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Sus cep ti bil ity of var i ous tek tite types to flu vial abra sion

Tomasz BRACHANIEC1, *

1 Uni ver sity of Silesia; Fac ulty of Earth Sci ences, De part ment of Geochemisty, Min er al ogy and Pe trog ra phy, Bêdziñska 60, 41-200 Sosnowiec, Po land

Brachaniec, T., 2019. Sus cep ti bil ity of var i ous tek tite types to flu vial abra sion. Geo log i cal Quar terly, 63 (1): 150–161, doi:

10.7306/gq.1461

As so ci ate ed i tor: Wojciech Granoszewski

Tek tites are glass bod ies, rich in sil ica, re sult ing from the im pact of a large bo lide into ground rocks. Sim i lar to other impactites they are prone to ero sive pro cesses, in clud ing flu vial abra sion. This study re ports the re sults of an ex per i men tal tum bling that aimed at es ti mat ing the po ten tial dis tance that tek tites from dif fer ent strewn fields (moldavites, bediasites and indochinites) and Lib yan Desert Glass (LDG) can with stand de pend ing on the ex per i men tal con di tions. The pres ent study con sisted of 15 cy cles, in which the type of sam ple de pos its (i.e. sand/gravel ra tio) and com puted trans port ve loc ity were changed, the lat ter be ing es ti mated at 2.5-6.5 km/h. The re sults clearly con firm the sus cep ti bil ity of tek tites to abra sion dur - ing tum bling. None of the tek tites with stood the es ti mated dis tance of 12 km dur ing the ex per i ment, but this may have been the re sult of the rel a tively small ini tial size of the glasses (~1.5 g). These ex per i ments doc u ment that LDG, de spite its even smaller ini tial size in the ex per i ments, can re sist abra sion and frag men ta tion better than the tek tites, thus, could prob a bly be trans ported far ther in a stream en vi ron ment. This is most likely caused by a much higher sil ica con tent in re la tion to the tek - tites from other groups. The es ti mated max i mum trans port dis tances, over which moldavites, bediasites and indochinites sur vived in the ex per i ments, are all very sim i lar. The great est weight loss for all the spec i mens was found af ter the first es ti - mated 2 km of tum bling. This is un doubt edly caused by the ir reg u lar ini tial shape of the tek tites and LDG. Sub se quent ob ser - va tions re corded mi nor weight losses, in as so ci a tion with more and more rounded glass shapes. The re sults of the study should be treated only as a gen eral scheme for the flu vial abra sion of tek tites, due to the in abil ity to ac cu rately re pro duce the nat u ral flu vial en vi ron ment.

Key words: tek tites, re work ing, abra sion, redeposition, river, gravel.

INTRODUCTION

The fall of a suf fi ciently large as ter oid into ground de pos its some times leads to the for ma tion of microtektites and/or tek - tites (Koeberl, 1993, 1994; Glass and Simonson, 2012; Bracha - niec et al., 2014a). Tek tite is a glass, the main com po nent of which is sil ica (SiO2), orig i nat ing from the rocks of Earth’s crust (Koeberl, 1986). Tek tites of ten dis play a high de gree of ho mo - ge ne ity (Werner and Borradaile, 1998; Rodovská et al., 2016;

Skála et al., 2016).Tek tites dif fer from each other by phys i cal and chem i cal fea tures, de ter mined partly by the melt ing of var i - ous rock types (Koeberl, 1990). So far, the oc cur rence of tek - tites on Earth is re lated mainly to the fol low ing Ce no zoic strewn - -fields (Fig. 1; Mc Call, 2001; Glass and Simonson, 2013): the Cen tral Eu ro pean (moldavites), the North Amer i can (bedia - sites, georgiaites), the Ivory Coast (ivorites), and the Austra - lasian (Aus tra lian tek tites – australites, Asian tek tites – indo -

chinites, thailandites, malaysianites, philippinites, rizalites, billito nites and javanites). Ad di tion ally, there are also Dar win Glass from Tas ma nia and Lib yan Desert Glass (LDG) from the Lib yan Desertin, west ern Egypt (Glass and Simonson, 2013).

Ac cord ing to non splash-forms of LDG, it should be clas si fied as im pact glass not tek tite (B. Glass, pers. comm., 2018). In the geo log i cal re cord, tek tites are sub ject to many pro cesses that can change their strati graphic po si tion (so-called “age par a - dox”) and make the iden ti fi ca tion of their source crater dif fi cult.

Such a pro cess is un doubt edly ero sion and redeposition, which was re corded in each of the four larg est strewn-fields on Earth (Mc Call, 2001). Tek tite re work ing can be in duced by tsuna - mites, flu vial pro cesses, turbidites and gla ciers, or even hu man ac tiv ity and tor na does (Shoe maker and Shoe maker, 1997;

Shoe maker and Uhlherr, 1999; Mc Call, 2000, 2001; Osinski et al., 2008; Buchner and Schmieder, 2009; Jimenez-Mar ti nez et al., 2015; Szopa et al., 2017). Bear ing in mind that the trans port of tek tites in the flu vial en vi ron ment (rivers and streams) is rel a - tively poorly un der stood, the main pur pose of this work was to test the sus cep ti bil ity of dif fer ent tek tite types to abra sion, in or - der to check which of them were the o ret i cally able to with stand the lon ger dis tance of re work ing, de pend ing on the con di tions (ve loc ity) and type of sed i ment (sand/gravel ra tio). It was not

* E-mail: tomasz.brachaniec@o2.pl

Received: March 7, 2018; accepted: January 11, 2019; first published online: March 22, 2019

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about ac cu rately re pro duc ing the ex act hydrogeological con di - tions for each type of tek tite, but about gen er at ing a gen eral model of their re spec tive abra sion in sim i lar con di tions. This study was in spired by the ex per i men tal tum bling car ried out on moldavites by Brachaniec (2018a, b).

METHODOLOGY

The tum bling ex per i ment on tek tites had been con ducted at the Fac ulty of Earth Sci ences of the Uni ver sity of Silesia, us ing a ro tat ing bar rel LPM-20 (Glass GmbH & Co. KG Spezialma - schinen), which was mod i fied to be ro tated with pre de fined speed. Its ra dius was 15 cm and height 40 cm. The vol ume of the bar rel was es ti mated to 0.028 m3 from these di men sions.

CYCLES, TUMBLING SPEED AND OBSERVATIONS

Dur ing the ex per i ment, 15 sep a rate cy cles were car ried out, all dif fer ing from each other by the tum bling speed and/or the type of sed i ment used. Be fore ev ery cy cle, sep a rated sed i ment sam ple (Ta ble 1) and all tek tites (for ev ery cy cle) were put into the bar rel. Each cy cle was di vided into sev eral stages that cor re sponded to trans - port dis tances (see Ta ble 2). Due to the fact that, in most cases, tek tite abra sion takes place in streams deeper than 30 cm, the bar rel was filled with wa ter. For the pur poses of the ex per i ment, tum bling speed for each cy cle had to be de ter - mined. Due to the fact that the aim was to elab o - rate a gen eral scheme for the tek tite abra sion, the river speeds were av er aged from lit er a ture data: in the USA up to 7 km/h (Schulze et al., 2005; Magirl et al., 2009), in Po land up to 3 km/h (Ha³adyj-Waszak, 1975, 1978, 1980), and in China up to 5 km/h (Jia et al., 2016). Ad di tion ally, based on the re sults of Ziada (2010), 3 km/h was ac cepted for the River Nile.

An av er age speed of 4.5 km/h was ac cepted for the whole ex per - i ment, in which this value was cen tral (Ta ble 1). Bear ing in mind the re sults of Brachaniec (2018a), the ob ser va tion of pro gres sive abra sion ev ery 2 km of trans port was thus con sid ered to give the best pic ture of the suc ces sive stages of tek tite ero sion.

Due to the dif fer ent tum bling speeds, this dis tance cor re - sponded to dif fer ent time in ter vals which were cal cu lated from RPM (rev o lu tions of bar rel per min ute; Table 1). Dur ing ev ery ob ser va tion stage, the bar rel was stopped and all ma te rial (de - pos its, tek tites, LDG) was sieved on a 5 mm mesh. Once re - moved from the bar rel, state pres er va tion of glasses was re - corded. Af ter each tum bling step, they were weighed, de scribed and put back in the bar rel for the next tum bling step. A new de - Fig. 1. The larg est Ce no zoic tek tite strewn-fields on Earth

(af ter Mc Call, 2001; Glass and Simonson, 2013; Giuli et al., 2014)

T a b l e 1 Meth od ol ogy in volved in ex per i men tal tum bling of tek tites

River ve loc ity

[km/h]

De posit sam ple

Cy cle RPM (rev o lu tions of bar rel per min ute)

m/s of trans port

Ob ser va tion sand [kg] gravel [kg]

2.5

1 3 Cy cle no. 1 40–0.6

ev ery 48 min (~2 km of trans port)

2 2 Cy cle no. 2 40–0.6

3 1 Cy cle no. 3 40–0.6

3.5

1 3 Cy cle no. 4 60–0.9

ev ery 34 min (~2 km of trans port)

2 2 Cy cle no. 5 60–0.9

3 1 Cy cle no. 6 60–0.9

4.5

1 3 Cy cle no. 7 80–1.2

ev ery 27 min (~2 km of trans port)

2 2 Cy cle no. 8 80–1.2

3 1 Cy cle no. 9 80–1.2

5.5

1 3 Cy cle no. 10 100–1.6

ev ery 22 min (~2 km of trans port)

2 2 Cy cle no. 11 100–1.6

3 1 Cy cle no. 12 100–1.6

6.5

1 3 Cy cle no. 13 120–1.9

ev ery 18 min (~2 km of trans port)

2 2 Cy cle no. 14 120–1.9

3 1 Cy cle no. 15 120–1.9

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T a b l e 2 Com piled re sults from ex per i men tal tum bling. Weight loss val ues rounded to zero dec i mal places

Cy cle

River ve loc ity

[km/h]

De pos its:

sand/gravel [kg]

Tek tite

Stages and weight loss [%]

Max i mum dis tance [km]

Stage 1

(0–2 km) Stage 2 (2–4 km)

Stage 3 (4–6km)

Stage 4 (6–8km)

Stage 5 (8–10km)

Cy cle

no. 1 2.5 1/3

mol. 56 23 15 – – 8

bed. 52 19 15 – – 8

indo. 53 20 15 – – 8

LDG 40 15 11 8 – 10

Cy cle

no. 2 2.5 2/2

mol. 51 19 16 – – 8

bed. 48 20 13 9 – 10

indo. 51 23 16 – – 8

LDG 38 17 11 6 – 10

Cy cle

no. 3 2.5 3/1

mol. 46 17 15 12 10 12

bed. 44 16 10 9 6 12

indo. 47 20 15 11 5 12

LDG 33 15 11 9 6 12

Cy cle

no. 4 3.5 1/3

mol. 59 24 17 11 – 10

bed. 55 21 17 – – 8

indo. 56 23 15 – – 8

LDG 44 17 14 11 – 10

Cy cle

no. 5 3.5 2/2

mol. 54 21 18 11 – 10

bed. 52 23 15 11 – 10

indo. 55 25 20 – – 8

LDG 41 19 13 11 9 12

Cy cle

no. 6 3.5 3/1

mol. 49 15 13 10 8 12

bed. 47 19 13 10 8 12

indo. 50 23 18 12 8 12

LDG 37 18 12 11 9 12

Cy cle

no. 7 4.5 1/3

mol. 61 27 18 – – 8

bed. 58 29 17 – – 8

indo. 58 25 19 – – 8

LDG 46 20 16 9 – 10

Cy cle

no. 8 4.5 2/2

mol. 56 22 17 14 – 10

bed. 55 26 17 – – 8

indo. 58 28 23 – – 8

LDG 45 24 16 11 – 10

Cy cle

no. 9 4.5 3/1

mol. 51 20 14 – – 8

bed. 51 22 14 12 – 10

indo. 54 24 16 11 – 10

LDG 41 19 13 12 10 12

Cy cle

no. 10 5.5 1/3

mol. 75 35 – – – 6

bed. 65 30 21 – – 8

indo. 63 26 21 – – 8

LDG 50 23 14 11 – 10

Cy cle

no. 11 5.5 2/2

mol. 61 32 16 – – 6

bed. 61 29 18 – – 6

indo. 61 31 24 – – 6

LDG 50 26 18 13 – 8

Cy cle

no. 12 5.5 3/1

mol. 56 21 15 – – 8

bed. 55 24 15 – – 8

indo. 57 27 20 – – 8

LDG 45 21 12 9 – 10

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posit sam ple was also put into the bar rel. Each cy cle ended when the glass be came <5 mm in di am e ter, which was ac - cepted as com plete de struc tion of the tek tite. Due to the fact that the av er age size of the tek tites is at least 1 cm and the weight is a few grams (Glass, 1982), glasses of such sizes were cho sen for the ex per i ment.

SELECTED TEKTITES

A to tal of 60 glasses were used in the ex per i ment, 15 from each group: moldavites, bediasites, indochinites and LDG. This means that three dif fer ent tek tites (moldavite, bediasite, molda - vite) and LDG were used in each cy cle. For the most sen si ble in ter pre ta tion of the tum bling re sults, the se lected spec i mens were cho sen based on their masses as close as pos si ble. The glass shape dur ing the ex per i ment was de ter mined us ing Power’s pat tern (1953).

SEDIMENT SAMPLES

The aim of the ex per i ment was to check how the abra sion af fects var i ous types of tek tite in dif fer ent types of sed i ment.

Be cause flu vial abra sion oc curs mainly in rivers, typ i cal flu vial sed i ments, such as sands and oval gravel grains, were used.

By chang ing the tum bling speed, the pro por tion of these two frac tions also changed in re la tion to 25–75 vol.%, 50–50 vol.%

and 75–25 vol.% (Table 1). The used sand was yel low and mod er ately sorted, while the gravel was made mostly of quartz peb bles with a di am e ter vary ing from 1 to 10 cm. One sand grain was ~1 mm in di am e ter.

RESULTS

The re sults of all per formed cy cles are de scribed be low.

The tum bling re sults are pre sented in Ap pen dixes 1–15 and

Ta ble 2. The av er age per cent age weight loss in re la tion to the re work ing dis tance cov ered by tek tites in each cy cle is shown in Fig ures 2–6.

CYCLE NO. 1

(2.5 km/h AND SAND/GRAVEL RATIO OF 1/3)

Gen er ally, the pat terns of abra sion of the tek tites in this cy - cle were very sim i lar, al though their ini tial shapes were very di - verse: very an gu lar (moldavite), sub-rounded (bediasite and indochinite) and rounded (LDG). The tek tites lost ~40–56% of their ini tial weight in stage 1. Moldavite be came sub-rounded in shape, while the rest of the tek tites re tain their orig i nal shape.

The sur face of the tek tites be came par tially smooth and, in the case of LDG, com pletely smooth, while the edges were roun - ded. Af ter stage 2, the weight loss reached 11–23 vol.%; all tek - tites be came rounded/well-rounded with a com pletely smooth sur face. The next ob ser va tion only re vealed an other loss of glass mass. Moldavite, bediasite and indochinite did not with - stand fur ther than 6 km of re work ing (less than 5 mm), while LDG did up above stage 4.

CYCLE NO. 2

(2.5 km/h AND SAND/GRAVEL RATIO OF 2/2)

The abra sion pat tern was rel a tively sim i lar to that of cy cle no. 1. How ever, due to the dif fer ent pro por tions of the de pos its (i.e. sand/gravel ra tio), the tek tites were slightly abraded at a slower pace. Once again moldavite dif fered in shape quite clearly from any other tek tite (very an gu lar in shape). Dur ing the first ob ser va tion, a weight loss of 37–51% was re corded. In con - trast to the pre vi ous cy cle, the glass sur face be came par tially matt. The shapes of all tek tites were de ter mined as sub- roun - ded. Dur ing this next stage, they be came rounded with in com - plete matt and flat sur face. Moldavite and indochinite with stood up through stage 3 of tum bling in con trast to other tek tites that made it through stage 4.

Tab. 2 cont.

Cy cle

River ve loc ity

[km/h]

De pos its:

sand/gravel [kg]

Tek tite

Stages and weight loss [%] Max i mum dis tance [km]

Stage 1

(0–2 km) Stage 2 (2–4 km)

Stage 3 (4–6km)

Stage 4 (6–8km)

Stage 5 (8–10km)

Cy cle

no. 13 6.5 1/3

mol. 84 – – – – 4

bed. 74 38 – – – 6

indo. 70 31 25 – – 8

LDG 55 25 17 13 – 10

Cy cle

no. 14 6.5 2/2

mol. 67 35 – – – 6

bed. 69 36 – – – 6

indo. 64 32 – – – 6

LDG 54 29 19 – – 8

Cy cle

no. 15 6.5 3/1

mol. 59 27 18 – – 8

bed. 58 28 – – – 6

indo. 61 29 21 – – 8

LDG 50 22 15 11 – 10

See text for ex pla na tions; mol. – moldavite, bed. – bediasite, indo. – indochinite, LDG – Lib yan Desert Glass (see also Ap pen dixes 1–15*, Fig. 7)

* Supplementary data associated with this article can be found, in the online version, at doi: 10.7306/gq.1461

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CYCLE NO. 3

(2.5 km/h AND SAND/GRAVEL RATIO OF 3/1)

The re sults of this cy cle dif fered from the pre ced ing two, es - pe cially from cy cle no. 1. It was mainly due to the higher amount of sand in the de posit sam ple. Orig i nal shapes of tek tites, ex - cept LDG (sub-rounded), were clas si fied as sub-an gu lar. Dur - ing the first stage, there was a no tice ably smaller weight loss (32-47%) in con trast to cy cle 1 and slightly less to cy cle 2. Tek - tites be came sub-rounded with a par tially matt sur face. Af ter stage 2, the spec i mens lost weight, but no sig nif i cant dif fer ence in shape and sur face sculp tur ing was noted. Af ter stage 3, the spec i mens be came rounded with a com pletely mat ted sur face with out re lief. An other weight loss was noted af ter stage 5.

The av er age tek tite weight loss on dif fer ent stages re lated to the re work ing dis tance for cy cles 1, 2 and 3 is pre sented in Fig ure 2.

CYCLE NO. 4

(3.5 km/h AND SAND/GRAVEL RATIO OF 1/3)

De spite the in crease of the tum bling speed, the re sults of this cy cle did not sig nif i cantly dif fer from those from cy cles 1, 2 and 3. All tek tites were ini tially sub-an gu lar in shape. The first range of weight loss fluc tu ated be tween 44 and 59%. Ac tu ally, the shape of glasses was not al tered, and their sur face be came partly smooth. Af ter 4 km of trans port, with a 17–24% weight loss, all tek tites be came rounded with a com pletely smooth sur - face. Af ter 6 km re work ing, the tek tites were just well-rounded in shape. Moldavite and LDG with stood a some what lon ger dis - tance of re work ing in con trast to bediasite and indochinite.

CYCLE NO. 5

(3.5 km/h AND SAND/GRAVEL RATIO OF 2/2)

In creas ing the amount of sand in the de posit sam ple in - duced a re duc tion of weight loss dur ing stage 1 (41–55%). The tek tite glass be came sub-rounded with a vis i ble matt sur face and smooth ing. Af ter stage 3, all the tek tites were rounded in shape and com pletely worn out. Dur ing this stage the last

indochinite ob ser va tion was also no ticed. Moldavite and bediasite were de stroyed be fore stage 5. LDG made it through stage 5 and be came well-rounded.

CYCLE NO. 6

(3.5 km/h AND SAND/GRAVEL RATIO OF 3/1)

In this cy cle, all tek tites made it through stage 5 as a re sult of the higher amount of sand at this tum bling speed. Their pre lim i - nary sub-an gu lar shapes turned to rounded af ter stage 3. The weight de crease af ter the first stage is ~37–49%; mean while, the first signs of abra sion were show ing. Af ter stage 4 the spec i - mens were al ready com pletely mat ted.

The av er age tek tite weight loss on dif fer ent stages re lated to the re work ing dis tance for cy cles 4, 5 and 6 is pre sented in Fig ure 3.

CYCLE NO. 7

(4.5 km/h AND SAND/GRAVEL RATIO OF 1/3)

Orig i nal tek tites were sub-rounded in shape, ex cept molda - vite, which was an gu lar. In creas ing the tum bling speed re sulted in a higher weight loss af ter stage 1 than in the pre vi ous cy cles (46–61%). The round ness of the spec i mens also in creased. On the sur face of moldavite and LDG, char ac ter is tic semi-cir cu lar traces of gravel abra sion were ob served. In this cy cle, LDG was the only one to make it through stage 5, while the re main ing spec i mens made it only through stage 4.

CYCLE NO. 8

(4.5 km/h AND SAND/GRAVEL RATIO OF 2/2)

Tek tite abra sion was sim i lar to that from cy cle no. 7. How - ever, due to the dif fer ent type of sed i ment, the glasses were eroded at a slower pace. Ini tially, moldavite dif fered in shape from other tek tites be cause it was very an gu lar in shape. Dur ing stage no. 1, the weight loss of all tek tites was in the range of 45–58%. Like in the pre vi ous cy cles, the glass sur face be came par tially mat ted al ready at this stage, and the tek tites were de - Fig. 2. Av er age tek tite weight loss re lated to the re work ing dis tance for each cy cle

at tum bling speed of 2.5 km/h (see also Ap pen dixes 1–3, Ta ble 2)

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ter mined as rounded. Dur ing the next stage the sur faces be - came com pletely mat ted and smooth. Moldavite and LDG made it through stage 4 in con trast to bediasite and indochinite that made it only through stage 3.

CYCLE NO. 9

(4.5 km/h AND SAND/GRAVEL RATIO OF 3/1)

Like wise in cy cle no. 3, pri mary shapes of tek tites, ex cept LDG (sub-rounded in shape), were clas si fied as sub-an gu lar.

Af ter 2 km, the weight loss of 41–54% was re corded. All tek tites be came sub-rounded with a matt sur face. Dur ing the next stage the glass be came rounded with a com pletely matt and flat sur - face. The short est dis tance (up to 8 km) was with stood by moldavite, while the lon gest one was by LDG (up to 12 km).

The av er age tek tite weight loss on dif fer ent stages re lated to the re work ing dis tance for cy cles 7, 8 and 9 is pre sented in Fig ure 4.

CYCLE NO. 10 (

5.5 km/h AND SAND/GRAVEL RATIO OF 1/3)

Fur ther speed in crease com bined with a large amount of gravel in the de posit con trib uted to the rapid ero sion of the tek - tites and LDG. Af ter 4 km all glasses were al ready rounded with mat ted, smooth sur faces. Traces of ero sion were only vis i ble on the sur face of moldavites. The weight loss was also sig nif i cantly higher in con trast to pre vi ous cy cles. Moldavite with stood only

<6 km, while bediasite and indochinite <8 km. Again, LDG with - stood the lon gest dis tance of up to 10 km.

Fig. 3. Av er age tek tite weight loss re lated to the re work ing dis tance for each cy cle at tum bling speed of 3.5 km/h (see also Ap pen dixes 4–6, Ta ble 2)

Fig. 4. Av er age tek tite weight loss re lated to the re work ing dis tance for each cy cle at tum bling speed of 4.5 km/h (see also Ap pen dixes 7–9, Ta ble 2)

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CYCLE NO. 11

(5.5 km/h AND SAND/GRAVEL RATION OF 2/2)

Re sults of stage no. 1 of this cy cle were a unique case in the whole ex per i ment: the weight loss of tek tite (ex cept LDG) was nearly iden ti cal and amounts ~61%. For com par i son, LDG lost

~50% of its ini tial weight. In the case of cy cle no. 10, strong abra sion was vis i ble. Sub-rounded shapes of tek tite were al - tered af ter 4 km of re work ing. Ad di tion ally, their sur face be - came mat ted. Again, LDG with stood the lon gest dis tance, ear - lier af ter 6 km, be com ing well-rounded in shape.

CYCLE NO. 12

(5.5 km/h AND SAND/GRAVEL RATION OF 3/1)

In this cy cle, the abra sion was slightly weaker than in the pre vi ous cy cle, but none of the tek tites with stood lon ger than 10 km. In the mid dle of their re work ing, they be came rounded with a char ac ter is tic mat ted sur face.

The av er age tek tite weight loss on dif fer ent stages re lated to the re work ing dis tance for cy cles 10, 11 and 12 is pre sented in Fig ure 5.

CYCLE NO. 13

(6.5 km/h AND SAND/GRAVEL RATIO OF 1/3)

This cy cle was char ac ter ized by the high est ero sion in the en tire ex per i ment. Pri mary sub-rounded tek tites be came rounded dur ing the first re work ing dis tance step. Weight loss in - creased to 84% in the moldavite case. This re sults in stage 1, be ing the only one that was no ticed on moldavite. Bediasite and indochinite with stood slightly far ther, but they did not with stand even 8 km. LDG with stood up to 10 km of re work ing with char - ac ter is tic traces of abra sion on its sur face.

CYCLE NO. 14

(6.5 km/h AND SAND/GRAVEL RATIO OF 2/2)

In this cy cle, the high est tum bling speed con trib uted to the fast est abra sion of the tek tites among all cy cles with sand/gravel ra tio of 2/2. Dur ing stage 1, the weight de crease was in the range of 54-69%. Sub-rounded tek tites be came rounded with mat ted sur faces. LDG with stood a max i mum dis - tance of 8 km, while the re main ing ones did less than 6 km.

CYCLE NO. 15

(6.5 km/h AND SAND/GRAVEL RATIO OF 3/1)

De spite the same tum bling speed as in the pre vi ous cy cle, more sand in the de posit sam ple was used. All tek tites be came mat ted af ter only 2 km of trans port, and were rounded. Bedia site did not with stand up to 6 km of re work ing con trary to moldavites and indochinite that the o ret i cally with stood 2 km more. LDG, how ever, was com pletely de stroyed af ter stage no. 4.

The av er age tek tite weight loss on dif fer ent stages re lated to the re work ing dis tance for cy cles 13, 14 and 15 is pre sented in Fig ure 6.

DISCUSSION

A SCHEME FOR TEKTITE ABRASION

This ex per i ment con firmed the low re sis tance of tek tites to flu vial abra sion. Ear lier, Bouška (1964), Žebera (1972), Lange (1996), Bouška et al. (1999) and Trnka and Houzar (2002) con firmed such claims, based on the strati graphic po si tion and the glass shape of moldavites. Ob ser va tions made dur ing tum bling have en abled de vel op ing a gen eral scheme of flu vial abra sion ob served on tek tites in this study. The speed of abra -

Fig. 5. Av er age tek tite weight loss re lated to the re work ing dis tance for each cy cle at tum bling speed of 5.5 km/h (see also Ap pen dixes 10–12, Ta ble 2)

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sion de pends largely on the ini tial shape. Among the se lected groups of tek tites, moldavites had the most an gu lar/sub-an gu - lar ini tial shapes and the most deeply and dif fer en ti ated sur - face sculp tur ing. There fore, in most cases, their weight loss at re spec tive stages is the great est (Figs. 2–6). In the cur rently de vel oped abra sion model, two ba sic steps of abra sion with sev eral abraded glass forms are dis tin guished, af fect ing tek - tites dur ing their re work ing. Both are shown in Fig ure 7. Un for - tu nately, they of ten over lap, mak ing their iden ti fi ca tion even more dif fi cult.

Step 1. This step is more de bat able. It de pends on the size, weight, shape, sur face sculp tur ing of the glass, and on the type of de posit and po ten tial river ve loc ity. Based on the re spec tive re sults, it can be as sumed that this step cov ers up to 50% of the weight loss over the to tal re work ing dis tance.

Dur ing it, the tek tite loses a sig nif i cant part of its ini tial mass (some times even the vast ma jor ity of it). The an gu lar glass shape be comes sub-an gu lar, some times and even rounded in sed i ments with high gravel con tent. Some times, with less ero - sion it seems the o ret i cally pos si ble to rec re ate its orig i nal shape. The glass sur face be comes flat ter, some times even com pletely flat. In sed i ments con tain ing much sand ma te rial, the sur face of the spec i mens is par tially mat ted. In cy cles with a high con tent of gravel, traces of abra sion can be vis i ble on the tek tite sur face.

Step 2. This step oc curs over 50–100% of the to tal re work - ing dis tance. Gen er ally, it oc curs af ter step 1, al though there is a chance of over lap. Dur ing this step, the tek tite be comes rounded and later well-rounded, so that its weight de crease is al ready rel a tively low com pared to step 1. It is not pos si ble to re - pro duce ini tial tek tite or LDG shape. The sur face be comes smooth, some times mat ted (greater sand amount in de pos its), and some times with traces of abra sion. Af ter this step, tek tites are to tally de stroyed.

RESULTS OF REPEATED CYCLES

The first and prob a bly most im por tant re sult of this ex per i - ment is the fact that, de spite the con sid er able dif fer en ti a tion of tum bling speed and type of sed i ment, none of the tek tites had with stood a dis tance lon ger than 12 km (Table 2 and Figs. 2–6).

It ob vi ously de pends on the ini tial size of the glass that can be quite large. Trnka and Houzar (2002) men tioned that some Muong Nong tek tites could pos si bly reach up to 100 kg. Fiske et al. (1999) claimed that these glasses could weight over 700 kg.

Lit er a ture data shows that moldavites could weigh 40 g (Hanus et al., 2016) or even 200 g (R. Skála, pers. comm., 2018), and LDG even more than 2 kg (Clay ton, 1933). An other note wor thy fact is clearly the greater po ten tial of tek tites for re work ing in con trast to LDG. This can not be solely ex plained by the dif fer - ence in the ini tial mass, this lat ter be ing rel a tively low, or the dif - fer ence in the ini tial shape of glass. This is prob a bly due to the pe cu liar chem i cal com po si tion of LDG, made of al most pure sil - ica and thus dis play ing a higher hard ness com pa ra ble to the re - work ing sed i ment (Table 3).

Quartz, com pos ing mainly river grav els, has a hard ness of

~7 on Mohs scale, while tek tites are ~5–6 (Simmons and Ahsian, 2007). Sim i lar chem i cal com po si tion and the same hard ness of moldavites, bediasite and indochinite caused very sim i lar re sults of their po ten tial re work ing – weight loss at in di - vid ual stages and rel a tive max i mal trans port dis tance. Dur ing cy cle no. 1, they were de stroyed be tween stages 3 and 4, un like LDG, that made it through stage 5. Sim i lar cases were re corded in cy cles nos. 5, 7, 9–15. Ob vi ously, the dif fer ences oc cur also in weight loss dur ing stages no. 1. In each case, LDG lost much less weight per cent age, al though its shape and ini tial mass were sim i lar to other tek tites. An in ter est ing is sue lies in the re - sults of stage 1 of cy cle no. 11, when tek tites, with the ex cep tion of LDG, lost prac ti cally the same weight per cent age. In ad di tion, Fig. 6. Av er age tek tite weight loss re lated to the re work ing dis tance for each cy cle

at tum bling speed of 6.5 km/h (see also Ap pen dixes 13–15, Ta ble 2)

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M.

Fig. 7. Two main steps of tek tites flu vial abra sion with main abraded glass forms, based on the re sults of tum bling cy cles

A – sub-rounded glass with sur face sculp tur ing; B – sub-rounded glass with matt sur face; C – rounded glass with low sphe ric ity and abra sion signs; D – rounded glass with low sphe ric ity and matt sur face; E – rounded glass with high sphe ric ity and matt sur face; F – sub-rounded glass with par tially matt sur face and abra sion signs; G – rounded glass with high sphe ric ity and abra sion signs; H – rounded glass with high sphe ric ity and al most flat sur - face; I – rounded glass with al most flat sur face; J – rounded glass with low sphe ric ity and abra sion signs; K – rounded glass with high sphe ric ity; L – rounded glass with flat sur face; M – rounded glass with high sphe ric ity and flat sur face; scale bar – 2 mm

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they all lasted over a sim i lar dis tance. This can be ex plained by their very sim i lar shapes. By far the far thest trans port was sup - ported by a sed i ment con tain ing larger pro por tions of sand.

Prac ti cally, in all cy cles where de pos its con tained a high amount of sand, tek tite re work ing was lon ger and tek tites and LDGs showed a lower weight loss for each stage. Ad di tion ally, the glass that was re worked in a greater per cent age of sand showed a much larger matt sur face than tek tites from cy cles con tain ing more gravel. Note wor thy are the large dif fer ences in weight loss in stages no. 1 and no. 2. De pend ing on the tum - bling speed and sand/gravel ra tio of the de pos its, these val ues vary from 33–84% for stage no. 1 to 15–38% for stage 2. This is first caused by the greater abra sion of ini tial tek tites with ir reg u - lar shapes and deep sculp tur ing of sur face. When the tek tite is al ready eroded and its shape be comes much more reg u lar, the weight loss is much smaller – from 10 to 25% for stage no. 3 and from 6 to 14% for stage no. 4. Stages no. 5 are char ac ter - ized by a very small weight loss, from 6 to 10%. It fol lows that the gen eral pat tern of abra sion looks rel a tively sim i lar (Figs.

2–6), in spite of many dif fer ences be tween tek tites and the con - di tions un der which they had been re worked. From these re - sults, it can also be con cluded that the type of sed i ments is much more im por tant for the prog ress of abra sion than the tum - bling speed. In the case of moldavites from stages no. 1 of cy - cles 1 and 3, the dif fer ence in weight loss was 10%, al though they were re worked at the same tum bling speed. A sim i lar dif - fer ence is noted in other cy cles for all tek tites. The high est value is 25% in the case of moldavite from stages no. 1 of cy cles 13 and 15. There are also small dif fer ences in weight loss in the case of tek tites from the same re work ing dis tance (stages) and type of sed i ment (sand/gravel ra tios), but dif fer ent tum bling speeds. For in stance, bediasite from stage no. 1 of cy cle no. 1 lost 52% of its ini tial weight. In the same stage, but from cy cle no. 4, it al ready lost 55% of its weight, and in cy cle no. 7–58%.

Com par i son of the other cy cles with each other sug gests that this dif fer ence is caused by the vari abil ity of the sed i ments (i.e.

sand/gravel ra tio), not by the dif fer ences in the spec i mens. In the case of cy cles nos. 1, 4, 7, 10, 13 and 15, moldavites lost their weight at the fast est pace. This can be ex plained by their

ini tial ir reg u lar shapes and deep sur face etch ing that was by far the most de vel oped and thus the most ex - posed to abra sion. When com par ing the re sults of cy - cle no. 13 with those ob tained by Brachaniec (2018a), there are gen eral sim i lar i ties in the per cent age weight loss and ‘trans port length’, de spite the dif fer ence in tum bling speed by 4 km/h. In cy cles with a high gravel con tent, the high est weight loss oc curs dur ing stage no. 1, reach ing 65% (Brachaniec, 2018a) and even 84% (this study).

Un doubt edly, the pre sented ex per i ment val i dates the sus cep ti bil ity of tek tites to flu vial abra sion. How - ever, these re sults and con clu sions are purely the o - ret i cal ones. The nat u ral en vi ron ment of tek tite re - work ing is con tin u ously chang ing. The en ergy level of the sur round ing en vi ron ment will never be con stant along the whole course of the river, just like the lo cal changes of river de pos its. Nat u ral con di tions have no chance of be ing re pro duced in the lab o ra tory; thus, the re sults should be sub se quently treated only as a gen eral scheme. More over, aim ing at more re li able tum bling re sults, iden ti cal tek tites would have to be used, which is also im pos si ble. Bear ing in mind the huge amount of tek tites pro duced af ter an im pact, e.g.

104 tons of moldavites lo cated in a geo log i cal re cord (Trnka and Houzar, 2002), these very same tek tites take many dif fer ent forms and shapes that later af fect their re work ing. As they do not take the reg u lar shape, the mea - sure ments of their di men sions can also be tainted by small er - rors. A sim i lar sit u a tion ex ists when deal ing with de pos its where re work ing takes place. For ex per i men tal pur poses, a typ i cally flu vial sed i ment was used for the en tire Ce no zoic. How ever, it should be kept in mind that the slight est change in fa cies will re - sult in changes in the de gree of tek tite ero sion, as ex em pli fied with the pro por tions of sand and gravel as shown in this study.

Nev er the less, the use of these both frac tions in the pre sented tum bling ex pe ri ence was nec es sar ily re quired since they usu - ally oc cur to gether in river sed i ments. Fur ther more, it should be taken into ac count that the re work ing pro cess it self can last hun dreds, thou sands or even mil lions of years, thus ex plain ing the dis crep ancy be tween the age of the tek tite-bear ing de pos its and that of the or i gin im pact event. Bear ing in mind the above - -men tioned ar gu ments, it should be noted that the re sults of such an ex per i men tal tum bling, es pe cially the weight loss dur - ing suc ces sive cy cles, should be only treated as an in dic a tive or der of mag ni tude highly vari able de pend ing on many en vi ron - men tal vari ables. To gether with de ter min ing the re work ing stage of found tek tites, it is also nec es sary to an a lyse the con di - tions un der which re work ing had been tak ing place.

SUMMARY

1. Im pact glasses have low re sis tance to flu vial abra sion.

Lon ger re work ing of LDG in con trast to other used tek tites is prob a bly caused by higher sil ica con tent;

2. Re sults of the pre sented ex per i ment show that the main weight loss of tek tites takes place dur ing the first stage of re - work ing. It is strictly con nected with their ini tial shapes and sur - face sculp tur ing;

3. Low en ergy of the en vi ron ment and de pos its with a con - sid er able sand con tent de ter mined lon ger re work ing of glasses;

4. The pre sented scheme of glasses abra sion is only a tip of this pro cess in real en vi ron ment, due to the pres ence of many chang ing con di tions, like en ergy flow and de posit li thol ogy.

T a b l e 3 Gen eral chem i cal com po si tion of tek tites

El e ments

[wt.%] Moldavite* Bediasite** Indochinite*** Lib yan Desert Glass****

SiO2 78.72 77.27 77.38 98.26

TiO2 0.2 0.7 0.71 0.07

Al2O3 10.75 13.07 10.93 0.53

FeOto tal 1.83 3.41 4.08 0.05

MnO 0.05 – 0.09 0.002

MgO 1.41 0.65 1.73 0.03

CaO 2.2 0.62 1.43 0.02

Na2O 0.54 1.63 0.98 0.27

K2O 3.57 2.27 2.39 0.06

P2O5 0.04 – – 0.01

TOTAL 99.31 99.64 99.71 99.3

* – av er age value from Koeberl et al. (1988), Lange (1995), Øanda et al.

(2008), Skála et al. (2009), Brachaniec et al. (2014b, 2015, 2016); Brachaniec (2017); ** – av er age value from Chaussidon and Koeberl (1995), Koeberl and Glass (1988); *** – av er age value from Yagi et al. (1982), Mazer et al. (1992), Amare and Koeberl (2006); **** – av er age value from Koeberl (1997), Guzzafame et al. (2009), Szopa et al. (2015)

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Ac knowl edge ments. The au thor would like to thank A. Muszyñski and R. Skála for pro vid ing valu able ad vice and con struc tive com ments on the manu script, as well as to W. Granoszewski for care ful ed i to rial han dling. The au thor also thanks B. Glass for many com ments dur ing prep a ra tion of the manu script. Pho to graphic as sis tance of W. Krawczyñski is

grate fully ac knowl edged. The au thor also wishes to thank M.

Salamon for pro vid ing the tum bling bar rel, and B. Ferré for im - prov ing the Eng lish ver sion.

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The method presented here is the key to the inductive construction of theorems on the higher order regularity of the solution of the problem (1), (2) with respect to the parameter

The major technical result which we obtain is of indepen- dent interest, and it states, in particular, that whenever a locally minimal group G having no small normal subgroups (in

Section 5 is devoted to an application of the inequality (1.4) to a special version of the XVIth Hilbert problem about the number of limit cycles for polynomial planar vector

The objective of the research study was to analyze the chemical composition, in- cluding amino acid composition, of the rapeseed protein-fibre concentrate (RPFC) as well as to

The radius of the circle circumscribing this triangle is equal to:A. The centre of the circle