I am currently doing some study on trace element bio-availability in soils in urban, rural and agricultural areas. However, I am not sure which chemical extraction method is acceptable for this purpose. Thank you for advice.
To estimate the bioavailable fraction of metals in soil you can perform the plant test, as mentioned by Bir Hassiba. You can also perform a single step extraction using 0.05M EDTA solution (L/S = 10 L/kg). The amount of metals extracted by EDTA is considered to be bioavailable.
DTPA is a good choice. In addition, DGT (diffusive gradient in thin films, a resin based technique) may be helpful. You can find details in "Copper uptake by Elsholtzia splendens and Silene vulgaris and assessment of copper phytoavailability in contaminated soils" http://www.sciencedirect.com/science/article/pii/S0269749103003786
One resource that is extremely useful is Rayment and Lyons 2010 (see the link below). It is the definitive handbook for soil testing in Australian laboratories. It details many of the accepted methods for soil analysis in Australia and elsewhere.
As to your second question, "the most accepted" depends really on who you are asking. I suspect researchers in different countries will have their own preferences. I can't suggest an answer, as I don't know what soil test(s) you will end up using, which plants (or animals, or water) you will be examining, or whether the soils you examine are going to vary significantly between your urban, rural and agricultural study areas. You will probably have to check the suitability of any test on your particular soils and compare it to the uptake in your biological samples.
Availability to which organism in which period of time ?
I think, there is no general answer for a bioavailable fraction anyway. For an alga, it is the water-soluble extract. For cereals (most experiments have been done with these), it is the amount dissolved by root exsudates. For Worms, this is governed by enzymes in the digestion tract. For vertebrates, it is the acid produced in the stomach, except for ruminants - their digestion is circumneutral and anaerobic.
Trees have longer cycles- they can store from less available fractions during resting periods, in their stems
I am currently favouring dilute acetic acid for the exchangeables + acid mobiles, and subsequently oxalate for the iron-oxide bound amounts; the latter is attacked by root exsudates, particularly to obtain phosphorus.
In case you want to trace contaminations, it will be shown by almost every mobile fraction, unless the trace element in question does not reprecipitate at other soil constituents (e.g. Ni, Cr in neutral salt Solutions)
Thank you for reply. My current interest is to assess the bioavailability of trace elements in soil solutions which may be absorb by plants. Appreciate you time in sharing your experience in this matter.