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**Introduction to soil water relationships**

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NS 2 Dec 1982, p 564

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Particle density (rs) Definitions Mass of soil particle divided by volume of soil particle Specific gravity, SG = ratio of mass of soil particle to mass of equal volume of water of water at 4°C Particle density in cgs or tonnes m-3 numerically equal to SG mean particle density depends on: ratio of OM to mineral matter constitution of soil minerals constitution of OM

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Determination SG bottle boiled water to remove dissolved air de-aerate for several hours with vacuum pump to remove air trapped between particles problem of floating OM Typical values organic matter = 1.3 g cm-3 quartz = 2.66 g cm-3 average for clay = 2.65 g cm-3 orthoclase = 2.5 to 2.6 g cm-3 mica = 2.8 to 3.2 g cm-3 limonite = 3.4 to 4.0 cm-3 Fe (OH)3 = 3.75 cm-3 normally taken as 2.65 cm-3

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**Bulk density (rb) and related parameters**

rb = mass of solids total volume Value is effected by particle density, degree of compaction, organic matter content

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Typical values: 0.9 for organic soil (peaty) to 1.8 for compacted sand Sand generally has a higher density than clay - why? What do we mean by heavy & light soils? Determination: soil coring devices problems of compaction oven drying at 105°C gamma ray transmission

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**Gamma ray transmission**

measures density – 2 probes - transmitter & detector

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Wet v dry bulk density Ms + Mw Vt

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**Coefficient of linear extensibility (COLE)**

Bulk density changes in swelling - shrinking soils. COLE is a measure of this Compares dry with saturated soil after it comes to equilibrium. Cracks complicate the problem of determining BD of swelling soils. Even allowing for cracks the overall density may be higher on shrinking as the surface becomes lower.

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Total pore space (T) = volume of (air + water) vol. of (air + soil + water)

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Volume of (air + water) = total volume (air + soil + water) - volume of soil where Vt and Vs are the volumes of the total sample and the soil particles respectively Vs = Ms /rs and Vt = Ms /rb where Ms is the mass of oven dry soil and rs and rb are the particle density and bulk density respectively. So:

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**rb = (1-T)/rs and so: and :**

Used in agricultural (soils) research especially for compaction studies. Typical values 0.3 to 0.6. Often expressed as a %.

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Packing density measure of compaction of particular texture class Void ratio (e) Used mainly in engineering applications e = volume of (air + water) volume of soil e = T/(1-T) [void ratio] Typically 0.3 to 2.0 Air filled porosity = volume of air volume of total

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**Moisture content and related parameters**

(a) Volumetric basis: volume of water volume of total qv = Vw/Vt (b) Gravimetric basis: mass of water mass of soil qm = Mw/Ms

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**As Vw = Mw/rw and Vt = Ms/rb then**

and so qv = qmrb/rw = qmrb/1 (not dimensionally correct) in metric measurements - density of water is 1 Often expressed as depth/depth for example mm/m

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**Degree of saturation (s)**

degree of saturation = volume of water volume of (water + air) s = qV/T Liquid ratio Liquid ratio = volume of water volume of solid

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An example to try A hole 30 cm X 30 cm x 30 cm is dug in a field. The wet soil weighs kg. The soil is taken back to the laboratory and oven dried. The final weight is kg. (a) What is the bulk density (b) What was the moisture content in the field (i) by volume (ii) by weight (c) If the mean particle density is 2.64, what is the total pore space

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**Graphical representation ....**

Q. Why is the moisture content less at depth?)

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**Measurement of soil moisture**

Laboratory definitive weigh, oven dry at 105°C for 24 hours, reweigh if volume of hole from which sample was taken is known, bulk density can be calculated and hence volumentric moisture content Field methods Include: neutron scattering gamma ray transmission time domain reflectometry all need calibration against laboratory method

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Neutron scattering

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**H scatters and slows neutrons very effectively - elastic collisions with atomic nuclei**

called “thermalisation” of fast neutrons - come to same thermal (vibrational) energy as atoms at ambient temperature hydrogen, has nucleus of about same size & mass as neutron and so has much greater thermalising effect on fast neutrons than any other element method detects mostly H atoms not water per se single probe containing radioactive source of high-energy neutrons such as radium-beryllium or americium-beryllium or caesium-137 thermal neutron density easily measured thermal neutron density may be calibrated against water concentration on volume basis of other sources of H are constant

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**Time domain reflectometry**

measures dielectric constant - ability of soil to transmit electromagnetic (radar) waves - mostly but not entirely dependent on water

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Theta Probe

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**Simple parameters to characterise H2O & O2 availability**

Soil water potential matric potential gravitational potential pressure potential

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Note on units Soil water potential is the energy density - usually per unit volume Since dimensions of energy is ML2T-2 (force x distance) dimensions of soil water potential has dimensions of ML-1T-2 Pressure is force per unit area so has units of MLT-2/L2 = ML-1T-2 Soil water potential thus has same units as pressure. It can this be expressed as bars, cm H2O, cm Hg, atmospheres SI unit of Pressure, and so energy density, is the Pascal 1 kPa = 10 mb, 1 bar = 100 kPa

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Capillarity and adsorbed water combine to produce matric potential

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**Permanent wilting point**

Usually taken as 15 (1500 kPa) bars, but may be more, e.g. 20 bars (2000 kPa). Water held between 1500 and 2000 kPa negligible in virtually all soils. PWP strongly correlated with clay. In reality, a dynamic property which depends on: potential evapotranspiration, unsaturated hydraulic conductivity of the soil, type of plant.

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Field capacity the upper limit of available water; traditionally defined as the moisture content of a soil 48 hours after saturation and subsequently being allowed to drain; a high proportion of irrigation water added above field capacity is “wasted”; FC has also been considered to be: 0.33 bars [33 kPa] in USA or 0.1 bars [10 kPa] in the UK FC also sometimes considered as the mean soil moisture content in winter (cold climates) when the potential evapotranspiration is small (and so drainage is main factor governing equilibrium moisture content.

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**The tension equivalent to FC will be at least equal to**

the air entry potential - see below. FC, PWP and AWC are strongly dependent on texture, OM and BD

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Air capacity Defined as the air content (%) at field capacity. Used in poaching studies. Low air capacity usually means poor aeration. Available water capacity Difference between FC and PWP (%) often x soil depth to give mm

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**Exercise The moisture content of a soil at field capacity was**

found to be 27.3% by weight. At wilting point, the moisture content was 19.7%. After oven drying of a volumetric sample, it was found that the bulk density was 1.42 g cm-3. What is the available water capactiy as a percentage of the volume? A crop has a rooting depth of 1.5 m. How much water is potentially available to the crop in mm equivalent. If irrigation is to take place when the AWC is depleted by 40%, how much water would need to be added?

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**Effect of bulk density on air capacity, wilting point &**

field capacity

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**Dependence of compaction on moisture content**

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Wet year Any suggestions? Dry year

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**Dynamic nature of FC, PWP, AWC**

It is important to realise that FC, PWP and AWC are commonly conceived as static soil properties but that in reality, the are used as proxies for characteristics of dynamic system. They do not take into account: field conditions such as underlying horizons; rainfall and or irrigation frequency and amount; hydraulic conductivity of the soil; run-off characteristics; roots extension; water infiltration and redistribution; drainage from soil profile; some water may drain at the same time as evapotranspiration takes place; ground cover changes;

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crop height changes climate, especially evapotranspiration rate effect the values Beware of too simplistic a view. Even so, FC, PWP and AWC are very useful concepts.

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**Measurement of soil potential**

Tensiometers After Richards, 1965

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**Electrical resistance methods**

Gypsum blocks Granular Matrix Sensors e.g. WATERMARK sensor from Irrometer Co, USA

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**Relationship of soil water potential to soil vapour pressure**

If vapour between soil particles is in equilibrium with held water, the vapour pressure is influenced by the “pull” of the soil water ... where : Yt is the sum of matric and osmotic potential is the density of the water at the prevailing temperature, R is the Universal Gas Constant M is the molecular weight of water T is the Temperature (°K) e is the vapour pressure in the soil pores e0 is the saturated vapour pressure of free water at the particular temperature

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**The phenomenon is used as the basis of:**

(a) the determination of the potential of a soil in the laboratory (often in order to determine the moisture release characteristics) by allowing a filter paper of known pore size / moisture release characteristics to come into equilibrium with the moist air over the soil which is also in equilibrium with the soil water potential. (b) to determine the soil water potential in the field by determining the humidity of the soil air using a thermocouple psychrometer

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**Moisture release characteristics**

Determination pressure plate apparatus sand; sand/kaolin bath apparatus filter paper - allow to come into equilibrium and weigh paper solution - mixture so that vapour pressure is known and this can be equated to soil potential, allow soil to come into equilibrium with solution use of pF scale

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Filter paper method top filter paper not in contact - measures sum of matric and osmotic potential of soil bottom filter paper is in pore contact so measures matric potential

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Hysteresis

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Typical curves Near air entry potential

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**Air entry potential (fe)**

Also known as air entry value or bubbling pressure = pressure at which largest pores begins to empty Related to structure and field capacity. fe corresponds to the largest pore size where and

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**f es is the air entry potential when the bulk density is f is in J/kg **

1.3 g cm-3 f is in J/kg dg the geometric mean particle diameter, is in mm, and sg is the geometric standard deviation of the particle sizes in mm (ranges from 1 to 30).

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**Example calculation of dg and sg (based on Campbell, p.9)**

It is assumed that clay has d < mm silt has < d < 0.05 mm sand has 0.05 < d < 2 mm The predictor equations assumes that particle size distribution is log normal Logarithm of geometrical mean is given by: ln dg = S mi ln di where the di are the textural class sizes and mi are the amounts in each class The di for the size classes are calculated from (lower limit + upper limit)/2

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**dclay = 0.001 mm; ln(dclay) = - 6.91 **

thus: dclay = mm; ln(dclay) = dsilt = mm; ln(dsilt) = dsand = mm; ln(dsand) = If a soil is 0.6 clay, 0.25 silt and 0.15 sand, then ln dg = (0.6 x ) + (0.25 x ) + (0.15 x 0.025) = = = mm

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**(ln sg )2 = f1(ln d1)2 + f2 (ln d2)2 + f3 (ln d3)2 - (ln dg)2**

Substituting this in the above equation, the standard air entry potential is - 12 J kg-1 To make allowances for bulk density, we need first to calculate sg. The normal standard deviation is given by: In a similar way, the logarithmic standard deviation is given by: (ln sg )2 = f1(ln d1)2 + f2 (ln d2)2 + f3 (ln d3)2 - (ln dg)2 The geometric SD is the antilog of the SD of the log transformed values. Thus: ln sg = 2.42 and so sg = e2.42 = 11.24 and b = 2 x x = = 26.25

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Thus for this soil, For bulk densities of 1.1, 1.3 and 1.5, the air entry potentials would be: - 0.84, - 12 J kg -1 respectively

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**Sand tension table (0 to 100 cm potential)**

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**Kaolin table (100 cm to 400 cm potential)**

H should be added to difference between atmospheric pressure and pressure in aspirator bottle

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Pressure plate method for potentials from 1 bar to 15 bars

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**Prediction of matric potential**

Not reliable but some workers use equations of the form: where qs = saturation % (vol) and Fe, the air entry potential is calculated as before from:

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Clays Treated here because flocculation in the field is an essential part of reclamation of sodic soils. Flocculation occurs when clay particles “stick” together because of electrical forces to form larger particles and hence improves the hydraulic properties of the clay Flocculation changes the hydraulic conductivities and the moisture holding properties of clay soils. Clay = 0.2 m -2m ; Colloidal clay: =< 0.2m ; m = 10-6 m Adsorption: concentration of one material at surface of another Absorption: uptake of one material into another

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**Colloidal material is surrounded by thin layer of solution**

which is different in composition from the solution (relatively) far away from the particles. Layer moves with the particle. Micelle: colloidal particle + hydration shell Intermicellar fluid : solution between micelles

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**Micelles usually negatively charged because of:**

isomorphic substitution: Si++++ in the clay may be substituted by Fe+++ or Al+++ which makes the clay short of + charge and so negatively charged - smectite or illite type materials Fe++ or Mg++ may replace Fe+++ or Al+++ in alumina or gibbsite sheets ionisation at the surface: e.g. appearance of OH - at the surface and edges of micelle H2O adsorption and subsequent ionisation & diffusion of H+ leaving a net negative charge because of the OH – preferential adsorption of anions from solution for example the adsorption of CO3- onto calcium carbonate leaving an associated ion in solution

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**Some mutual attraction occurs between particles because of edge effects**

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Double layer Double layer is name given to accumulation of positively charged ions around negatively charged micelles – some attached, some in solution controls flocculation and dispersion dependent on cation type cation concentration pH the thicker the double layer, the greater the net repulsion and the more dispersed a soil becomes important in structure and aggregation and reclamation of saline and sodic soils

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Negative ion concentration in solution increases with distance & positive ion concentration decreases negatively charged soil particle + a layer of cations directly satisfies some of the negative charge + diffuse second layer eventually reaches same concentration as surrounding bulk solution

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**Helmholtz model - assumes the charge concentration **

Different models: Helmholtz model - assumes the charge concentration decreases linearly with distance Gouy-Chapman model - assumes charge concentration decreases exponentially with distance Stern model - assumes linear decrease in the Stern layer near the surface and then an exponential decrease - thickness of Stern layer normally taken as equal to the ionic radius of the adsorbed species. Taylor & Ashcroft, Fig. 5.7

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**The double layer is depressed by increasing the**

valency of the ions in the intermicellar solution and hence the packing of the charge near the micelle surface. This is known as the depression of the double layer.

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**smaller cations, like Mg2+, will decrease double layer thickness**

Effect of cation type + + smaller cations, like Mg2+, will decrease double layer thickness larger cations, like Na+, will increase double layer thickness

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**If concentration of intermicellar solution is increased,**

concentration of ions in double layer reaches concentration of intermicellar concentration nearer the micelle surface

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**Effect of Cation Concentration**

+ + high ionic concentrations will decrease double layer thickness low ionic concentrations will increase double layer thickness

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**pH Kaolinite edge OH O Si Si Si OH Al Al Al OH neutral pH lower pH**

(+1/2) OH Si Al (+1/2) (-1/2) lower pH higher pH OH O Si Al (-1/2) (-1)

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**London - van der Vaals forces**

In addition to repulsive forces caused by accumulated positive charges, there is also an attractive force between clay particles caused by London - van der Vaals forces. These forces, which occur even between electrically neutral atoms, are due to the fact that, although the average electrical field of a neutral spherical atom is zero, the instantaneous field is not zero but fluctuates with the movements of the electrons in the atom (or ion). When 2 atoms (or ions) approach, they can synchronise their electronic motions so that the electrical charge in one surges towards the other when the fluctuations in this second atom happen to leave its nuclear field somewhat exposed in this particular direction.

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**Depending on relative strength of forces of attraction and**

forces of repulsion, attractive van der Waals forces may predominate in which case flocculation takes place.

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Figure . In addition to attractive van der Waals forces, there are forces of repulsion between particles in suspension. The potential energy of attraction and also that of repulsion varies with distance from the particle surface. Curve 1 is an example of repulsion, and curve 6 is an example of attraction. These two curves vary with the colloid and the kinds and amounts of electrolytes. Thus, when curves 1 and 6 are summed for different conditions, they produce curves similar to 2 to 5. Curve 2 represents a stable suspension because the energy of repulsion predominates. Addition of more electrolyte will suppress the double layer and produce a curve similar to 3, 4 or 5 depending on the amount added. With curve 3, there is still an energy barrier to flocculation, but when the particles surmount the energy barrier and approach closer than point C, the forces of attraction predominate and the particles stick together. A suspension represented by curve 5 flocculates spontaneously and cannot be redispersed unless the curve is shifted back toward curve 2. This shift may be accomplished through expanding the double layer by changing the kinds and/or amounts of the electrolyte. Fig in Taylor & Ashcroft

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**The thickness of the double layer is altered by both the**

concentration and the ratio of divalent to monovalent ions (and the ratio of tri-valent ions to mono-valent ions). If the constitution and concentration of the soil solution is changed, the constitution of the ions in the double layer will change. Replacement of monovalent ions by divalent ions in the double layer makes it thinner and so more easy for Van der Waals forces to take over and make the particles stick together Langmuir equation Relates the amount of adsorption onto clay particles to the concentration of the solution. Look it up.

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Specific surface Important effect on: cation exchange retention and release of various chemicals (nutrients and pollutants) swelling of clays retention of water engineering properties (e.g. plasticity, cohesion, strength )

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am = As/Ms av = As/Vs ab = As/Vt where a is the specific surface, As is the total surface area in the sample, Ms is the mass of solids, Vs is the volume of the solids, Vt is the total volume of the sample. Suffixes m, v and b refer to whether specific surface is on a mass basis, volume of solids basis or volume of total soil basis.

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**Measured from amount of gas absorbed at certain T and P.**

Can also be estimated from particle size distribution & distribution of minerals NB. surface area/volume for sphere = 6/d = av Typical values

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**Texture and particle size distribution**

Definitions of sand, silt, clay 1 = 10-6 m = 10-3 mm sand: silt: clay : < 2

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**Texture triangles (using above definitions)**

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Mechanical analysis Separation of particles OM removed by H2O2 sometimes CaCO3 cementing agent removed by HCl deflocculation by adding Calgon (sodium hexametaphosphate) mechanical agitation (shaking, stirring, ultrasound) Sieving Use sieves down to 0.05 mm (very fine sand)

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**Fd = 6phru Sedimentation Theory**

Falling particle in a fluid experiences a downward force and resistance force (drag) in opposite direction. Stokes (1851) found that the drag was given by: Fd = 6phru u is terminal velocity, h is the viscosity, r is the radius of the sphere

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**6phru = 4/3 p r3 g(rs - rf) When the two forces are in equilibrium,**

particle reaches a “terminal velocity”. In that condition, downward force on the particle = gravity - upthrust due to fluid density Upthrust = weight of particle - weight of fluid displaced weight of particle = 4/3 p r3 rs g where rs is the particle density weight of water displaced = 4/3 p r3 rf g where rw is the density of fluid So upthrust is 4/3 p r3 (rs - rf) g At terminal velocity, 6phru = 4/3 p r3 g(rs - rf)

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**which can be rearranged as:**

where d is the diameter of the particle. Since u = h/t where h is height dropped and t is the time elapsed t = h/u and so and

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Pipette method All particles > d(h, t) will have settled out by time t Proportion of original can be determined by taking a sample After 8 hours only clay is left in suspension Hydrometer Measures density of remaining soil suspension instead of taking a sample X-ray transmission methods Transmission related to density. Gives continuous distribution

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Soil structure see handout

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