Items 1 - 6 SHEAR STRENGTH OF SOILS • Resistance to shear forces • Coulomb's law Now , let us start our study of soil mechanics and foundations. The basic aim of Soil Mechanics and Foundation Engineering written by Dr.K.R. Arora is to present the fundamentals of the subject in a simplified manner. ''Geotechnical Engineering'' may be considered to include both soil mechanics and foundation engineering. In fact, according to Terzaghi, it is difficult to draw a.
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The first is to present basic concepts and fundamental principles of soil mechanics and foundations in a simple pedagogy using the students' background in. Practices of Soil Mechanics an d Foundation Engineering. This was constructed in the 17th century principles and practices of soil mechanics and foundations . Proceedings of the Eighth Regional Conference for Africa on Soil Mechanics and Foundation Engineering /Harare / Geotechnical evaluations for tailings.
Available in all digital devices Snapshot About the book About The Books Soil Mechanics And Foundation Engineering provides detailed description of the various properties and analysis of the behaviours of different types of Soils and Soil deposits, over which are rested the foundations of the different types of structures, like buildings, bridges,roads, machines, etc. The design of the different types of foundations to be adopted to suit particular soil deposits and the proposed structure, without causing excess differential or total settlement or any other failure of the underneath soil, to ensure the safety of the structure, has been explained in this volume in a simple language. The design of stable shapes for earthen embankments has been also exhaustively covered. The soil reinforcements and geotextiles, being used in modern days, have also been described in details with practical examples. The expansive and collapsible soils have also been described, giving details of special precautions required to be taken in providing structures onsuch soil deposits.
Water is allowed to flow through a cylindrical sam ple of soil under a constant head II. The outflow Q is collected in a graduated cylinder at a convenient duration t. A compacted soil sample or a sample extracted from the field is placed in a metal or acrylic cylinder Fig. Porous stones are positioned at the top and bottom faces of the sample to prevent its disintegration and to allow water to percolate through it.
Water flows through the sample from a standpipe attached to the top of the cylinder. The head of water h changes with time as flow occurs through the soil. At different times, the head of water is recorded.
Let dh be the drop in head over a tim loss in the tube is FO R the cross-section al area, s length of the soil sample, and h is t. The constant-head test is used to detennine the coefficient ofpenneability of coarse-grained soils.
The falling-head test is used to detennine the coefficient of permeability offine-grained soils.
The total head was kept constant at 30 cm and the amount of water collected in 5 seconds was 40 cm 3. The tesr,. Strategy From the data given, you can readily apply D t cy Solution 2. Strategy Since this is a falling-head test, you should use Eq. Make sure you are using consistent units.
G Calculate the parameters required in Eq. The soil mass is homQgeneous, isotropic, and of infinite size.
Darcy's law is valid. Flow is radial toward the well. The hydraulic gradient at any point in the water-bearing stratum is constant and is equal to the slope of groundwater surface Dupuit's assumptions. Let dz be the drop in total head over a distance dr. Then according to Dupuit's assumption the hydraulic gradient is.
This test is only practical for coarse-grained soils. Pumping tests lower the groundwater, which then causes stress changes in the soil. Since the groundwater is not lowered uniformly as shown by the drawdown curve in Fig. Consequently, pumping tests near existing structures can cause them to settle unevenly.
You should consider the possibility of differential settlement on existing structures when you plan a pumping test. Also, it is sometimes necessary to temporarily lower the groundwater level for construction. The process of lowering the groundwater is called dewatering. Water, although regarded as the "foe" in geotechnical engineering, can be used to improve soil strength, reduce soil deformations under loads, and reduce the permeability.
Next, we will study how water can assist in the improvement of soils. How can we increase the dry unit weight? Examination iE. A nfodified Pr test was de eloped or c paction of airfields to support hea aire f I ads. In the modifi ed Pro tor tesl, a hamme r with a mass 4. T ieal unit weighl- water content plots are shown in f ig. If Gs is know w. If G s is not known, you can substitute a value of 2. Equation 2. You plot these curves as follows: Substitute arbitrarily chosen values of w, approximately within the range of water content on your graph.
Repeat for a different value of 5. This line represents the mini The achievement of zero Proctor test, using higher leve. You may have seen various types of rollers being used in road construction.
Each type of roller has special mechanical systems to effectively compact a particular soil type. For example, a sheepsfoot roller Fig.
Various types of equipment are available to check the amount of compac- 61 FO R 2. Photos courtesy of Vibromax America, Inc. Three popular apparatuses are 1 the sand cone, 2 the balloon, and 3 nuclear density meters. It consists of a glass or plastic jar with a funnel attached to the neck of the jar.
The procedure for a sand cone test is as follows: FO 62 D ry umt. The cylinder is filled with water. The procedure for the balloon test is as follows: Fill the cylinder with water and record its volume, VI' 2.
Excavate a small hole in the soil and determine the weight of the excavated soil W. Determine the water content of the excavated soil w. Record the volume of wat 6. Calculate the unit weigb; FO nt of a soil at a particular site. Photo courtesy of Seaman Nuclear Corp. Compaction is the densijication of a soil by the expulsion of air and the rearrangement of soil particles. The Proctor test is used to determine the maximum dry unit weight and the optimum water content and serves as the reference for field specijications of compaction.
Higher compactive effort increases the maximum dry unit weight and reduces the optimum water content. Compaction increases strength, lowers compressibility'; and reduces the permeability of soils. A variety offield equipment is used to check the dry unit weights achieved in the field Popular fiel! Mum unit Compaction test results.
Extract the desired Step 4: W e have So' Is are o bserved and recove red during a soil investigation of a pro oseCl site. A s9-i invest igati n'is an essential part of the design and construct ion of a p ro posed structu al sy te bu ildings, dams, roads and highways, etc. You i!! To eva luate the general sui tabil ity of the site for the p roposed project. To enable an adequate and economical design to be made.
A client may wish 1J ta e a great r risk than normal to save money and set limits on the type At e t of e site investigation.
Some local building codes have provisions that set out the extent 0 a. A sti a ' 0; must be developed in phases. FO 66 Phase rite a eport. The report must contain a clear description of the site, ethods of exploration, soil profile, test methods and results, and t location of the groundwater. During the site visit Phase II , you should work out most of the soil exploration program.
A detailed soil exploration consists of: Numbering of the boreholes or test pits. Planned depth of each borehole or test pit. Methods and procedures for advancing the boreholes. Sampling instructions for at least the first borehole. Changes in the sampling instructions often occur after the first bo 'eho e.
Requirements for groundwater observations. Borings should penetrate at least 1 m into rock. In very stiff clays, borings should penetrate 5 m to 7 m to prove that the thickness of the strata is adequate.
Soil samples are usually obtained by attaching an open-ended thin-walled tube-called a Shelby tube or, simply, a sampling tube-to drill rods and forcing it down into the soil.
The tube is carefully withdrawn, hopefully , with the soil inside it. FO Power augers Truck mounted and equipped continuous flight augers that bar a hole to mm i ai a eter. Augers can have a solid stem. A site investigation is necessary to determine the nature of the soils at a proposed site for design and construction. A soil investigation needs careful planning and is usually done in phases.
A number of tools are available for soil exploration. You need to use judgment as to the type appropriatefor a given project. Redrawn from Blanchet et aI. A brief summary of what we covered follows. Soils are derived from the weathering of rocks and consist of gravels, sands, silts, and clays in decreasing order of particle size. Soils are conveniently idealized as three-phase materials: The physical properties of a soil depend on the relative proportion of these constituents in a given mass.
Soils are classified into groups through their particle sizes and Atterberg limits. Soils within the same group are likely to have similar mechanical behavior and construction use. Flow of water through soils is governed by Darcy's law. A soil mass can be made denser by removing the air constituents through 2. The main physical parameters for soils are the particle sizes, void ratio, liquid limit, plastic limit, shrinkage limit, plasticity and liquidity indices, and the coefficient of permeability.
Water can significantly change the characteristics of soils.
Number of trucks Step 4: Weight of dry soil in one truckload: Wd Weight of water: The cost of downloading the soil and the cost of excavation are the same for each borrow pit. The only cost difference is transportation cost. The table below provides the void ratio and the transportation cost for each borrow pit. Which borrow pit would be the most economical? The dry mass, aft en drying, is grams. Determine the a water content, b void ratio, c salurat a unit weight, and d effective unit weight.
The bulk unit weight and water content of the soil in the borrow pit are A highway fill is to be constructed using this soil. We wjll ve to determine only the two elastk constants om our labo tory or fie ld tests. We ing I!
An importa nt task of a geotechn ical engineer is to determine the st resses and strains that are imposed on a soil mass by externa l loads. It is customary to assume that the st rains in the soils are small and this assumption allows us to apply our knowledge of mechanics of elastic bodies to soils. Small strains mean infi nitesimal strains. For a realistic description o f soils, elastic analysis is not satisfactory.
We need soil models that can duplicate the complexity of soil behavior. In this chapter, we will review some fundamental principles of mechanics and st rength of materials and apply these principles to soils as elastic porous materials. This chapler contains a catalog of a large number of equations for soil stresses and strains. You may become weary of these eq uations but they arc necessary for the analyses of the mechanical behavior of soils.
You do not have. Stresses and strains Mohr's circle E lasticity-Hooke's law 'cs and strength of ' Sample Practical Situation l' 0 stprage tanks. If two separate foundations are placed too close to each other.
An example o f tilting of structures caused by stress overlap is shown in Fig. These silos tilted toward each other at the top because stresse the soi l overlap at and near the internal edges of their fou ndations. The fo ndations are too close to each other.
Total stress u is the stress in the voids. Elastic material: What are normal and shear stresses? What is stress slate and how is it determined? Is soil an elastic material? What are the limitations in analyzing soils based on the assump tion that they soils are elastic materials?
What are shear strains, vertical strains, volumetric strains, and deviatoric strains? How do I use elastic analysis to estimate the elastic settlement of soils and what are the limitations? What are mean and deviatoric stresses?
What are the differences between plane conditions? What is effective stress? We will discuss princi I resses late! Soils cannOI sustain any appreciable"tensile y: A shear sQ"e. JS is Ihe load p er unit area on a plane paraUdto the direction of Ihe shear fo rce. SSu an normal strtSSu on planes oj zero shear Siress. Soils can only sustain compressive stresses. What happens when we apply stresses to a deformable mate rial? From the last section, you may answer that the material deforms, and you are absolutely correct.
Different materials respond d ifferently to applied loads. Next, we will examine some typical responses of deformable materials to apR led loads to serve as a base to characterize the load ing responses of soils.
The loading co litia n we apply here is ca llt ui aXiall Oading. The change in vertical stress i , J 3. The ratio of the radial 0 ateral sttain to the rtical train is ca ll ed Poisson's ratio, v. SSClions 3. P we get different ue '6. In this! If we apply a load P t t hai ca uses a d placement 6. Here , elastic S lope IS E,. The ateria will yield al some value of 0"1, w iell CJ axes. AB, T he essen. An elastic rna trial recO. Soils are dasloplaslie materials. What's next.
I n the next two sections, we will write the genera l expression for Hooke's law, wh ich is t he fu ndamenta l law for linear elastic materials, and then conside r two loading cases appropriate to soils. For a general state of stress Fig. If you know the s'8nu the mate I 1 parameter E and v, you can usc Eq.
E, and v. For example, the vertical displacement. Hooke's law applies to a linearly elastic material. As a first approximation, you can use Hooke's law to calctJlO: For nonlinear materials, Hooke's law is used with an. The stresses and strains in three when applied to real problems. Let us consi er a water tank or an oil tank founded on a mass ;11 trated in Fi 3.
The answer is no, since the stres ' s at th. Hooke' la 'fo r the axisymmetric condition is 3. A plane strain condition is one in which the strain in one or more ai- rections is zero or small enough to be neglected. Calculate the lateral force per unit length. The geotechnical engineer assumed, based on experience, 93 3. Solution 3. Jm a stress cop dition.
The element is dir t U r he center of the tank , so Ihe We have used the elastic equations to ca lcul ate stresses, strains, and displacements in soils assuming that soils are linear, isotropic, elastic materials. We will briefly discuss anisotropic, elastic materials in the next section.
The difference in stresses in induced anisotropy. In the laboratory, the direction of loading of soil samples taken from the field is invariably vertical. Consequently, we cannot determine the five desired elastic parameters from conventional laboratory tests. Graham and Houlsby suggested a method to overcome the lack of knowledge of the five desired elastic parameters in solving problems on transverse anisotropy. However, their method is beyond the scope of this book.
For axisymmetric conditions, the transverse anisotropic, elastic equations are irecti 3. The essential poinls are: Two forms of allisotropy an praenl ill soils. You need 10 Ji. Example 3. Determine by superpositio 0. We now know how to calculate stresses and strains in soils if we assume soils are elastic, homogeneous materials. One of the important tasks for engineering works is to determine strength or failure of materials.
We can draw an analogy of the strength of materials with the strength of a chain. The cain is only as strong as its weakest link.
For soils, failure may be initiated at a poi w ithin a soil mass and then propagate through it; this is known as progressive fai reo The tress state at a point in a soil mass due to applied boundary forces y equal t o the strength of the soil, thereby initiating failure.
Therefore, as e g1 ed to know the stress state at a point due to applied loads. We will using your knowledge in strength of materials. The stresses at these points are the major principal stress, TI! The stress CT, acts on the horizontal plane and the stress CT..
If we d ra w these planes in Mo hr's circle , they intersect at a point, P. Point P is ca lled lhe pole of the stress circle. It is a specia l poi nt because any line passing through the pole will intcr. Let us see how this works. Suppose we wan t to fi nd the stresses on a plane incli ned at an angle a to the horizon ta l plane as depicted by MN in Fig.
Draw a line from P to IT. Determ ine the stresses on a plane inclined at 3 principal stress plane. St,p 1, Use Eqs. The stresses w e have calcu lated are for soils as solid elastic materials, We have not accounted for the pressure within the soil pore spaces. This principle is the most important principle in soil mechanics. The truss deforms from changes in loads carried by each member. If the truss is loaded in air o r submerged in watt! Values of X for a silt are shown in Fig.
To determine the effective stress in a soil mass, the pore water pressure must be known. Pore water pressu res are measured by p.. The effect" stress in a soil mass not subjected to external loads is found from t of the soil and the depth of grou ndwater. The total verticaf ess is 3. You wouldl ave e ncountered capillary action in your physics course when you studied menisci.
W e can get an understanding of capillarity in soils by idealizing the conti nuous void spaces as capillary tubes. Consider a single idealized tube as shown in Fig. T he height at which water will rise in the tube can be fou nd from statics. Summing forces vertically u pward forces are negative. Since T, a, and 'Yw are 3. As water flows through soil it exerts a frictional drag on the soil particles resulting in head losses.
The frictional drag is called seepage force in soil mechanics. From st atic t: For e ample, a canti e er recai mng all , shown in Fig. The retai ned soil left side of wa ll plies.. The path followed by a p,article f wllte depicted by AB in Fig. The effective stress increases and, consequently, an additional outward lateral force is applied on the left side of the wall.
On the right side of the wall, the seepage stresses are upward and the effective stress decreases. The lateral resistance provided by the embedment is reduced. Seepage stresses in this problem playa double ro increase the lateral disturbing force and reduce the lateral resistance in red ing the st bility of a geotechnical structure.
In Chapters 9 through 11, you ill t dy the ffects of seepage on the stability of several types of geotechni FO 1. The effective stress represents the average-SIre carried" y the soil solids and is the difference between the t tal stre s antJ. The effective stress principle applies 0 Deformations of soils are e.. Soils, especially silts and fine ds, dan be affected by capillary action. Capillary action results iwnega five pore wate.
Downward seepage in: Calculate the effecti ve stress. Total stress: Calculate the unit weights. Strategy You ha ve to ". But an element of soil in he 9 ound is als subject d to"fatera l stresses. Next, we will in trod uce an eq uat ion that re lates the ve ieal an late ral effective stresses. We will revisit the atrest coefficient in Chapters 5, 6, and You must remember that Ko applies only to effective not total stresses. To fi nd the latera l total stress, you must add the pore water pressu re.
Remember that lhe pore water pressure is hydrostatic and, at any given depth, the pore water pressures in all direCli ms are equal. F O Strategy The stresses on the horizontal and vertical planes on the soil element are principal stresses no shear stress occurs on these planes. You need to apply Ko to the effective stress and then add the pore water pressure to get the lateral total stress.
A semi-infinite mass is bounded on one side and extends infinitely all other directions; this is also called an "elastic half-space. Equations and charts forseveral types of surface loads based on the above assumptions are presented. Most soils exist in layers with finite thicknesses. The solution based on a semi-infinite soil mass will not be accurate for these layered soils.
In Appendix B, you will find selected graphs and tables for vertical stress increases in onelayer and two-layer soils. A comprehensive set of equations for a variety of loading situations is available in Poulos and Davis An example of a point load is the vertical load Equ lion 3.
Constant depth Q , Ioteelm " Tu '"' 1T. A practit;lI eXamt. JStrip Load A str ;'oad is Ihe load transmitted by a structure of finit e wid th and infinite length o n a soil surface. Two types of strip loads are common in geotcchnical engineering.
One is a load th at imposes a uniform stress o n the soil, for example , the middle section of a long emban kmcnl Fig. The other is a load tha t induces a triangular stress distri bulion over an area of widlh B Fig.
T" "" 1! Below edge: The influence factor for the vertical stress 3. You can program your calculator or usc a spreadsheet program to find It. You must be careful in the last te rm Ian - I in progra mming.
I method. The vertical stress increase under the center of the load is. The area.. Set the scale, shown on the chart, equal to the depth at which the increase 2. We will call this the depth scale. Identify the point on the loaded area below which the stress is required. Let us say this point is A. Plot the loaded area using the depth scale with point A at the center of the chart. Count the number of segments Ns covered by the scaled loaded area.
Calculate the increase in vertical stress i The essential points are: The increases in stresses below"a surjp ce load are found by assuriUng the soil is an elastic, semi-infinite 2. Use the equation for a point load.
Use Eq. The load on the slab is kN. Determine the vertica sl ss increase at a depth of 3 m 3 under the ceoter of the slab. Q neT, poiot C Fig. You shoultf ivide the area so that the point of inlerest is Find the centroid. The scale on the chart is set equal to the; depth. Mean stress causes volume changes. Equation 3. You only need to apply the equations gi ven in the pre T he negative sign for the radial displacement indi a es an expap l tQ.
The strains, in. The maximum lateral displacement applied a t e top is O. Calculate the principal, volumeteic, and dejiatOri1 ains. Strategy You ar? Let us rble 10 a hemispherica ole anH stack the other on top of it Fig. We wilt calt this loading "A". We can represent loading " A" by a Jin as shown in Fig. The line OA is called a load path or a force path. There are now two components offorce. If the frictional resistance at the contacts of the two marbles is less than the horizontal force, the top marble will slide relative to the bottom.
You should recall from your mechanics or physics course that the frictional resistance is fLFz Coulomb's law , where fL is the coefficient of friction at the contact between the two marbles. Our one-dimensional system now has two modes of instability or failure-one due to relative sliding and the other due to crushing of the marbles. The force path for loading "B" is represented by OB in Fig.
The ssential point or principle. We wiU call this load ing condition, loading "1. Conseq uently, we are going to usc the incremental form of the stress invaria nts. Point B in Fig. The implication is that the volume of our soil sample remains constant. In Chapter 5, we will discuss drained and undrained load ing conditions in more detail. For loading " 2," the total stress path is AB. In this book, we will represent total stress paths by dashed lines.
If OU f soil were an isotropic, elastic material, then accordi to Eg. Remember the truss analogy we used for effective stresseb..
In this case, fip cannot be o.. T eslmplicattons or Egs. Since G E. Mimura, and A. Mimura, A. Shrivastava, T. Shibata, and M.
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