block toppling instability to occur the following 2 criteria should be satisfied: 1. There are two sets of discontinuity planes whose intersections dip into the slope 2. There is a set of discontinuity planes to form the bases of the toppling blocks These conditions provide the formation of complete rock blocks. 3 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Kinematic Analysis – Direct block toppling Failure • Instability overlay for direct block toppling failure for use with both intersections and poles • For very steep slopes the failure overlay may extend beyond the -20o to +20o orientations from the dip direction of the slope CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 4 2 06/12/2021 Illustration of the direct toppling instability modes (Hudson & Harrison, 1997) 5 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Tutorial 4 – Kinematic Analysis A road cut is being proposed through a rock mass having the following main fractures: Joint Set 1 2 3 Dip /Dip direction 10/290 70/115 90/025 Assume that the road can take any direction. Which longitudinal road directions would you opt out so as to eliminate the possibility of direct rock toppling and flexural toppling failures on any of the two sides of the road? Assume that direct rock toppling failure can occur for fractures that have their direction within +/-20o to the normal of the cut-face. CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 6 3 06/12/2021 Kinematic Analysis – Flexural toppling Failure For flexural toppling instability to occur the following 2 criteria should be satisfied: 1. There is 1 set of discontinuity planes dipping into the slope, at a sufficiently high angle to generate inter-layer slip 2. The dip direction of the slip planes should lie within approximately +/- 20o of the slope No requirement for a discontinuity set forming the bases of the blocks in this case. 7 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Kinematic Analysis – Flexural toppling Dip direction o of slope 20 80/130 Slide plane 20o ψ 50/295 Slope face Φ=35o β For flexural toppling failure to occur (90 - ψ) + φ < β CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 8 4 06/12/2021 Kinematic Analysis – Flexural toppling CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 9 Kinematic Analysis – Flexural toppling CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 10 5 06/12/2021 Tutorial 5 – Kinematic Analysis Consider the case of a rock mass having the following main fractures: Joint Set 1 2 Dip /Dip direction 75/190 40/020 1. Assume a friction angle φ = 30o. Imagine that a beach is located exactly at the foot of a cliff made up of this rock mass with its normal having a trend of 110o. Is flexural toppling kinematical feasible in this case? 2. At which slope angle would this kind of failure become kinematical unfeasible if we assume a slope dip of 90o? 3. You are concerned that in actual fact φ is more realistically equal to 20o. What initial observations would you suggest to determine φ? CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 11 6 09/12/2021 CVE3621 Geotechnical Engineering 1 Year 3, Semester 1 Lecture 10 Rock Engineering in Practice Christian Schembri BE&A(Hons), MSc(Lond) DIC, Perit christian.schembri@um.edu.mt CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 1 Before we start, allow me to make mention of some reminders CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 2 1 09/12/2021 CHILE vs DIANE Ideally rock masses are CHILE Continuous Homogeneous Isotropic Linearly Elastic but because of fractures spatial variations directional variations micro and macro fractures Rock masses are DIANE Discontinuous Inhomogeneous Anisotropic Non Elastic The properties of rock depend on the scale we are looking at rock – the chances are that ‘defects’ increase with increasing size 3 CVE 3621 - Geotechnical Engineering 1 – Christian Schembri Rock mass = Intact rock + Discontinuities Discontinuity sets Intact Rock Discontinuities Surface Outcrop Intact Rock Borehole data CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 4 2 09/12/2021 Structural vs Geotechnical Engineering Materials Quality of Materials Design Structural Engineering Chosen and specified Controllable Linearly‐elastic (most commonly) Stiffness Moduli Constant Uncertainty Relatively low Geotechnical Engineering Natural Highly variable Non‐elastic Variable High Geotechnical engineering design therefore requires a sound knowledge of the properties of the ground CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 5 Burland’s Soil Mechanics Triangle Geotechnical Engineering Structural Engineering CVE 3621 - Geotechnical Engineering 1 – Christian Schembri 6 3 09/12/2021 Wedge sliding failure – Site 1 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 7 Wedge sliding failure – Site 2 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 8 4 09/12/2021 9 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Rock block failure – Site 3 Movement in existing structures adjacent to sites being excavated CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 10 5 09/12/2021 Rock Wedges – Site 4 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 11 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 12 6 09/12/2021 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 13 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 14 7 09/12/2021 Rock Wedges Site 5 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 15 Rock Wedges Site 6 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 16 8 09/12/2021 Is failure in rock engineering avoidable? • The properties and form of rock masses vary considerably • It may be possible to predict rock mass properties and geometry however with: – a degree of uncertainty – a limited amount of knowledge • The engineering behaviour of rock would then need to be predicted with further layers of uncertainty due to lack of reliability in determining the parameters and imprecise modelling CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 17 Is failure in rock engineering avoidable? • The likeliness of rock failure may be difficult to determine with precision. • Risk of rock failure may be reduced through: – A good ground investigation – Through the phasing of ground investigation such that one phase informs the next – A proper identification of the project requirements – A proper identification of possible failure modes CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 18 9 09/12/2021 Is failure in rock engineering avoidable? • The observational method in geotechnical engineering is officially documented in clause 2.7 of MSA EN 1997-1 Eurocode 7 – Geotechnical Design. General Rules. • This approach involves careful observation of the rock mass as works progress, collating a database of rock mass characteristics in the process, in such a way that the expected behaviour can be estimated, and if necessary, mitigated. It allows for informed decisions on rock mass stability prior to approaching the more critical areas. 19 CVE 3621 - Geotechnical Engineering 1 - Christian Schembri The Observational Method A sliding plane away from the loaded area/site boundary Apertures of discontinuities and variable rock mass qualities CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 20 10 09/12/2021 The Observational Method Provides an opportunity for obtaining first hand experience of the ground. First hand visual observations and obtaining a feel of the rock through the use of simple tools such as the geologic hammer are very valuable in engineering practice and research alike. CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 21 The collection of data as work progresses gives an opportunity for supervising works, the obtaining of a representative data set and the time to devise structurally sound solutions. CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 22 11 09/12/2021 Analysis using discontinuity surveys Failure possible (Y/N) Comments Shallower Steeper Intersections within envelope Yes Possibility from intersection of J3 and J4. Plunge of intersection is 72o. 36o 86o Poles within envelope Negligible Only 2 poles within envelope. 60o 90o No (minimal) Condition not satisfied. Negligible Only 2 poles within envelope. Failure Mode Criterion Wedge (green) Planar (red) Direct Toppling (orange) Flexural Toppling CVE 3621 - Geotechnical Engineering 1 - Christian Schembri Poles and intersections within envelope Poles within envelope Discontinuities dip angles at which failures may occur 85o 89o 23 Combining visual observations with discontinuity analysis such as stereonets… CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 24 12 09/12/2021 …gives information whether a pole refers to a major or minor discontinuity in terms of the discontinuity properties Orientation (Dip direction and dip angle) Discontinuity Sets Spacing Persistence Surface Roughness Joint Wall Strength Aperture Infill Material Groundwater CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 25 Site work should not be limited… • Towards identifying wedges or sliding planes only • But should be directed towards understanding the geologic context and therefore a number of other geologic features CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 26 13 09/12/2021 Site work should not be limited… This aptitude will help us to identify a number of ground processes which will aid us in identifying the possible ground hazards and imposed actions for which we would need to design. CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 27 Rock fracturing may be related to various ground processes such as land slides Deep seated landslide in Blue Clay resulted in the rock cliff above to retreat CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 28 14 09/12/2021 Effect on man-made structures CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 29 Variety of ground engineering problems CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 30 15 09/12/2021 Design of foundations on karstic rocks One should first attempt to characterise the voids such as their spatial distribution, size, infill and surrounding rock quality A number of techniques are available CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 31 Design of foundations on karstic rocks Characterisation would be followed by the identification of plausible failure modes. One would then design for redundancy such that if a particular failure occurs, the supported structure would not collapse or possibly settle. Solutions may include: • The construction of foundation beams to bridge any voids (allowing for redundancy) • The treatment of voids through grouting/concreting • The use of deep foundations which may be combined with shallow foundations CVE 3621 - Geotechnical Engineering 1 - Christian Schembri 32 16
