Soil Compressibility and Settlement PDF

Soil compressibility and settlement Compressibility and settlement  Relationship between ground movement and the stability of related structures is a complex one.  Several mechanisms may produce ground movement and there are many types of structures, each with a varying poten...

Soil compressibility and settlement Compressibility and settlement  Relationship between ground movement and the stability of related structures is a complex one.  Several mechanisms may produce ground movement and there are many types of structures, each with a varying potential to withstand or to be distressed by movement. Compressibility and settlement  Brick and masonry construction are exceedingly brittle and may sustain cracks and even structural damage following very small foundation displacements.  Others may be constructed to sustain movements of considerable magnitude without suffering real damage.  Soil conditions change from before to during and also after construction. Compressibility and settlement  Prediction of these changes presents the most difficult task to the designer.  Most building damage that occurs because of foundation movement occurs when unforeseen soil conditions suddenly arise.  Amount and rate of foundation settlement due to certain mechanisms can be estimated. Compressibility and settlement  Estimates will remain reasonably reliable providing that the soil conditions assumed for the calculation are: i. A fair representation of the actual conditions ii. Likely to persist throughout the life of the building. Potential causes of settlement Compaction Process whereby the soil particles are forced into a closer state of packing with a corresponding reduction in volume and the expulsion of air Vibrations due to traffic movement, heavy machinery and certain construction operations, such as pile-driving, can lead to compaction. In earthquake zones, seismic shock waves may have a similar effect. Most susceptible soils are loosely-packed sands or gravel- sands and fill material, particularly those which have been placed without adequate rolling or tamping. Potential causes of settlement (contd..) Consolidation In saturated cohesive soils the effect of increasing the load is to squeeze out some of the porewater; process referred to as consolidation. A gradual reduction in volume takes place until internal pressure equilibrium is reached. A reduction in loading may cause swelling, providing that the soil can remain saturated. Most susceptible soils are normally-consolidated clays and silts, and certain types of saturated fill. Potential causes of settlement (contd..) Elastic distortion All solid materials distort when they are loaded. Soils, being of a particulate nature, distort partly due to compaction or consolidation, and partly as a result of elastic distortion. Elastic distortion takes place in all soils almost immediately after the load is imposed, the settlement caused by this process is termed immediate settlement. Potential causes of settlement (contd..) Moisture movement Some types of clay show a marked increase or decrease in volume as the moisture content is increased or decreased respectively. Such clays are termed shrinkable or expansive clays These clays characteristically possess high liquid limits and plasticity indices. Potential causes of settlement (contd..) Effects of vegetation Radial extent of some tree root systems is greater than the height of the tree; may also reach depths of several metres. Removal of such trees means that more moisture is held in the soil and so swelling occurs. Planting of seedlings adjacent to buildings should be carefully controlled where shrinkable clays exist. Potential causes of settlement (contd..) Effects of groundwater lowering Pumping of water from an excavation leads to a lowering of the water table. Settlement can result from this reduction in hydrostatic conditions due to: i. In some clays, a decrease in moisture content will result in a decrease in volume. Soil above the reduced groundwater level may therefore shrink. ii. Increase of the effective overburden stress on the layers below. Soil (especially in soft clays or peat) beneath the reduced groundwater level may consolidate by the increase in effective stress. Potential causes of settlement (contd..) Effects of temperature changes Severe shrinkage can occur in clay soils as they dry out beneath foundations to furnaces, kilns, ovens and boilers. It Is usual to provide an open or rubble-filled air gap between such heat sources and the foundation soil Frost heave at sustained low temperature in some soils such as silts, fine sands and chalky soils. Severe expansion can also take place in soils under cold storage buildings. Potential causes of settlement (contd..) Effects of seepage and scouring In certain soils, such as fine dry sands and loess, the movement of water can move some of the fine particles. Scouring is the removal of material by surface water and streams; can also occur where sewers or water mains have been fractured. Where excavations are taken place well below groundwater level such as within coffer dams, the upward flow of water may cause a form of instability called piping. Dissolution of mineral cement in the matrix of certain rocks and soils. Potential causes of settlement (contd..) Loss of lateral support Excavation of deep holes alongside foundation – often leading to serious, even catastrophic building failure. Bearing capacity of the soil directly beneath a footing is dependent on the lateral support afforded it by the soil alongside; in calculating the ultimate bearing capacity of the soil this is taken into account. If removed (such as in untimbered excavation) the likely outcome is a shear slip in the soil beneath the footing. Settlement might also occur as a result of movement of natural earth slopes or cuttings, due to sliding or flowing. Potential causes of settlement (contd..) Effects of mining subsidence Longwall method of mining coal in which the coal is continuously worked across a wide face. As the working advance the space left is partly filled with waste material and the pit props removed. The roof then slowly crushes down, bringing with it all of the overburden up to the surface where settlement takes place. A settlement wave is apparent at the surface, the displacement lagging behind slightly, but following the direction of the advance of the coal face. It is possible to calculate the extent of this settlement and to predict the delay. Consolidation theory Introduction  Consolidation – gradual reduction in volume of a fully saturated soil of low permeability due to drainage of some of the pore water, the process continuing until all the excess pore water pressure set by an increase in total stress has been completely dissipated  A soil is said to be fully consolidated when its volume remains constant under a constant state of stress. Introduction contd…  One-dimensional consolidation – a condition of zero lateral strain is implicit  The reverse of consolidation (swelling) -gradual increase in volume of a soil under negative excess pore water pressure Introduction contd…  Consolidation settlement – vertical displacement of the surface corresponding to the volume change at any stage of the consolidation process  Results if a structure is built over a layer of saturated clay or if the water table is lowered permanently in a stratum overlying a clay layer Introduction contd…  When an excavation is made in a saturated clay, heaving (the reverse of settlement) will result in the bottom of the excavation due to swelling of the clay.  Where significant lateral strain takes place, there will be an immediate settlement due to deformation of the soil under undrained conditions, in addition to consolidation settlement. The Oedometer Test  The characteristics of a soil during one-dimensional consolidation or swelling can be determined by means of the oedometer test.  Test specimen is in the form of a disc, held inside a metal ring and lying between two porous stones.  The upper porous stone, which can move inside the ring with a small clearance, is fixed below a metal loading cap through which pressure can be applied to the specimen. Figure 1.The oedometer (after Craig, 2002) The Oedometer Test (contd..)  The ring confining the specimen may be either fixed or floating: the inside of the ring should have a smooth polished surface to reduce side friction.  Confining ring imposes a condition of zero lateral strain on the specimen, the ratio of lateral to vertical effective stress being K0, the coefficient of earth pressure at rest.  The compression of the specimen under pressure is measured by means of a dial gauge operating on the loading cap. The Oedometer Test (contd..)  Test procedure has been standardized in BS 1377 (Part 5) which specifies that the oedometer shall be of the fixed ring type.  The initial pressure will depend on the type of soil, then a sequence of pressures is applied to the specimen, each being double the previous value.  Each Pressure is normally maintained for a period of 24 hours, compression readings being observed at suitable intervals during this period. The Oedometer Test (contd..)  At the end of the increment period, when the excess pore water pressure has completely dissipated, the applied pressure equals the effective vertical stress in the specimen.  Results presented by plotting the thickness (or percentage change in thickness) of the specimen or the void ratio at the end of each increment period against the corresponding effective stress. The Oedometer Test (contd..)  The effective stress may either be plotted to a natural or a logarithmic scale.  If desired, the expansion of the specimen can be measured under successive decreases in applied pressure.  Even if the swelling characteristics of the soil are not required, the expansion of the specimen due to the removal of the final pressure should be measured. The Oedometer Test (contd..)  The void ratio at the end of each increment period can be calculated from the dial gauge readings and either the water content or dry weight of the specimen at the end of the test.  Referring to the phase diagram in Figure 2, there are two methods of calculation.  ∆H Water H0 H1 Solids Hs Figure 2. Phase diagram (modified from Craig, 2002)  Method 1 Water content measured at end of test = w1 Void ratio at end of test = e1 = w1Gs (assuming Sr = 100 %) Thickness of specimen at start of test = H0 Change in thickness during test = ∆H Void ratio at start of test = e0 = e1 + ∆ e Where: ∆e 1+ e0 = ∆H H0 In the same way ∆e can be calculated up to the end of any increment period Method 2 Dry weight measured at end of test = Ms (i.e. mass of solids) Thickness at end of any increment period = H1 Area of specimen = A Equivalent thickness of solids = Hs = Ms/AGsρw Void ratio, H 1−Hs H1 e1 = = −1 Hs Hs Figure 3. Void ratio – effective stress relationship (after Craig, 2002). Compressibility characteristics  The plots show an initial compression followed by expansion and recompression.  The shapes of the curves are related to stress history of the clay.  The e - logσ´ relationship for a normally consolidated clay is linear (or nearly so) and is called the virgin compression line. Compressibility characteristics  For an overconsolidated clay, its state will be represented by a point on the expansion or recompression parts of the e - logσ´ plot.  The recompression curve ultimately joins the virgin compression line: further compression then occurs along the virgin line.  During compression, changes in soil structure continuously take place and the clay does not revert to the original structure during expansion. Compressibility characteristics  The plots show that a clay in the overconsolidated state will be much less compressible than the same clay in a normally consolidated state.  Compressibility of the clay can be represented by: 1. The coefficient of volume compressibility (mv) 2. The compression index (Cc) Compressibility characteristics The coefficient of volume compressibility (mv)  Defined as the volume change per unit volume per unit increase in effective stress. Units are (m2/MN)  Volume change may be expressed in terms of either void ratio or specimen thickness. Compressibility characteristics  If for an increase in effective stress from σ´0 to σ´1, the void ratio decreases from e0 to e 1, then: 1  e0 − e1  mv =   1+ e0  σ 1−σ 0  ′ ′ = 1  H 0 −H 1  H 0  σ ′1−σ 0′   The value of mv for a particular soil is not constant but depends on the stress range over which it is calculated. Compressibility characteristics The compression index (Cc) – is the slope of the linear portion of the e - logσ´ plot and is dimensionless. For any two points on the linear portion of the plot: e0 − e1 Cc = log(σ1′ / σ 0′) The expansion part of the e - logσ´ plot can be approximated to a straight line, the slope of which is referred to as the expansion index Ce. Preconsolidation pressure (σ´c)  Cassangrande proposed an empirical construction to obtain from the e - logσ´ curve for an overconsolidated clay.  Whenever possible σ´c for an overconsolidated clay should not be exceeded in construction.  Compression will not usually be great if the effective vertical stress remains below σ´c : only if σ´c is exceeded will compression be large.  Produce back the straight Figure 4. Determination of line part BC of the curve preconsolidation pressure (after Craig, 2002).  Determine the point (D) of maximum curvature on the recompression part (AB)  Draw the tangent to the curve at D and bisect the angle between the tangent and the horizontal through D.  The vertical through the point of intersection of the bisector and CB produced gives the approximate value σ´c. Limitations of the Oedometer test  The assumption made in the oedometer test is that the soil is completely saturated and the strain rate is one dimensional.  If these conditions are fulfilled the immediate settlement recorded in an oedometer test should be zero.  It is however common to find that an immediate settlement is recorded due to several causes: Limitations of the Oedometer test (contd..) a. a significant degree of unsaturation – usually the specimen is allowed to soak for a considerable period before loading is commenced, but this does not adequately saturate the sample; b. an (inevitable) imperfect fit of the disc of soil in the ring so that lateral strains occur until full contact is developed; thus excessive compressibilities may be recorded at the lower stress levels; Limitations of the Oedometer test (contd..) c. a bedding error in the measurement of the change of thickness – a calibration procedure using a steel dummy sample should be used to calibrate the oedometer.  The pore pressure response to an increase in load increment is not instantaneous but, typically, takes up to several minutes before pressures have been equalized within the sample. Limitations of the Oedometer test (contd..)  Unless the sample is sealed before drainage commences the laboratory data will be in error during the first few minutes of the new loading cycle.  Standard oedometers do not have provision for sealing the sample so that the equalization does not occur prior to commencement of drainage.  In situ e - logσ´ curve  Slight disturbance of sample due to sample and preparation of specimen in an oedometer test  An increase in the degree of specimen disturbance results in a slight decrease in the slope of the virgin compression line.  Thus, slope of the line representing virgin compression of the in situ soil will be slightly greater than the slope of the virgin line obtained in a laboratory test In situ e - logσ´ curve (Contd..)  No appreciable error will be involved in taking the in situ void ratio as equal to the void ratio e0 at the start of the laboratory test.  Schmertman (1953) pointed out that the laboratory virgin line may be expected to intersect the in situ virgin line at a void ratio of approximately 0.42 times the initial void ratio.  Thus the in situ virgin line can be taken as the line EF in Figure 5 where the coordinates of E are logσ´c and e0, and F is the point on the laboratory virgin line at a void ratio of 0.42e0. In situ e - logσ´ curve (Contd..)  In the case of overconsolidated clays, the in situ condition is represented by the point G having coordinates σ´0 and e0, where σ´0 is the present effective overburden pressure.  The in situ recompression curve can be approximated to the straight line GH parallel to the mean slope of the laboratory recompression curve. Figure 5. In situ e - logσ´ curve (after Craig, 2002).  Rate of consolidation It may be assumed the the immediate settlement due to elastic compression of the soil takes place instantaneously following an increase in stress. However, some time must elapse while the water seeps from the soil and the excess porewater pressure is dissipated. Rate of consolidation depends mainly on the permeability of the soil  Rate of consolidation Also depends on deformational creep in the soil skeleton and on the compressibility of soil constituents such as air, water vapour, organic matter and the solid matter itself. Soils which give rise to most settlement problems, however, are fully saturated clays and silts, often of alluvial or estuarine origin.  Rate of consolidation Therefore, it is convenient to consider: Primary consolidation as being that change in volume due to the seepage of pore water from a saturated soil, and Secondary consolidation as that resulting from creep, slippage between particles.  Terzaghi’s theory of consolidation Terzaghi presented a theory for the evaluation of primary consolidation. The following assumptions were made: 1. The soil is homogenous. 2. The soil is fully saturated 3. The solid particles and water are incompressible. 4. Compression and flow are one-dimensional (vertical) 5. Strains are small 6. Darcy’s law is valid at all hydraulic gradients.  Terzaghi’s theory of consolidation 7. The coefficient of permeability and the coefficient of volume compressibility remain constant throughout the process. 8. There is a unique relationship, independent of time, between void ratio and effective stress. The main limitations of Terzaghi’s theory is assumption 8. Experimental results show that the relationship between void ratio and effective stress is not independent of time. The theory relates the following three quantities: 1. The excess pore water pressure (ue). 2. The depth (z) below the top of the clay layer. 3. The time (t) from the instantaneous application of a total stress increment. Consider an element having dimensions dx, dy and dz within a clay layer of thickness 2d as shown in Figure 6. An increment of total stress Δσ is applied to the element. Figure 6. Element within a clay It can be shown that layer (after Craig, 2002) 𝐾𝐾 cv = 𝑚𝑚𝑣𝑣 𝛾𝛾𝑤𝑤 Where cv is the coefficient of consolidation in m2/year, k is the permeability and γw is the unit weight of water. Solution of the consolidation equation The total stress increment is assumed to be applied instantaneously. At zero time, therefore, the increment will be carried entirely by the pore water, i.e. the initial value of excess pore water pressure (ui) is equal to Δσ and the initial condition is: ue = ui for 0 ≤ z ≤ 2d when t = 0 Solution of the consolidation equation The upper and lower boundaries of the clay layer are assumed to be free-draining, the permeability of the soil adjacent to each boundary being very high compared to that of the clay. Thus the boundary conditions at any time after the application of Δσ are: ue = 0 for z = 0 and z = 2d when t > 0 Solution of the consolidation equation It can be shown that 𝑐𝑐𝑣𝑣 𝑡𝑡 𝑇𝑇𝑣𝑣 = 𝑑𝑑 2 Where Tv is a dimensionless number called the time factor. The progress of consolidation can be shown by plotting a series of ue against z for different values of t. Such curves are called isochrones and there form will depend on the initial distribution of excess porewater pressure and the drainage conditions at the boundaries of the clay layer. Solution of the consolidation equation A layer for which both the upper and lower boundaries are free –draining is described as an open layer. A layer for which only one boundary is free-draining is a half-closed layer. Examples of isochrones shown in Figure 7. Figure 7. Isochrones Solution of the consolidation equation For (a) the initial distribution of ui is constant and for an open layer of thickness 2d the isochrones are symmetrical about the centre line. The upper half of this diagram also represents the case of a half-closed layer of thickness d. The slope of an isochrone at any depth gives the hydraulic gradient and also indicates the direction of flow.  In (c) and (d) of the figure, with a triangular distribution of ui, the direction of flow changes over certain parts of the layer. In part (c) the lower boundary is impermeable and for a time swelling takes place in the lower part of the layer. In practical problems it is the average degree of consolidation (U) over the depth of the layer as a whole that is of interest, the consolidation settlement at time t being given by the product of U and the final settlement. Curves 1, 2 and 3 in Figure 8 represent the solution of the consolidation equation for different cases shown in Figure 9 Figure 8. Relationship between average degree of consolidation and time factor (after Craig, 2002) Figure 9. Initial variations of excess pore water pressure.  Determination of coefficient of consolidation cv The value of cv for a particular increment in the oedometer test can be determined by comparing the characteristics of the experimental and theoretical consolidation curves, referred to as curve fitting. Time is plotted to a square root or logarithmic scale. Once the value of cv has been determined, the coefficient of permeability k can be calculated.  Determination of coefficient of consolidation cv Two common methods used are: 1. The log time method due to Casagrande 2. The root time method due to Taylor The root time method due to Taylor Figure 10 shows the forms of the experimental and theoretical curves, the dial gauge readings being plotted against the square root of time in minutes and the average degree of consolidation against the square root of time factor. The theoretical curve is liner up to 60% consolidation and at 90% consolidation the abscissa (AC) is 1.15 times the abscissa (AB) of the production of the linear part of the curve.  This characteristic is used to determine the point on the experimental curve corresponding to U = 90%. Figure 10. the root time method.  The root time method due to Taylor The experimental curve usually consists of a short curve representing initial compression, a linear part and a second curve. The point (D) corresponding to U = 0 is obtained by producing back the linear part of the curve to the ordinate at zero time. A straight line (DE) is then drawn having abscissae 1.15 times the corresponding abscissae on the linear part of the experimental curve. The root time method due to Taylor The intersection of the line DE with the experimental curve locates the point (a90) corresponding to U = 90% and the corresponding √t90 can be obtained. The value of Tv corresponding to U = 90% is 0.848 and the coefficient of consolidation is given by: 0,848𝑑𝑑 2 𝑐𝑐𝑣𝑣 = 𝑡𝑡90