Example Tlb
An embankment has a slope of 1 vertical to 2 horizontal. The properties of the soil are c' 25kN m2, lt p' 20 , 7 16kN m3. The height of the embankment is 31 m and the average pore pressure ratio is 0.4. Using Bishop and Morgenstern's charts, determine the factor of safety for the slope. On the charts of n values are plotted a series of dotted lines labelled rue. The authors have shown that if the relevant rue value is less than the actual design ru then the set of charts with the next highest...
Info Qtw
a Wall geometry Fig. 7.15 Example 7.3 Part b CP2 method. a Wall geometry Fig. 7.15 Example 7.3 Part b CP2 method. Using Rankine's theory with 4 gt ' 30 Ka 0.33 Kp 3.0 Minimum depth is required and since Fp 2.0 has already been applied to the pressure distribution, 7.6.5 Treatment of ground water conditions In order to carry out the stability analysis of a retaining wall involving ground water it is necessary to know the values of the water pressures acting on both sides of the wall. If there...
Exercise Ivp
Using the slip circle shown in Fig. 5.36, determine the F values for ru 0.4, 0.6 and 0.8. Plot ru against F. 7 23.3 kN m3, c' 17.1 kN m2, lt j gt ' 37 . Answer By rigorous method F 1.5 1.0 0.5 Using Bishop and Morgenstern's charts, determine the factors of safety for the following slopes i ru 0.5, c' 5.37kN m2, lt f gt ' 40 , 7 14.4kN m3, H 15.2m, slope 3 1. ii ru 0.3, c' 7.2kN m2, lt gt ' 39 , 7 12.8kN m3, H 76.4m, slope 2 1. iii ru 0.5, d 20kN m2, 7 17.7kN m3, lt f gt ' 25 , H 25m, angle of...
H Rts
Owing to the drainage at the top and bottom of the layer the value of u will immediately fall to zero at these points. With the mathematical solution it is possible to determine u at time t for any point within the layer. If these values of pore pressures are plotted, a curve known as an isochrone can be drawn through the points Fig. 10.3b . The maximum excess pore pressure is seen to be at the centre of the layer and, for any point, the applied pressure Fig. 10.3 Variation of excess pore...
T Nsk
12.8.2 Alternative and safer way to determine c' and 4 gt for an unsaturated soil Procedure is to first fully saturate the sample and then to determine c' and 4 gt '. A pressure source is connected to the pore water in the sample which is then increased in pressure. This increase in pressure is referred to as the back water pressure and must be of sufficient intensity so that any air present in the soil will dissolve into the soil water and the sample will become fully saturated. The sample is...
Residual strength of soil
In an investigation concerning the stability of a clay slope, the normal procedure is to take representative samples, conduct shear tests, establish the strength parameters c' and lt gt ' from the peak values of the tests, and conduct an effective stress analysis. For this analysis the shear strength of the soil can be expressed by the equation There have been many cases of slips in clay slopes which have afforded a means of checking this procedure. Obviously when a slope slipped its factor of...
Info Lma
In this case, 0'. When this happens the formula for Ka reduces to Ka cos 0'. Hence Thrust 7Ka 0.819 x 19 x 194.5 kN This thrust is assumed to be parallel to the slope, i.e. at 35 to the horizontal. Horizontal component 194.5 x cos 35 159 kN Increase in horizontal thrust 95 kN m length of wall Instead of considering the equilibrium of an element in a stressed mass, Coulomb's theory considers the soil as a whole. If a wall supporting a cohesionless acting soil is suddenly removed the soil will...
P
SILT M-SOIL , M, plots below A-line m and C may be combined as FINE SOIL, F. CLAY, C, plots above A-line I SILT M-SOIL , M, plots below A-line m and C may be combined as FINE SOIL, F. CLAY, C, plots above A-line I Liquid limit percent Fig. 1.7 Plasticity chart for the BSCS after BS5930 1981 . Liquid limit percent Fig. 1.7 Plasticity chart for the BSCS after BS5930 1981 . The main soil types are designated by capital letters The classification 'F' is intended for use when there is difficulty in...
I Ngj
Beam supports at least 1 m either side Beam supports at least 1 m either side a Arrangement Fig. 8.17 Measurements of set. As an alternative to jetting, vibration techniques can be used to place piles in granular soils. Vibrators are not efficient in clays but can be used if piles are to be extracted. Generally built up with a series of short sections of precast concrete, this pile is jacked into the ground and progressively increased in length by the addition of a pile section whenever space...
Example Vir
Using Fig. 2.9f, determine the loss through seepage under the dam in cubic metres per year if k 3 x 10-6 m s and the level of water above the base of the dam is 10 m upstream and 2 m downstream. The length of the dam perpendicular to the plane of seepage is 300 m. Total seepage loss per year 300 x 8.8 x 60 x 60 x 24 x 365 x 10 6 m3 Figure 2.10 shows a sample of soil encased in a vessel of cross-sectional area A, with upward flow of water through the soil taking place under a constant head. The...
Measurement of soil suction
From a geotechnical point of view there are two components of soil suction as follows 1 Matric suction that part of the water retention energy created by the soil matrix. 2 Osmotic suction that part of the water retention energy created by the presence of dissolved salts in the soil water. It should be noted that these two forms of soil suction are completely independent and have no effect on each other. The total suction exhibited by a soil is obviously the summation of the matric and the...
Info Hgz
The standard force penetration curve, corresponding to 100 per cent CBR has the following values Plunger penetration mm 2 4 6 8 Plunger load kN 11.5 17.6 22.2 26.3 Determine the CBR value of the subgrade. Solution The standard penetration curve is shown drawn in Fig. 11.12. The test points are plotted and a smooth curve drawn through them. In this case there is no need for the correction procedure as the curve is concave upwards in its initial stages. From the test curve it is seen that at 2.5...
Info Jfo
Soil A From the grading curve it is seen that this soil consists of some 57 per cent gravel and 43 per cent sand and is therefore predominantly gravel. The curve has a horizontal portion indicating that the soil has only a small percentage of soil particles within this range. It is therefore gap graded. The soil is a gap graded sandy GRAVEL. Group symbol GPgS. Soil B From the grading curve it is immediately seen that this soil is a sand with most of its particles about the same size. The soil...
Reinforced soil
The principle of reinforced soil is that a mass of soil can be given tensile strength in a specific direction if lengths of a material capable of carrying tension are embedded within it in the required direction. This idea has been known for centuries. The Bible quotes the use of straw to strengthen unburnt clay bricks, and, from ancient times, fascine mattresses have been used to strengthen soft soil deposits prior to road construction. Ziggurats, built in Iraq, consisted of dried earth...
Info Lzd
Fig. 8.14 Allowable bearing pressure from the standard penetration test after Terzaghi and Peck, 1948 . Fig. 8.14 Allowable bearing pressure from the standard penetration test after Terzaghi and Peck, 1948 . level occurs at a depth of at least B below the foundation level. Between these two limits the amount of reduction can be estimated by linear interpolation. If settlement is of no consequence it is possible to think in terms of ultimate bearing capacity using the approximate relationship...
Stress paths in threedimensional stress space
We have considered two different forms of two-dimensional stress paths in Chapters 3 and 9 and we must now examine the form of these paths if they were plotted in three-dimensional space defined by p', q and v. If we consider the plane q-p' then we can plot the effective stress paths for undrained shear in a manner similar to the previous two-dimensional stress paths. Remember that q 03 and that The resulting diagram is shown in Fig. 13.4a. The points A,, A2 and A3 lie on the isotropic normal...
Triaxial Test Cd Mohr Circle
Normal stress Fig. 9.13 Points of maximum shear stress. Normal stress Fig. 9.13 Points of maximum shear stress. If a Mohr circle diagram of stress is examined Fig. 9.13 the point of maximum shear has the co-ordinates s and t where a 1 and 0-3 being the total principal stresses. In terms of effective stresses, a and a'3, the point of maximum shear has the co-ordinates s' and t' where If a soil is subjected to a range of values of a and a the point of maximum shear stress can be obtained for each...
Newmark Influence Diagram Soil
With the Newmark chart in Fig. 4.8, determine the vertical stress increment at a depth of 5 m in Example 4.4. As z is 5 m, the distance AB on the chart represents 5 m to the same scale as that to which the foundation must be drawn. Owing to the symmetry only a quarter of the foundation need be considered Fig. 4.8 , the number of influence units enclosed by this quarter being 13.9. 7Z 4 x 13.9 x 200 x 0.005 56kN m2 This method is simple but can become very tedious it is used for peculiarly...
Behaviour of soils under shear
Before discussing this important subject the following definitions must be established. Overburden The overburden pressure at a point in a soil mass is simply the weight of the material above it. The effective overburden is the pressure from this material less the pore water pressure due to the height of water extending from the point up to the water table. Normally consolidated clay Clay which, at no time in its history, has been subjected to pressures greater than its existing overburden...
Influence charts for vertical stress increments
It may not be possible to employ Fadum's method for irregularly shaped foundations and a numerical solution is then only possible by the use of Boussinesq's coefficients, K, and the principle of superposition. Fig. 4.8 The Newmark chart for vertical stress under a foundation. Fig. 4.8 The Newmark chart for vertical stress under a foundation. An alternative method that removes the numerical work is to utilise the influence charts devised by Newmark in 1942 Fig. 4.8 . It can be shown that, at a...
Example Rbu
A concentrated load of 400 kN acts on the surface of a soil. Determine the vertical stress increments at points directly beneath the load to a depth of 10 m. For points below the load r 0 and at all depths r z 0, whilst from Fig. 4.5 it is seen that K 0.48. This method is only applicable to a point load, which is a rare occurrence in soil mechanics, but the method can be extended by the principle of superposition to cover the case of a foundation exerting a uniform pressure on the soil. A plan...
Info Oyq
Fig. 10.7 The square root of time 'fitting' method. Fig. 10.7 The square root of time 'fitting' method. of suitability. A consolidation test sample is always drained on both surfaces and in the formula H is taken as half the mean thickness of the sample for the pressure range considered. At first glance it would seem that cv could not possibly be constant, even for a fairly small pressure range, because as the effective stress is increased the void ratio decreases and both k and mv decrease...
I 1
Fig. 2.7 Flow net for seepage beneath a dam. Fig. 2.7 Flow net for seepage beneath a dam. maximum along a path normal to the equipotentials and in isotropic soil the flow follows the paths of the steepest gradients, so that flow lines cross equipotential lines at right angles. Figure 2.7 shows a typical flow net representing seepage through a soil beneath a dam. The flow is assumed to be two dimensional, a condition that covers a large number of seepage problems encountered in practice. From...
Consolidation settlement
This effect occurs in clays where the value of permeability prevents the initial excess pore water pressures from draining away immediately. The design loading used to calculate consolidation settlement must be consistent with this effect. A large wheel load rolling along a roadway resting on a clay will cause an immediate settlement that is in theory completely recoverable once the wheel has passed, but if the same load is applied permanently there will in addition be consolidation. Judgement...
Info Emc
Immediate settlement of a thin clay layer The coefficients of Tables 9.1 and 9.2 only apply to foundations on deep soil layers. Vertical stresses extend to about 4B below a strip footing and the formulae, strictly speaking, are not applicable to layers thinner than this, although little error is incurred if the coefficients are used for layers of thicknesses greater than 2.OB. A drawback of the method is that it can only be applied to a layer immediately below the foundation. For cases when the...
Info Bpk
Fig. 8.20 a - c Methods for testing a pile, d Load to settlement relationship. Sometimes the piles to be used permanently can be used to test a pile as shown in Fig. 8.20c. The form of load to settlement relationship obtained from a loading test is shown in Fig. 8.20d. Loading is continued until failure occurs, except for large diameter bored piles which, having a working load of some 25 MN, would require massive kentledges if failure loads were to be achieved. General practice has become to...
Gravity wall
7.2.1 Mass construction gravity walls This type of wall depends upon its weight for its stability and is built of such a thickness that the overturning effect of the lateral earth pressure that it is subjected to does not induce tensile stresses within it. The walls are built in mass concrete or cemented precast concrete blocks, brick, stone, etc. and are generally used for low walls becoming uneconomic for high walls. The cross-section of the wall is trapezoidal with a base width between 0.3...
D Nyd
- I . 1 z 1 7Z 2ttc 1 -- -l-7t B 2-7t c The above formula only applies to a strip footing, and if the foundation is of finite dimensions then the effect of the ends must be included. To obtain this it is assumed that when the cohesion along the perimeter of the sector has reached its maximum value, c, the value of cohesion at some point on the sector at distance r from O is cr cr B. Rotational resistance of an elemental ring, dr, thick Moment about O x7rrdrxr 7r r dr B B Total moment of both...
Info Pkc
The normalised plot is shown in Fig. 13.13. Overconsolidated clays We have established that the stress paths of normally consolidated clays lie on the Roscoe surface and, in order to complete the picture, we must determine whether the stress paths of overconsolidated clays also lie on this surface or whether they have a unique surface of their own. Figure 13.14 shows a series of normalised stress paths of undrained shear obtained from tests carried out on overconsolidated clays. As expected,...
Analogy of consolidation settlement
The model shown in Fig. 10.1 helps to give an understanding of the consolidation process. When load is applied to the piston it will be carried initially by the water pressure created, but due to the weep hole there will be a slow bleeding of water from the cylinder accompanied by a progressive settlement of the piston until the spring is compressed to its corresponding load. In the analogy, the spring represents the compressible soil skeleton and the water represents the water in the voids of...
Desk study
The desk study is generally the first stage in a site investigation. It involves collecting and collating published information about the site under investigation and pulling it all together to build a conceptual model of the site. This model can then be used to guide the rest of the investigation, especially the ground investigation. Much of the information gathered at the desk study stage is contained in maps, published reports, aerial photographs and personal recollection. The sources of...
Ground improvement
A simple definition of in situ improvement of a soil deposit is the increase in its shear strength along with a reduction in its compressibility. 14.5.1 Drainage or consolidation techniques Surcharge loading Surcharge loading is probably the simplest method of ground improvement and can be applied to cohesive soils. The technique involves subjecting the surface of the soil to a temporary loading using some method such as the placing of temporary earth fill, water filled tanks or tension piles...
cosec ip sinip j
Assuming that 6 0.50' 17.5 see page 203 , substituting lt f gt ' 35 , 3 0 , 6 17.5 and -0 90 into the formula for Ka Pa 0.5Ka7H2 0.5 x 0.246 x 19 x 52 58.43 kN This value is inclined at 17.5 to the normal to the back of the wall so that the total horizontal active thrust according to Coulomb, is 58.43 x cos 17.5 55.7 kN. Note If 6 had been assumed equal to 0 the calculated value of total horizontal thrust would have been the same as that obtained by the Rankine theory of Example 6.1. Solution B...
Exercise Daw
A sample of silty clay was found by immersion in mercury to have a volume of 14.88 ml, whilst its mass at natural moisture content was 28.81 g and the particle specific gravity was 2.7. Calculate the void ratio and degree of saturation if, after oven drying, the sample had a mass of 24.83 g. Answer e 0.617, Sr 70 per cent EXERCISE 1.7 A sample of moist sand was cut out of a natural deposit by means of a sampling cylinder. The volume of the cylinder was 478 ml the weight of the sample alone was...
I Yqe
gt T r Sub-base - lt The value of the stiffness modulus of the subgrade is required if the stresses and strains in the pavement and the subgrade are to be calculated. Subgrade strength is expressed in terms of its California Bearing Ratio CBR value. The CBR value is measured by an empirical test devised by the California State Highway Association and is simply the resistance to a penetration of 2.54 mm of a standard cylindrical plunger of 49.6 mm diameter, expressed as a percentage of the...
Site reconnaissance
A walk over the site can often help to give an idea of the work that will be required. Differences in vegetation often indicate changes in subsoil conditions, and any cutting, quarry or river on or near the site should be examined. Site access, overhead restrictions, signs of slope instability are further examples of aspects which can be observed during the walk over survey. 14.3.1 Site exploration methods Test or trial pits A test pit is simply a hole dug in the ground that is large enough for...
Nd B Plp
fs 2N kN m2 fs NkN m2 fs 0.67N kN m2 N the uncorrected blow count at the pile base N the average uncorrected N value over the embedded length of the pile D embedded length of the pile in the end bearing stratum B width, or diameter, of pile. An alternative method is to use the results of the Dutch cone test. Typical results from such a test are shown in Fig. 8.22 and are given in the form of a plot showing the variation of the cone penetrations resistance with depth. For the ultimate base...
Average degree of consolidation
Instead of thinking in terms of Uz, the degree of consolidation of a particular point at depth z, we think in terms of U, the average state of consolidation throughout the whole layer. The amount of consolidation still to be undergone at a certain time is represented by the area enclosed under the particular isochrone, and the total consolidation is represented by the area of the initial excess pore pressure distribution diagram Fig. 10.3a . The consolidation achieved at this isochrone is...
Info Jis
Fig. 1.1 Materials encountered during excavation. A layer of organic soil, usually not more than 500 mm thick, in which humus highly organic partly decomposed vegetable matter is often found. The portion of the Earth's crust affected by current weathering and lying between the topsoil and the unweathered soil below. In humid climates humic acid can be formed by rain water causing decomposition of humus. This acid leaches out iron and alumina oxides down into the lower layers where they act as...
Info Che
Consider the upper soil layer 1-sin 30 _ Pa4 5 0-33 x 16 x 3 16kN m2 Consider the lower soil layer 1-sin 20 ws Weight of upper soil 16x3 q 7 Unit weight of lower soil 24 The active pressure jumps from 16 to 23.5 kN m2 at El. 4.5 m. he 2 4.5 6.5 m Pa0 0.49 x 24 x 6.5 76.3 kN m2 The active pressure diagram is shown in Fig. 6.13b and the value of the total active thrust is simply the area of this diagram 16x 23.5 x 4.5 52.8 x 248.6kN 2 2 b Coulomb theory Consider the upper soil layer For 0' 30 , 6...
Info Yws
5.5.4 Rapid determination of F for a homogeneous, regular slope with a constant pore pressure ratio If on a trial slip circle the value of F is determined for various values of ru and the results plotted, a linear relationship is found between F and ru see Example 5.7 . The usual values of ru encountered in practice range from 0.0 to 0.7 and it has been established that this linear relationship between F and ru applies over this range. The factor of safety, F, may therefore be determined from...
Unsaturated Soils
12.1 Partially saturated, or unsaturated, soils When the voids of a soil contain both air and water the soil is said to be partially saturated. The pressure of the air in the soil is given the symbol ua and the pressure of the water is given the symbol uw. The degree of saturation is defined by the ratio Volume of water r Volume of voids Apart from the research field, partially saturated soils, or unsaturated soils, as they are now being called, have not been given as much attention from the...
Critical State Theory
Up to this point the material contained in the chapters of this book has used three models of soil behaviour the Mohr Coulomb model, for the prediction of soil shear strengths the soil modelled as an elastic medium, for the estimation of stresses induced by applied loads and for immediate settlement problems the soil modelled as analogous in behaviour to that of a dashpot and a spring supported piston, for consolidation settlement evaluations
The Roscoe surface
For any value of the consolidation pressure p gt there will be a corresponding position for A and hence an infinite number of possible planes, drained or undrained, on which stress paths travelling from A to B may lie. A number of planes with their stress paths are shown in Figs 13.1 la undrained and 13.1 lb drained . If we place the two sets of stress paths together we see that they appear to lie on a three-dimensional surface bounded by the critical state line at the top and by the normal...
Specification of the field compacted density
11.4.1 Compactive effort in the field The amount of compactive effort delivered to a point in a soil during compaction depends upon both the mass of the compacting unit and the number of times that it runs over the point, i.e. the number of passes . Obviously the greater the number of passes the greater the compactive effort but, as discussed in the previous section, this greater compactive effort will not necessarily achieve a higher dry density. The number of passes must correspond to the...
Critical state theory 1
Over the last 40 years a fourth model of soil behaviour has been established and stems from the work of Roscoe et al. who, in 1958, suggested that, within saturated remoulded clays subjected to loadings that created a constant and low rate of increasing strain, there existed both a critical void ratio line and a yield surface. Reporting on various triaxial test results the authors showed that, when subjected to this form of loading, clays would reach, and pass through, a failure point without...
Main types of compaction plant
The three main types of compaction equipment are The compaction plant described below is categorised in terms of total mass. The static mass per metre width of roll is the total mass on the roll divided by the width of the roll. Where a roller has more than one axle the machine's category is determined using the roller which gives the greatest value of mass per unit width. Probably the most commonly used roller in the world is the smooth wheeled roller. It consists of hollow steel drums so that...
Exercise Isw
A 2m thick layer of clay, drained at its upper surface only, is subjected to a triangular distribution of initial excess pore water pressure varying from 1000 kN m2 at the upper surface to 0.0 at the base. The cv value of the clay is 1.8 x 10 3 m2 month. By dividing the layer into 4 equal slices, determine, numerically, the degree of consolidation after 4 years. Note If the total time is split into seven increments, r 0.494.
In situ tests carried out during earthwork construction
Tests for bulk density and moisture content must be carried out at regular intervals if proper control of the compaction is to be achieved. American practice, now widely used in the UK, is to take at least four density tests per 8 hour shift with a minimum of one test for each 400 m3 of earthwork compacted. Fig. 11.6 Core cutter for clay soil. 11.5.1 Bulk density determination Core-cutter method Details of the core-cutter apparatus, which is suitable for cohesive soils, are given in Fig. 11.6....
Equilibrium moisture content
The placing of an impervious road surface isolates the soil beneath from rainfall, evaporation and plant transpiration so that, after the construction of such a surface, the water content values within the soil tend to settle down to a set of more or less steady values. At each depth considered a particular steady water content value applies and this value, which is somewhere between the winter and summer values of water content at the same depth when the soil is unprotected, is termed the...