There is a very modest literature on the shape of loess particles; there is a fairly extensive literature on the size of loess particles. The size of the particles comprising a loess deposit is seen as one of the chief characteristics of the deposit. Another major characteristic is the open structure, the loose packing of particles- which confers on the loess deposit its interesting metastability and allows for collapsibility- usually via the hydroconsolidation mechanism. The shape of the particles has some effect on the nature of the packing.
It has been proposed that the default shape of a loess particle is a tabular, blade shape of fairly extreme proportions ( Rogers & Smalley 1993). There have been two approaches to the calculation of the expected shapes of loess particles: a very simple probabilistic approach which indicated that most silt particles would be of a Zingg class 3m nature (i.e. blades) and a slightly more sophisticated approach which supported this idea and suggested that the proportions of the Zingg box would be 8:5:2. That is a very flat box to contain the typical loess particle.
A word about Zingg. One of a range of proposals for defining particle shape the Zingg method utilised the ratio of the sides of the typical box which contained the particle. There is an explanation in the Pettijohn book on 'Sedimentary Rocks' - there is another explanation in Smalley 1966.
Zingg named or defined four shapes: class 1 the disc, where a = b > c, a flattish particle; class 2 the sphere or cube, where a = b =c ; the blade where a >b >c; and the stick or rod where a = b < c. The probabilistic calculation,( with a 10% accuracy) showed that 72% of silt particles would be of Zingg class 3 (an obvious and intuitive result). The nice thing about the Zingg approach was that it allowed numbers to be deployed for the first time in shape discussions. The 72% was the first calculation of the amount of shape.
Rogers, C.D.F., Smalley, I.J. 1993. The shape of loess particles. Naturwissenschaften 80, 461-462.
Smalley, I.J. 1966. The expected shapes of blocks and grains. Journal of Sedimentary Petrology 36, 626-629.
Howarth, J. 2010. The shape of loess particles reviewed. Open Geosciences 2, 41-44.
Digression on Zingg, by Domokos et al 2010. By considering the ellipsoid, Smalley's modified Zingg classes are given as I a =b >c disc, II a = b= c sphere, III a >b >c blade and IV a > b =c rod. The classical Zingg approach and Smalley's approach can be unified if an internal parameter O </=p</=1 is introduced, the classical Zingg system corresponds to p = 2/3, Smalley's suggestion corresponds to p = 1.
Domokos, G., Sipas, A., Szabo, T., Varkoniji, P. 2010. Pebble shape and equilibrium. Mathematical geosciences 42, 29-47 doi 10.1007/5 11004-009-9520-4
The simple Monte Carlo method produces a Zingg III shape with proportions 8:5:2. This has not been improved upon since 1993 but it still seems a bit extreme. This is a very blade shaped particle; it could certainly contribute to an extremely open packing if delivered by some suitable airfall method. Now the basic approach is to be deployed again on a very speculative venture- to determine the random shape of a closed depression in a loess deposit (what we call a 'Hardcastle Hollow' in NZ).
Wending its way to probable publication in Geomorphology is a paper by Kolodynska-Gawrysiak et al on 'Closed depressions' in loess landscapes which provokes a thought on the nature of these depressions- and their possibly random (plan) shapes.
John Hardcastle wrote in 1908: "Peculiar features of the Timaru loess are the numerous hollows in the surface, the larger of which, half an acre to an acre or two in extent, in their natural state retained water enough to allow peat and sedges to flourish in them." Could this be a random dispersion of random shaped depressions? Can we generate some random lake shapes; the question becomes can we generate random rectangles?- and what is the default random rectangle?.
Generating the random rectangle- using the Rogers-Smalley method: We need random numbers; we take them from the Kendall & Babington Smith random number tables- this may seem like a rather antique method of generating random numbers but it does guarantee that the numbers are properly random; the KBS numbers have been tested for randomness. We operate over a restricted number range, 1-10 -so generate 40 random numbers- that gives 20 rectangles- arrange in 2 columns (as generated) with large sides in one column, small sides in another
10 2
9 4
10 5
4 1
2 2
7 2
9 4
4 3
9 3
6 4
10 4
3 2
10 7
10 2
7 4
1 1
7 6
9 5
10 4
8 2
There we are- 20 rectangles; now add up each column; 145 and 67, thus 145/67 gives our default rectangle = 2.23: 1. Do this lots of times and get a real average value.
Random subsidence in a landscape of collapsible loess; we have a Zingg box (2d variety) for the closed depressions formed. If Zingg measures are done the shape of the enclosed depressions will be defined (when averages are taken) by the default rectangle. This is the 2d version of the 3d Rogers-Smalley loess particle. There are probably proper mathematical ways of calculating the side ratio for the default rectangle. It would be useful if they could be investigated- because they could probably be used on the default loess particle
There is an elegant and thorough study of depressions in Romania which provides some real data on the shape of closed depressions in loess deposits:
Grecu, F., Eftene, A., Ghita, C., Benabbas, C. 2015. The loess micro-depressions within the Romanian plain; Morphometric and morphodynamic analysis. Revista de geomorfologie 17, 5-18.
An analysis of length and breadth measurements shows ratios around the 2:1 mark; more study of these results is indicated.
New Year 2017: a few more tests on the random rectangle- tend to support the idea that the random rectangle is a 2:1 rectangle. We find references to random collapsed regions in the S.Z.Rozycki book on loess- more details later.
It has been proposed that the default shape of a loess particle is a tabular, blade shape of fairly extreme proportions ( Rogers & Smalley 1993). There have been two approaches to the calculation of the expected shapes of loess particles: a very simple probabilistic approach which indicated that most silt particles would be of a Zingg class 3m nature (i.e. blades) and a slightly more sophisticated approach which supported this idea and suggested that the proportions of the Zingg box would be 8:5:2. That is a very flat box to contain the typical loess particle.
A word about Zingg. One of a range of proposals for defining particle shape the Zingg method utilised the ratio of the sides of the typical box which contained the particle. There is an explanation in the Pettijohn book on 'Sedimentary Rocks' - there is another explanation in Smalley 1966.
Zingg named or defined four shapes: class 1 the disc, where a = b > c, a flattish particle; class 2 the sphere or cube, where a = b =c ; the blade where a >b >c; and the stick or rod where a = b < c. The probabilistic calculation,( with a 10% accuracy) showed that 72% of silt particles would be of Zingg class 3 (an obvious and intuitive result). The nice thing about the Zingg approach was that it allowed numbers to be deployed for the first time in shape discussions. The 72% was the first calculation of the amount of shape.
Rogers, C.D.F., Smalley, I.J. 1993. The shape of loess particles. Naturwissenschaften 80, 461-462.
Smalley, I.J. 1966. The expected shapes of blocks and grains. Journal of Sedimentary Petrology 36, 626-629.
Howarth, J. 2010. The shape of loess particles reviewed. Open Geosciences 2, 41-44.
Digression on Zingg, by Domokos et al 2010. By considering the ellipsoid, Smalley's modified Zingg classes are given as I a =b >c disc, II a = b= c sphere, III a >b >c blade and IV a > b =c rod. The classical Zingg approach and Smalley's approach can be unified if an internal parameter O </=p</=1 is introduced, the classical Zingg system corresponds to p = 2/3, Smalley's suggestion corresponds to p = 1.
Domokos, G., Sipas, A., Szabo, T., Varkoniji, P. 2010. Pebble shape and equilibrium. Mathematical geosciences 42, 29-47 doi 10.1007/5 11004-009-9520-4
The simple Monte Carlo method produces a Zingg III shape with proportions 8:5:2. This has not been improved upon since 1993 but it still seems a bit extreme. This is a very blade shaped particle; it could certainly contribute to an extremely open packing if delivered by some suitable airfall method. Now the basic approach is to be deployed again on a very speculative venture- to determine the random shape of a closed depression in a loess deposit (what we call a 'Hardcastle Hollow' in NZ).
Wending its way to probable publication in Geomorphology is a paper by Kolodynska-Gawrysiak et al on 'Closed depressions' in loess landscapes which provokes a thought on the nature of these depressions- and their possibly random (plan) shapes.
John Hardcastle wrote in 1908: "Peculiar features of the Timaru loess are the numerous hollows in the surface, the larger of which, half an acre to an acre or two in extent, in their natural state retained water enough to allow peat and sedges to flourish in them." Could this be a random dispersion of random shaped depressions? Can we generate some random lake shapes; the question becomes can we generate random rectangles?- and what is the default random rectangle?.
Generating the random rectangle- using the Rogers-Smalley method: We need random numbers; we take them from the Kendall & Babington Smith random number tables- this may seem like a rather antique method of generating random numbers but it does guarantee that the numbers are properly random; the KBS numbers have been tested for randomness. We operate over a restricted number range, 1-10 -so generate 40 random numbers- that gives 20 rectangles- arrange in 2 columns (as generated) with large sides in one column, small sides in another
10 2
9 4
10 5
4 1
2 2
7 2
9 4
4 3
9 3
6 4
10 4
3 2
10 7
10 2
7 4
1 1
7 6
9 5
10 4
8 2
There we are- 20 rectangles; now add up each column; 145 and 67, thus 145/67 gives our default rectangle = 2.23: 1. Do this lots of times and get a real average value.
Random subsidence in a landscape of collapsible loess; we have a Zingg box (2d variety) for the closed depressions formed. If Zingg measures are done the shape of the enclosed depressions will be defined (when averages are taken) by the default rectangle. This is the 2d version of the 3d Rogers-Smalley loess particle. There are probably proper mathematical ways of calculating the side ratio for the default rectangle. It would be useful if they could be investigated- because they could probably be used on the default loess particleThere is an elegant and thorough study of depressions in Romania which provides some real data on the shape of closed depressions in loess deposits:
Grecu, F., Eftene, A., Ghita, C., Benabbas, C. 2015. The loess micro-depressions within the Romanian plain; Morphometric and morphodynamic analysis. Revista de geomorfologie 17, 5-18.
An analysis of length and breadth measurements shows ratios around the 2:1 mark; more study of these results is indicated.
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