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What is th e specifIC gravity of the soil grains? Substitu ting in Equat ion 2.
A m long scction of a 15 m wide canal is being deepened 1. The efflu ent from the dredge has a unit weight of Jfthe effl uent is being pumped at a rate of L per min utc, how many operational hours will be required to complete the d redge work?
Y"" '" AI m -thick fill is compacted by a railer, and the thickness reduced by 90 mm. If the in i- tial void ratio of the fill was 0. Let's consider a I m area in plan. The undisturbed soil at a borrow pit has a bulk unit weight of The soil from this borrow will be used to construct a compacted fill with a finished volume of 42, m 3 The soil is excavated by machinery and placed in trucks, each with a capacity of 4. In the construction process, the trucks dump the soil at the site, then the soil is spread and broken up.
Assuming each load is to the full capacity, how many truckloads are required to construct the fill? What would be the volume of the pit in the borrow area? How many liters of water should be added to a truckload? The water content of the borrow pit an d the truck must be the same. In add ition, the mass of the soil grains at the fill and the borrow pit is the same. At the borrow pit In the truck Althe fill.
Borrow pit: Compacted fill: M, per truckload is An irregularly shaped, undisturbed soillurnp has a mass of g. To measure the volu me, it was required 10 thinly coat the sa mple wi th wax the mass and volume of which can be neglected and weigh it subme rged in water when suspended by a string. The submerged mass of the sampl e is g. Later, th e wate r content of the sample and the specific gravity of the soi l grains were determined to be Determine the void ratio and the degree of satu ratio n of the sample.
A sample of an irregular lump of saturated day with a mass of The total mass of the coated lump was The volume of the coated lump was determined to be cm l by the water displacement method as used in Worked Example 9.
After carefully removing the wax, the lump of day was oven dried to a dry mass of The specific gravity of the wax is 0. Determine the water content, dry unit weight, and the specific gravity of the soil gr-ains. Show the results graphically and in tabular form. Let's consider g of fly ash and g of sand. Larger void ratios correspond to larger dry densities d.
The void ratio cannot exceed 1. From the expressions for Pm' P Tabulate the specific gravity values of different soil and rock formin g minerals e. Phose Relations A thin-walled sampling tube of a 75 mm internal diameter is pushed into the wall of an excavation, and a mm long undisturbed sample with a mass of When dried in the oven, the mass was 1. Assum ing that the specific gravity of the soil grains is 2.
A large piece of rock with a vol um e of 0. The specific gravity of the rock mineral is 2. What is the weight of this rock? Assume the rock is dry. A soil -water suspension is made by adding water to 50 g of d ry soil , making m! The speci fic gravity of the soil grains is 2. What is the total mass of the suspension? The sample extruded from the mold has a mass of g. Find the void ratio.
If the sam ple is soaked in water at the same void rat io. A sa mple of soil is compacted into a cyli n. Specific graVity of the soil grai ns is 2. Compute the degree of saturation, den- sity. The soil used in constructing an embankment is obtai ned from a borrow area where the in situ void rat io is 1.
The soil at the embankment is requi red to be compacted to a void ratio of 0. If the finishe d volume of th e embankment is 90, m3, what would be the volume of lhe soil excavated al the borrow area?
A suhhase for an ai rport rUllway m wide. Thi s soil is being transported into trucks having a capaci ty of 8 ml. In th e subbase course, the soil w: How many truckloads will be required to co mplete the job?
How many liters of water should be added to each truckload? If the subh. The bulk unit weight and water content of a soil at a borrow pit are A highway fill is being constructed using the soil from this borrow at a dry unit weight of A soil to be used in the construction of an embankment is obtai ned by hydraulic dredging of a nearby canal.
The embankment is to be: The in situ saturated density of the soil at the bottom of the canal is 1. The effluent from the dredging operation, having a density of 1. The specific gravity of the soil grains is 2. How many operational ho urs would be requi red to dredge sufficient soil for the embankment? A contractor needs m1 of aggregate base for a highway construction project. It will be compacted to a dry unit weight of How many tons of aggregate should the contractor download?
J Answer: A sandy soil consists of perfectly spherical grains of the same diameter. At the loosest pos- sible packing, the particles are stacked directly above each other. Show that the void ratio is 0. Phase Relations There are few possible arrangements for a denser packing.
You can with some difficulty show that the corresponding void ratios are 0. Use the diagram shown below to visualize this. See how the void ratio decreases with the increasing number of contact points. In coarse- xrained soils where the grains are larger than 0. Tn fine-grained soils where the grains are smaller than 0. The borderline between coarsc- and fi ne-grained soils is O.
Based on the grain sizes, soils can be grouped as clays. Within these m ajor groups, soils can still behave differently, and we will look at some systematic methods of classifyi ng the m into distinct subgroups.
Let's discuss these th ree separately. In sieve analysis, a coarse-grained soil is passed through a set of sieves stacked with opening sizes increasing upward. Figure 3. When 1. The same exercise is now ca rried out on another soil with a stack of sieves Figure 3. The percentage of soil finer tha n 0. Sometimes in North America, s ieves are specified by a sieve number instead of by the size of the openings.
In the case offine-grained soils, a hydrometer is used to determine the grain size. A hydrom- eter is a floating device used for measuring the density of a liquid. It is placed in a soil-water suspension where about 50 g of fine-grained soil is mixed with water to make m l of sus- pension Figure 3.
The hydrometer is used to measure the density of the suspension at dif- ferent times for a period of one day or longer. As the grains settle, the density of the suspension de- creases.
The time-denSity record is translated into grain size percentage passing data using Stokes' law. The hydrometer data can be merged with those from sieve analysis for the complete grain size d istribution. Since the grain sizes vary in a wide range.
Example 3. Using the data from sieve analysis shown in Figure 3. Let's compute the cumulative percent passing each sieve size and present as: Size mm 9. Iy I '''1' i I Til: The grain size d istribution gives a complete and quantit ative picture of the relative pro portions of the different grain sizes within the so il mass. At this stage. In Example 3. Th e shape of the g rain s ize distribution curve is described through two simple parameters: A coarse-grained soil is said to be well-graded if it consists of soil grai ns represe nting a wide range of sizes where the smaller grains fill the voids created by the larger g rains, thus producing a dense packing.
A coarse-grained soil that can not be described as well -graded is a poorly graded soiL In the previous examplE: Uniformly graded soils and gap-graded soils are two special cases of poorly graded soils.
In uniform ly graded soils, most of the grains are about the same size or vary within a narrow range. In a gap-graded soil, there are no grains in a specific size range. Often the soil contains both coarse- an d fine-grained soils, and it may be required to do both sieve analysis and hydro meter analysis. W-hen it is d ifficult to separate the fines from the coarse, wet sieving is recommended. Here the soil is washed through the sieves. The density of packing is quantified through the simple param- eter, relative density Dr' also known as density index In and defined as:.
Terms such as loose a nd dense are often us ed when referr ing to the density of packing of g ranular soils.
Figu re 3. In terms of unit weights, relative density can be expressed as:. I Loo", Medium dE! When the grai ns are angular there is more interlocking among the grain s. For example, in roadwork, angular aggregates would provide better inte rlocking and resistance against dislodgement. In the loosest state, g of dry sand filled the mold. If the void ratio of this sand at the site is 0. They look like flakes or needles. Their surfaces are electricaUy charged due to a charge imbalance between the cations and anions in their atomic structures.
Since the particles are flakey and finer than 2 j. Large sp4:! To understand the behavior of days, it is necessary to have some knowledge about clay mineralogy. The atomic structure of a clay m: When several of these units are joined together along a common base, they make tetrahedral and octahedral sheets, which are represe nted schematically with the symbols shown in Figures 3.
Sb and 3. An octahedral sheet containing aluminum cations is called gibbsite, and when it contains mag- nesium cations, it is called brucite. Different clay minerals are produced by stacking tetrahedral and octahedral sheets in differ- ent ways. Three of the most common minerals, kaolinite, illite, and montmorillonite, are shown schematically in Figure 3. Kaolinite is formed by stacking several layers of alternating tet-.
Hydro yl or oxygen. They are held together by strong hyd rogen bonds that preven t them from separating. Kaolinite is used in cera mics, paper, paint, and medicine. Illite is fo rmed by stacking several layers 0. They are held together by potassium ions. Montmorilloniles Figu re 3. When water gets between the layers, they are easily separated and there will be a substantial increase in volume.
Mo ntmorillonitic clays arc called expansive or reactive clays. This shrink-swell behavior causes billions of dollars worth of dam age to bUildings and roads across the globe. Other day min erals that are of some interest in geotech ni cal engineering are cl1lorite. There is always a charge imbalance within a d ay particle due to substitution of cations within th e pore water, and the net effect is to make the day particle negatively charged.
The charge deficiency Le. Depend ing on the mineralogy of the day par- ticles and chemistry of the pore water, the clay particles can form different Jabrics.
Two of the extreme situations are dispersed also known as oriented and flocculated fabric s. In a dispersed fabric , most of the d ay particles are oriented in the same direction. In a fl occulated fabric. The scanning electron micrograph of a dis- persed kaolinite clay fabric is shown in Figure Ajanta Sachan, liT Kanpur, India.
Attc rbcrg, a Swedish scic ntist, in for pottery and were later mod ifi ed to suit geotechnical engineering needs by Arthur Casagrande in When a dry fine -grained soil is mixed with wate. Atterberg limits are simply borderline water contents that separate the different consistencies the fine-grained soils can have. These borderline water contents are shrinkaf e limit, plastic limit and liquid limit.
Shrinkage limit SL or w. Plaslic limit PL or w,, is the lowest water content at which the soi l shows plastic behavior. Above the liquid limit LL or lVt , the soil flows like a liquid. These original definitions of the Atterberg lim its are rather vague and are not reproducible, espeCially by inexperienced operators.
Casagrande standardized the test procedures which are discussed below. Soil Classification Plasticity inde: Soil fraction small er than mm is used in the laborato ry tests fo r LL and PL. Liq- uid limit is dctermi ned by two different methods: Casagrande's percu. In Casagrande's percussion cup method, the moist soil pat is placed in the cup and a standard groove is cut using a grooving tool Figure 3.
The cup is raised and dropped over a height of 10 rum , h itti ng a hard rubber or m icarl a plastic base, and th e numbe r of blows required to make the groove dose over In a Swedish fall con e test, a stainless steel conc, having a mass of 80 g and angle of 30, is initi ally positi oned to touc h th e moist soil sample in a sta ndard cup Figu re 3. It is released to fall freely and penetrate the moist soil fo r 5 seconds, and th e penetra tion is recorded at different watcr contents.
The waler content at which the penetration is 20 mm is the li qUid limit. Plastic limit is defined as the lowest water con tent at wh ich the soil can be rolled into a 3 mm 'Is in. Liquidity jndex LI or IL is a measure of how closc the natural water content w n is to the liquid li mit, and is defi ned as: Unear shrinkage LS is a simple tesllo measure the polential of the day to shrink, which is also an indirect measure of the plasticity.
Here, a soil pat mixed at water content near the liquid limit is placed in a standard mold Figure 3. Und erstandably, the clay component in X is more plastic than the one in Y.
This is quantified by the term activity A. Thus, the activities of clays X and Yare 2 and 0. Large r activity values e. Therefore, it is necessary to communicate the soil description as precisely as possible, from the site to th e design office.
A soil classification system does just that. It is a s ,stematic method that groups soils of similar behavior, describes them, and classifies them. The strict guidelines and the standard terms proposed eliminate any ambiguity and make it a universal language among geotechnical engi neers. There are several soil classification systems currently in use. Th e American Association of State Highway Transportation Official s AASHTO cl assification system is quite popular for roadwork where soils are grouped according to thei r suitability as subgrade or embankment m aterials.
Army Corps of Engineers to make it suitable for wider geotechnical applications. The coarse-grained soils are classified based on their grain size distribution and the fine -grained soils based on Atterberg limits. The four major soil groups in the uses,defined on the basis of the grain size, a rc gravel G. Two other special groups aTC organic soils 0 and peat Pt. Organ iC soils are mostly clays containi ng o rga niC mater ial that may have come fro m decomposed living organ isms, plants, and animaJs.
Fine-grained soils are described on the basis of plasticity as low L or high H. These are summ arized in Table 3. Table 3. Fine-grained soils are classifi ed based on Atterberg limits, irrespec tive of the relative pro - portions of d ays and silts, which a re of little value in classifi cation. Most llne- grained soils plot near the A-line. The U-line is the upper limit for any fine -grained soils.
A coarse-grained soil with negli gible fi nes. A coarse-grained soil with substantial fines that can have a significant influence on the soil behavior. A fin e-grain ed soil. A coarse-grained soil with some fi nes that can influence the soil behavior.
All possible symbols and the four groups of the uses are sum ma ri zed in Figure 3.
Group A -8 includes highly orga nic soils e. As with other classifi cation syste ms, sieve analysis and Atterbcrg limits are used in assign ing the above symbols. A-3 soils are clean. Depending on the quadrant they fall into, they ar e assigned symbols A , A-2 -S, A, alld A It is also necessary to assign a numbe r known as group index Gl wiLhi n pa rent heses after the symboL Group index is defined as:.
Gl should be rounded off to the nearest integer and should be taken as zero when negative and fo r soil groups A- I-a, A- I -b, A-3, A, and A- 2-S. This is easier wit h coarse-grained soils where one can includ e q ualitative information on grain size fine, med ium , o r coarse , grain shape, color, homogeneity, gradation, stale oj com - paction or cementation , presence ojjines, etc.
Fine-grained soils can be identi fi ed as days or silts hased on dry. A moist pat of cl ay feels sticky between the fingers. Dry st,-ength is a qualitative measure of how easy it is to crush a dry lump of fine -grained soil between the fingers.
C lays have high d ry strength. A dilatancy test involves placing a moist pat of soil in the palm and shaki ng it vigorously to see how q uickly water rises to the surface. The standard terms used for describ ing d ilatancy are q uick. Silts show quick d ilatancy and clays show slow to none. Based on what we have discussed up to now, a compariso n of clays and nonclays Le. Clays "Ion-clays silts, sands and gravels.
Uniformly graded soils are poorly graded.
Grain size distributions are ma inly for coarse-grained soils; Auerbcrg limits are fo r fines. Clay particles are negatively charged flakes with a high surface area and are smaller than 2 tJ-m in size; they are plastic and sticky cohe- sive. A fine-grained soil is classified as clay or silt based on Atterberg limits- not on relative proport ions. The first t hing one should knm This determines how the symbol is assigned and how the soil is described.
The grain size distribution data fo r three soi ls are given below. C lassify t he three soils. The Ow. OJ ' Ow. Cu, and C values. W ith 6. Since the fines have low dry strength, they a re silt y. It can be classified as well-graded, silty, sandy gravel with a symbol of GW-GM. Soil B is uniformly graded sand, with all grai ns in the range of 0. It can be clas - sified as uniformly graded sand with a symbol of SP.
Soil C is a gap-graded soil that has no grains present in the size range of 0. Therefore, the soil can be classified as gap-graded, clayey gravelly sand with a symbo l ofSP-SC. The grain size distribution curve of a soil is described as:. Is the soil well graded or po orly grad ed? Assuming the largest grain within th e soil is 50 mm, describe the so il with the uses symbol. This equation was p roposed by Fuller and 'Tho mpson for mix design of aggregates in selecting the right mix fo r a well-graded soil.
Classify the following soils using the given grain size distribution an d Atterberg limits data. Fines showing quick dilatancy --? Poorly graded.
Fines have high dry strength --? Clayey gravelly sands.
Gravelly, sandy high-plastic silt. State whether the foll owi ng are true or false. The coefficient of uniformity has to be greater than unity b. The plastic limit is always greater than the plasticity index d. The shrinkage limit is a lways less than the plastic lim it e.
Soils with larger g ra ins have la rger specific surfaces f. How are the density-time measurements in a hydrometer translated into grain size percentage-passing data?
Write a word essay on clay mineralogy cover ing cation exchange capac- ity, isomorphous substitution, and diffuse double layer in relation to what was discussed in 3.
Two coarse-grained Soils A and B have grain size distribution curves that are approxi- mately parallel.
A is coarser than B. Com pare their D IO , Oso, em",,' and emin values, stating wh ich is larger. Give your reasons. Calculate the specific surface of 1 mm, 0. See how the specific surfa ce increases with the reduction in grain size. Compare these values to those of the flakey clay m inerals such as kaolinite, illite, and montmorillonite. The maximum and min imum vo id ratios of a granular soil are l.
What are the porosi ties at maximum and minimum void ratios? Classify the soi ls, givi ng their uses symbols and descriptions. In some cases, there may be more than one. Which of the following is not a valid uses symbol? The sieve analysis data of a soil are given below. The tines showed very low dry strength. Without plotting the grain size distribu tion curve, describe the soil, giving it the uses symbol. Sieve size mm 9. Two samples of crushed mine tailings A and B are mixed in equal proportions by weight.
Find the percentage of fines and the average specific gravity of the grains in the mix. This book has free material available for download from the Web Added Value'" resource center at www. For example, the granular soils at a proposed site for a high-rise building may be in a looser state than desired, suggesting potential future stability problems or settlement problems, or both.
The landfill clay liner that lies at the bottom of a landfi ll may allow morc leachate than desired to flow through. The simplest remedy in both ci rcumstances is to compact the soils to ensure they have adequate strength and stiffness to limit any postconstruction settle- ment and stability problems, and to limit the qua. Compaction is one of th e most popular ground improvement techniques carried out in earthworks associated with roads, embankments, landfi lls, buildings, and backfills behind retaining walls.
Generally, the main objective is to increase the strength and stiffness of the soil and reduce the permeabil- ity of the soil, all of which are achieved through a red uction in the void ratio. Some common machinery used in earthmoving is shown in Figures 4. The soil excavated from the borrow area is transported to the site, whe re it is sprinkled with a specific quantity of water and compacted to the appropriate density. Acti ng like a lubricant, water sticks to the soil grains and facilitates the compaction process, thus den: Sify ing the soiL Reduction in void ratio is a measure of the effectiveness of compaction.
Since void ratio is never measured directly, it is indirectly quantified through the dry density of the compacted earthwork. It can be seen intuitively and in Equation 2.
Figure 4. This is illustrated through Exam ple 4. Example 4. A soil is compacted in a cylindr,ical mold with a volume of cm at six differ- ent water contents, using the same compactive effort Test 1. After compaction, the samples were extruded and weighed.
The same test was repeated. The water contents and wet masses of the samples from the two tests are given. The volume of the compacted sample is: The computed values are shown. The dry density vs. Continued 1. From both tests in Example 4. A further increase in water content results in a reduction in the dry density. Increasing the compactive effort see Example 4.
The optimum water content and the maximum dry density of the two tests are: A curve d rawn through the peaks of all compachon curves with different compactivc efforts on the same soil is known as the line of optimum. The compacted earthwork will have very good geotechnical characteristics Le. Particularly in clayey soils, the behavior of the compacted earthwork is quite sensitive to the water content in the vicinity of the optimum water content.
Therefore, it is necessary to know the optimum water content and the maximum dry density of a soil under a specific compactive effort in order TO specify the right values for the field work. Terms such as dry of optimum or wet of optimum are used depending on if the com pac lion is carried out at a water content less or greater than the optimum water content The phase diagrams of the compacted soil at different water contents are shown in Figure 4.
The variatiuns uf dry density and void rat iu against the water cuntent are shuwn in Figures 4. Air Air Air Air Air. Water Water Water Waler Water. Laboratory compaction tests were developed by R. Proctor in the , replicating the field compaction process in a cylindrical compaction mold with a volume of about 1 liter.
The test details arc summarized in Table 4. Show that the compactive effort im parted to the soil in a standard Proctor com - paction test is kJlm'. Work done per blow "'" 2. Table 4. Hammer drop mm Therefore, in any soil Le. I has a specific value of S. Thus, Equation 4. TIle calculated values are shown. These are plotted as shown. Therefore, it is neces- sary that any compaction test point must lie to the left of the zero air void curve, which is a good check.
II is quite common to show the zero air void curve along with the com paction curves. The S-contours in Example 4. In term s of a, Equation 4. They are not the same. The compac- tive effort can be in the form of static pressures e. Wh ile clays can be compacted effectively by a kneading action, vibrator y com - paction is the most effective in granular soils. In clayey soils in particular, the behavior of the compac ted earthwork can be very sensitive 10 the water content A comparison is given in Table 4.
Compacting dry or wet of optimum has its own advantages and disadvantages. Depending on the expected performance of the compacted earthwork in service.
For example, a landfill liner should have low permeability and ductility to minimi7. On the other hand. In method specification, the engineer representing the client takes responsibility fo r the fin ished product and specifies every detail including type of roller, number of passes.
In end-product specification. The specified requirements gene rally inclu de a narrow range of water content and dry d ensity of the compacted earthwork. This is expressed through a variable known as relative compaction R, defi ned as:. Ie Figure 4. Low ul. Sand cone tests are destructive i.
These control tests are carried o ut on the compacted earthwork at a specified frequency e. When discussing coarse-grained soils, it is possible to specify the density in terms of relative density than relative compaction.
Lee and Singh suggested that they are related by:. Standard Proctor compaction was carried out on a clayey sand, and the compac- tion curve is shown in the figure. Find the void ratio and degree of saturation at the optimum water content. The mass of the soil removed from the hole was g, which became g on drying. Does the compaction meet the specifications? From the figure. At optimum, Gp 2. Pd,iYJd 2" 0.
Sand replacement test: The compaction does not meet the specifications; it satisfies dry density but not the water content. Optimum watcr contcnt and maximum dry density for a specific soil are not ftxed values; they vary with the compactive effort. You can work in terms of densities and masses or unit weights and weights.
In clayey soils, the behavior of compacted earthwork is very sensi- tive to the water content, depending on whether the clay is com- pacted to the dry or wet of optimum. Therefore, a stringent control is necessary. Compaction Draw the zero air vo id curve to see if it in tersects the compaction curve. A field denSity test was later carried out to check the quality of comp action.
A hole was dug in the compacted earthwork and g soil was removed. The volume of the hole, as measured through a sand cone test, was cm'. Does the compaction meet the specifica- tions? Let's use Equation 4. This gives: Plotting these fou r points on the above plot shows that the compaction curve full y lies to the left of the zero air void cur ve.
From the laboratory: Specifi cations: IJ S The control test shows that the compaction meets the specifications with respect to both water content and relative compaction. Stan dard Proctor: Modified Proctor: Plot the compact ion curves along with the zero air void curve and find the opti- mum water content and the maximum dry density for each test. Compaction control tests were carri ed out at four different fi eld locations, and the results are as follows:.
Control Volume of Mass of wet Mass of dry test no. Compute the dry density, bulk density, and the water content fo r each test and plot the points in the above graph along with the compaction curves. Dete rmine which of the four control tests meet the specifications, and give reasons why the specifica tions were not met for the tests that failed. Th e computed values are shown in the plot. Speci fi cations require that: Only the control tests falling with in the sh aded region would meet both water content and relative compaction criteria.
Control test 1: Too dry and low dry density Control test 2: Meets the specificat ions fall. Too wet and low dry density Control test 4: Control test itself is invalid-lies to the right of zero air void curve. Write a SOO- word essay on the diffe rent types of roll ers used in compaction, clearly stating. Include pictures wherevcr possible. Discuss the ground improvement techniques dynamic compaction and vibrof1otatiol1.
Include pictures. A stand ard Proctor compaction test was carried out on a silty clay, using a I L compaction mold. The tests were carried o ut with six different water contents. Every time, the enti re compacted sample was extruded from the metal mold, and the wet and dry masses were determ ined. The test data are summarized below. Mass 01 wet sample g Mass 01 dry sample g Plot the compaction curve and find the optimum water content and maximum dry density.
Plot the void ratio against the ,"vater content in the same plot to show that the void ratio is the min imum at opti m um water content. Draw the zero air void curve. Docs it intersect the compaction cu rve? What would be the degree of saturation of a sample compacted at the optimum water content in a standard Proctor co mpaction test? Why are these two different? A compacted fi ll was made to the following specificat ions: A sand cone test was do ne as part of the control measure.
Here, an cm J hole was dug in to the ground, from wh ich g soil was removed. An 85 g sam ple of this soil was dried in an oven to Determ ine if the compacted earthwork meets the specifi cations h. Find the degree of saturation and the ai r content at the opti mum water content 1. They are made of an assemblage of soil grains of different sizes and shapes. They contain three phases: In geotechnical engineering analyses, the soil mass is often assumed to be a continuous medium for conven ience, where the presence of three phases is neglected and the entire soil mass is assumed to behave as a homoge- neous and isotropic elastic body.
This is far from reality, but it enables us to solve the problem. In a particu late medium where the voids are fi lled with air and water, th e normal stresses CT are shared by the soil grains, watef, and air.
In this chapter. We will not worry about partiall y saturated soils where some of the normal stresses are carried by the air with in the voids. The component of normal Slress acting on the soil grains is known as the effectivI! The remainder of the normal stress carried by the water within the voids is known as pore wliler pressure or neutral stress u. From now o n, we will denote vertical normal stress and horizontal normal stress as 1. Note that pore water pressure.
In this chapter, we will only deal with the vertical stresses. This is often called overburden pressure. Let the saturated unit we ight and sub- merged unit weight be 'Y Al and 'Y' respecti vely. The tota l vertical stress at point X in Figu re 5. The pores are all interconnected, and hence the hydrostatic pore water pressure at this point is:. Therefo re, th e effective verti cal normal stress becomes:.
Figure 5. Totol Stress. When the water table is at some depth below the ground level as shown in Figure 5. I12 5. Example 5. In a sandy terrain, the water table lies at a depth of 3 m below ground level.
Bulk and saturated unit weights of the sand are What is the effective vertical stress at 10 m depth? When the soil is partially saturated, the situation is more complex. Here, the normal stresses on the soil elements are shared by the soil grains, pore water, and the pore air.
Thus Equation 5. In satu- rated soils. When a glass capillary tube of inner diameter d is placed in a d ish containing water as shown in Figure 5. The water column of height h, that appears to be hanging from the inner walls is in equilibrium under two forces: Therefore, for equil ibrium: Sub- stituting these values in the equation above. II, b ecomes:. It is clear from Equation 5. How does this relate to soi ls?
The interconnected voids within the soil skeleton act as capillar y. Negative po'. Total Stress. Capillary rise can vary from a few mm in gravels to several meters in clays. Capillary pressures are similar to suction and hence the resulting po re water pressures are negat ive j. The capillary effects are present when there is no change in total stress. Due to the high capillar y pressures in clays, the effective stresses near the ground level can be significantly higher than we would expect.
Figure S. In other words, water rises into the voids, almost filling them but not having any buoyancy effect. Below the water table, the soil is saturated and submerged. The pore water pressures at A, B, C, and D are given by: This works in all ,soils, in all directions, and at all times.
II is ill significant in coarse-grained soils. Capillary pressures are negative. They increase the effective stresses. Plot the variations of total and effective vertical stresses and pore water pressure w ith depth for the soil profile shown. The values of IT,,, u, and lTv' computed at the layer interfaces are shown.
W ithin a layer, the un it weights being constants 0 ", u, and av' increase linearly. The water table in an 8 m thick silty sand deposit lies at a depth 3 m below the ground level. The en tire soil above th e water table is. The values a,. Note the negative capillar y pressure and the effective stress of To tal Stress.
The soil profile and the plots generated using th c va lucs given in the table are shown in the followi ng fi gu res. The water table is 4 m below the ground level. Plot the variation of a".
Neglect the capillary effects. A river is 3 m deep with the riverbed consis ting of a thick bed of sand having a saturated unit weight o f If the water level rises by 2 m. If the water level drops by 2 Ill , what would be the new effect ive vertical stress at 4 III below the riverbed? The Pacifi c Ocean is m deep at some locations. The seabed consists of a sandy deposit with a saturated un it weight of In a clayey sandy silt deposit, the water table is 3.
The top 2 ill of sand can be assumed to be d ry. The saturated and dry unit weights of the soil are Calc ulate th e effect ive vertical stress at 8 m below the surface. In the context of geotechnical engineering, the porous medium is soils, and the fluid is water at ambient temperature.
A petroleum engineer may be interested in the flow of oil through rocks. An environmental engineer may be looking at the flow of leachate through the com pacted clay liner at thf: Generally, coarser soil g rains means larger voids and higher permeability.
Therefore, gravels are more permeable than silts. Hydraulic conductivity is another term used for permeability, especially in environmental engineering literature. The flow of water through soils is called seepage, which takes place when there is a difference in water levels on two sides upstream and dowl'1stream of a structure such as a dam Figure 6. Sheet piles are watertight walls made of interlocking sections of steel, timber, or concrete that are driven into the ground.
The heads in Equation 6. The elevation head z is simply the height of the point above a datum a reference level , which can be selected at any height. When the point of inter- est lies below the datum, the elevat ion head is negative. At point P in figure 6. I1, and hence the pressure head is Seopage Soil. Sheet pile ,.
Upstream Downstream. Figure 6. Datum B Water o p. Example 6. You will learn the material through several worked examples that are representative of realistic field situations whereby geotechnical engineering principles are applied to solve real-life problems.
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