Analyzing Sedimentary Rocks to Evaluate Paleo Dimensions and Flow Dynamics of Permian Barakar River of Rajmahal Gondwana Sub-Basin of Eastern India

Abstract

The cross strata and planar strata of sedimentary rocks are used in estimating paleo dimensions and flow dynamics of Permian Barakar River of eastern India. Quantitative estimates indicate that mean bed form became thinner i.e., from 1.363 m to 0.928 m to 34.21 m–23.33 m, as the Barakar River flowed with flow velocity of between 90 cm/sec and 157 cm/sec from Fox Ridge situated to the south on a steeper slope which becomes gentler downstream. The friction factor (0.036) is on higher side indicating low flow resistance while bed shear stresses remain competent, even during low paleo-discharges to transport coarse-pebble bed. Rouse number, Z, is decreased from Brahmini (3.38) to Hurra (1.71) implying predominant bed-load in upstream and local transition to mixed load in the downstream. Bed load formed 17.74 to 15.62 percent in upstream and reduced to 10.14–7.94 percent in downstream suggesting bed load channel for the former and mixed load channel for the latter corroborating estimated Rouse Number (Z) values. The trunk Barakar River on an average was about 2260 km long, 817 m wide and 13.63 m deep with channel belt width in between 6310 and 2205 m. The river channel sinuosity was in place of sinuosity 1.361 in the south-southwest part and progressively became more sinuous in the northern and northeastern part of the basin (1.728) with maximum sinuosity of 1.955. The catchment area of the Barakar River lies between 10,700 to 422,600 km2 and paleo-discharge between 22,070–4510 m3/sec with the maximum 66,000 m3/sec and whose mean annual flood was in the range of 170,600–42,260 m3/sec. These parameters suggest that initially multi-thread and broad Barakar River became narrow and single thread in downstream and had its outlet in the northeast (Sikkim, Assam and Bangladesh) towards the Tethys Ocean during Permian times.

1. Introduction

Internal sedimentary bed forms such as dunes and ripples, which are believed to be truncated in the preserved geologic record, can now have their full heights estimated from cross bedding-sets and cosets within quantitative uncertainty and order of magnitude [1, 2, 3, 4]. Recent researches provide a methodology to evaluate paleo dimensions and flow dynamics of ancient fluvial systems [5, 6, 7]. Fluvial paleo-channels can be scaled from numerical equations based on grain size along with channel depth and width measurements and augmented by flow depth estimated from estimated dune bed form height from cross bedding set thickness using data of cross bedding set thickness [2, 3, 8]. Calculated parameters include mean bed form height, channel depth, channel belt width, channel width, paleoslope, boundary shear stress; Darcy-Weisbach friction factor, paleoflow velocity, and paleo discharge provide insight into basin analysis.

An attempt is made to scale the paleo-dimensions and flow dynamics of fluvial channels of Early Permian Barakar River. These parameters together with sedimentary rock record provide meaningful interpretations of fluvial architecture, the evolution of fluvial style.

2. Study area, stratigraphy and sedimentological sketch

The Rajmahal sub- basin of eastern India is part of the Gondwana Master basin and covers a large area of Bengal basin, North Bengal and Purnea. There are four sub basins (coalfields) from south to north i.e. Brahmini, Pachwara, Chuperbhita and Hurra (Figure 1A). The Gondwana rocks are bounded by the river Ganga to the north, by Rajmahal volcanic to the east, by rugged metamorphic to the west and by laterite and recent alluvium to the south. The unclassified Archean rocks form the basement of the Gondwana rocks in the Rajmahal sub-basin with a pronounced unconformity, though at places the contact is faulted. Isolated patches of Talchir rocks are seen along the western periphery of the basin. This formation is succeeded by the Karharbari Formation, composed of grits, conglomerates and sandstones. The overlying coal bearing Barakar Formation directly rests over the Archean basement at most places and is exposed along the river valleys where the overlying traps and Triassic sediments are denuded. The Early Permian Barakar rocks are overlain by the Dubrajpur Formation (Late Triassic), which is, intern, followed by Rajmahal traps and Inter-trappean rocks (Early Cretaceous to Early Jurassic).The contacts between Early Permian, Late Triassic and Early Cretaceous are unconformable. A generalized stratigraphic sequence of the Gondwana rocks of Rajmahal sub-basin is shown in Figure 1B.

Figure 1.

(A) Location and geological map; and (B) subsurface Gondwana stratigraphy of Rajmahal sub-basin of eastern India (based on bore hole log).

Gondwana sedimentation in Rajmahal sub-basin commenced with the deposition of the Talchir sediments under glacial and fluvio-glacial, glacio-lacustrine and/or shallow marine environments [9]. Following retreat of Talchir ice, the rejuvenated rivers flowed dominantly towards the northwest and northeast and deposited shallow waters gravelly and sandy sediments as discontinuous patches gradationally above Talchir as Karharbari Formation. The overlying Barakar rocks are characterized by fining upward cycles of coarse to medium sandstones with interbedded siltstone, shale and thick to thin coal seams [10, 11]. These rocks were deposited by laterally migrating river channels in response to varying discharge and/or intermittent differential subsidence/tectonism, and led to the development of peat swamps in the flood plains and protected lakes.

3. Methodology

3.1 Field observations and basic data

Sedimentological data is collected from 26 localities measuring 5–10 meter vertical sections mostly along the river and small tributaries in all the four areas. Once all outcrops were located, multiple measurements were collected including set-thickness, average grain sizes, and total thickness. Cross-bed sets thickness were measured in the z-plane with 30 cm scale and the minimum distance between measured vertical sections was roughly 0.50 km. The cross bedding sets in the study area are interpreted to be mostly dunes for the following reasons:

(1) cross bedding sets are truncated, (2) Paleocurrent directions were much less variable than one would expect in bars, (3) even if there are some bars within the data, they are usually made up of many layers of truncated dunes, and (4) all ripples observed on the outcrops were flowing in the same direction as the cross bedding sets rather than in a separate direction as see on a bar [12, 13].

3.1.1 Cross-sets

Cross-set heights were measured as these data can be used to reconstruct original bedform heights and formative flow depths. Trough- and planar cross bedding, which are genetically indicative of bed load transport, were present at nearly all studied field sites. They occurred predominantly in sand grade deposits, but omnipresent in pebble grade deposits of southern coalfields. To establish mean cross-set heights, the sampling strategy of [7] was followed.

3.1.2 Grain size

Grain sizes were measured at each outcrop. These measurements are taken using a standard 10× hand lens and a grain size card. Grains were identified in each set according to Udden-Wentword grain size scale. Grains within each set tended to be unimodal or at least largely represented by one size; this made finding the average size within cross bedding sets and was substituted for D₅₀ which represents the median of the grain size distribution used in this study.

Sedimentological data so acquired from the Barakar exposures include grain size, cross bedding height, and bar-form height. These data were then used to determine multiple channel geometry, paleohydraulic parameters and paleo dynamics including: mean bed form height, channel depth and width, channel belt width, paleoslope, boundary shear stress, Darcy-Weisbach friction factor, paleoflow velocity, paleodrainage, and overall drainage area by the methods outlined below.

4. Quantitative paleo-dimensions

4.1 Bedform height and channel depth (H_m) & (Dc)

To calculate original bedform heights from average cross-set measurement, the empirical relationship [14] was used. These equations determined relationships between the mean value of the exponential tail of the probability density function (PDF) for cross-set thicknesses and dune heights [14, 15]. The work [14, 16] has shown that the dune height (H_m) can be estimated from mean cross–set thickness (S_m) using a regression equation:

$${\mathit{H}}_{\mathrm{m}}=5.3\mathrm{\beta }+0.001{\mathrm{\beta }}^2$$

Where β = S_m/1.8.

This can be simplified as:

$${\mathit{H}}_{\mathrm{m}}=2.90{\left(\pm 0.70\right)}^{\ast }{\mathit{S}}_{\mathrm{m}}$$E1

Where 2.90 are the mean and 0.70 is the standard deviation. H_m is the mean dune height; S_m is the mean cross-set thickness, β is the mean value of the exponential tail of the probability density function (PDF) for topographic height relative datum. While Eq. (1) relating formative dune heights to preserved cross bedding sets perhaps unusual in a wide variety of natural forces and random events accompanying the formation of such cross-sets. Nevertheless’ the above equation is valid for a wide range of flume and river experiments [1, 2] to suggest that abnormally thick, isolated cross bedding sets formed by unit bars should be excluded from the data. The formative dune height is calculated from the preserved cross-sets and erosional surfaces at the top and bottom of cross bedding sets are almost horizontal so it is unlikely that aggradations and degradations played any role in the expression of cross-sets within the Barakar sandstone.

Equations for relating dune height to channel depth were developed [14] (Eq. (2)) show that flow depth is typically 8 to 10 times mean dune height. Alternatively, ref. [17] empirical relationship (Eq. (3)) based on the relation between bankfull depth and dune height referred to as Dc = 11.6 H_m^0.84 can be used as a measure of maximum channel bankfull flow depth (Dc)

$$8<\mathit{Dc}/{\mathit{H}}_{\mathrm{m}}<10$$E2

$$\mathit{Dc}=11.6{{\mathit{H}}_{\mathrm{m}}}^{0.84},0.1\mathrm{m}<\mathit{Dc}<100\mathrm{m}$$E3

Where Dc is river channel depth and H_m is mean dune height.

The method of using cross-beds to determine channel flow depth has been tested in several modern and ancient rivers [14, 15, 18]. Based on measured sections thickness of dune scale cross-strata sets are on average 47 ± 31 cm (Brahmini sub-basin); 43 ± 28 cm (Pachwara sub-basin); 37 ± 20 cm (Chuperbhita sub-basin); and 31 ± 14 cm (Hurra sub-basin)’ respectively. Setting (S_m) = 47─30 cm, the above Eq. (1) yields a mean dune height (H_m), varying from 0.928–1.363 m for the above four Gondwana sub- basins from south to north. These reconstructed mean dune heights agree closely with those reported by ref. [2] of 0.90–1.52 m and ref. [1] of 1.07–1.42 m from ancient fluvial channel bars. According to ref. [14] bankfull flow depth is typically 8 to 10 times mean dune height. This suggests bankfull flow depths (Dc) of between 7.25–13.63 m. Using ref. [17] relationship, average bankfull channel depth of Barakar sandstone is varying between 10.87–14.96 m. We thus determine maximum (i.e. bankfull) flow depths to be about 13.0 m.

The paleochannel flow depth was estimated from the thickness of lateral macroform using the equation [19]; a 10% reduction in thickness for the conversion of sand to sandstone as a result of compaction appears conservative following Ingles and Grant suggestion, therefore, divided by 0.9 to convert these measures to original bankfull depth.

$$\mathit{Dc}={\mathit{D}}^{\ast }/0.9$$E4

Where D* is the maximum channel bankfull flow depth, which is represented by the thickness of the sandstone macroform, 0.9 compensates for the compaction factor.

The average thickness of the fining-upward facies sequence of the Barakar sandstone varies from 15 m in Brahmini sub-basin in the north through Pachwara sub-basin and Chuperbhita sub-basin to 10 m in Hurra sub-basin in south. The bankfull depth so calculated yield a value in between 11.12–16.67 m which is similar to those calculated from Eqs. (2) and (3) calculated above.

4.2 Bedform length (L_b)

Ref. [20] have presented a model relating bedform length (L_b) to bedform height (H_m) as:

$${\mathit{H}}_{\mathrm{m}}={\mathrm{\partial }}_0{{{\mathit{L}}_{\mathrm{b}}}^{\partial }}_1$$

Where ∂₀ and ∂₁ are empirical parameters with associated uncertainties and values are ∂₀ = 0.0513; ∂₁ = 0.7744 [21] (Table 1) and L_b is bedform length. Substituting the values of empirical parameter in Eq. (5) we get

Parameter	Empirical equation	Brahmini sub basin	Pachwara sub basin	Chuperbhita sub basin	Hurra sub basin
Mean cross-bed thickness (m)	Sm	0.47	0.43	0.37	0.31
Mean particle Size(mm)	(D50)	0.72	0.57	0.45	0.35
Dune height (Hm)	Hm = 2.90 (±0.70) Sm	1.363	1.247	1.073	0.928
Flow Depth(m)	8 < Dc/Hm < 10	10.91–13.63	9.64–12.52	8.58–10.73	7.25–9.23
	Dc = 11.6 Hm^0.84	14.96	13.87	12.56	10.87
	Dc = D*/0.9	13.54	12.48	11.30	9.78
Bedform-length (m)	Hm = 0.0513Lb^0.7744	34.21	31.34	26.97	23.33
	Hm = 0.0677Lb^0.8090	25.52	23.27	20.77	17.65
	Hm = 0.21Lb^0.56	28.18	23.99	18.36	14.16
Channel width (m)	Wc = 8.88 * Dc^1.82	817	697	534	408
	Wc = 64.4 *Dc^1.54	2956	2586	2063	1380
Channel belt width (m)	Wcb = 59.9 Dc^1.80	6310	5534	4305	2205
	Wc = (Wcb/6.89) ^1.01	6780	5370	3240	2800
Sediment load parameter (M)	F = 255 M ^−1.08	3.07	3.52	5.41	6.92
Percentage of total load as bed load	55/M	17.74; Bed load; channel	15.60; Bed load; channel	10.14; Mixed load; channel	7.94; Mixed load; channel
Rouse Number (Z)	Z = Ws/βκ U*	3.58	3.46	2.01	1.71
Reynolds Particle Number (Rep)	Rep = √ R gD50D50/v	79.957	49.415	29.573	16.975
Channel Slope (Sc)	Sc = τ^*bf50RD50/Dc	0.000162	0.000152	0.000139	0.000116
	LogSc = α0 + α1 log D50 + α2 log Dc	0.000138	0.000144	0.000159	0.000176
	Sc^½ = nVc/Dc	0.000065	0.000052	0.000045	0.000038
Froude Number (Fr)	Fr = Vc/√ g Dc	0.136	0.111	0.108	0.102
Boundary stress shear N/m^2 or Pa	τb = ρ g DcSc	10.68	8.66	6.77	5.24
Critical shear stress; N/m^2 or Pa	τcr = τ* (ρs–ρw) g D50	0.169	0.152	0.174	0.204
Velocity(m/sec)	Vc = (R ^0.67Sc^0.50)/n	1.57	1.35	1.12	0.92
	Vc = [(8 g R Sc/f)] ^0.50	1.89	1.77	1.52	1.27
Manning Roughness Coefficient (n)	n = 0.039 D50^0.167	0.036	0.025	0.023	0.021
Darcy-Weisbach Friction factor (f)	(8/f)^0.50 = 2.2 (Dc/D50) ^−0.055Sc ^−0.275	0.037	0.036	0.035	0.033
Channel sinuosity(Sch)	Sch = 3.5(Wc/Dc) ^0.20	1.361	1.517	1.621	1.632
	Log Sch = 3.68 –0.0684 L + 0.00032 L^2	1.383	1.570	1.663	1.728
Discharge (m^3/sec)	Qw = Wc DcVc	22,070	12,865	5880	4510
Mean Annual flood; (m^3/sec)	Log Qflood = 2.084–0.070 log DA^2+ 0.865 Log DA	170,600	112,200	65,450	48,640
Drainage Area (km^2)	DA = 249 Dc^2.44	107,004	86,536	60,512	42,260
	Qw = 0.0161 DA^0.9839	136 × 10^3	81 × 10^3	37 × 10^3	28 × 10^3
Length of River (km)	L = 1.109 DA^0.545	703	631	525	427

Table 1.

Paleo- dimensions, flow dynamics and paleochannel parameters of early Permian Barakar River.

$${\mathit{H}}_{\mathrm{m}}=0.0513{{\mathit{L}}_{\mathrm{b}}}^{0.7744}$$E5

An empirical relationship between bedform length and bed forms height has been presented by ref. [22] as:

$${\mathit{H}}_{\mathrm{m}}=0.0677{{\mathit{L}}_{\mathrm{b}}}^{0.8090}$$E6

On the other hand, ref. [23] who used the data from the Rio Parana (Argentina) and those from the Lower Rhine (The Netherland) and Negro (Brazil) obtained relationship between bed form height and length which affords another assessment of the bed form length.

$${\mathit{H}}_{\mathrm{m}}=0.21{{\mathit{L}}_{\mathrm{b}}}^{0.560}$$E7

When previously estimated value of H_m is substituted, Eq. (5) indicates that the bedform length of dunes was about 34.21 m in Brahmini sub-basin and decreased down the paleoslope to about 23.33 m in Hurra sub-basin; Eq. (6) indicates bedform height in between 25.52 m and 17.65 m, and from Eq. (7) it is 28.18 m and 14.16 m in up dip basins (Brahmini, Pachwara) and decreased down dip to 18.36 m and 14.16 m in down dip basins (Chuperbhita, Hurra). The overlap in these three approximations suggests that the bedform length of the Barakar River was about 34.21 to 14.16 m. These dunes are classified as large dunes and such dunes become progressively smaller and their lengths become shorter as the flow strength decreases. For equilibrium dunes, the maximum steepness, H_m/L_b. is approximately 0.055 (L_b = dune wavelength), L_b/D_c is approximately 6, and the minimum D_c/H_m is approximately 3. It appears that for all types of river dunes irrespective of those not in equilibrium with the flow in the Barakar sandstone have Dc/H_m average between 6 and 10. Recently ref. [24] suggests that steeper slopes tend to develop elongate, narrow braid bars than rivers with shallower slopes supports above contention that during deposition of Lower Barakar sediments, the River had long braid bars (≈35 m) than during deposition of Upper Barakar (≈15 m).

4.3 Channel width (W_c)

There are a number of empirical equations relating average bankfull channel depth to river channel width, many of which are thoroughly communicated and evaluated [13, 25]. However, the empirical equations used here are those they developed on river depth to channel width [1, 26] as

$${\mathit{W}}_{\mathrm{c}}={8.88}^{\ast }{{\mathit{D}}_{\mathrm{c}}}^{1.82}$$E8

$$\mathit{W}\mathrm{c}={64.4}^{\ast }{{\mathit{D}}_{\mathrm{c}}}^{1.54}$$E9

Where, W_c = width of channel, and D_c = bankfull channel depth. Put down the value of channel depth in Eq. (8) we get the width of channel in between 408 m −817 m, and Eq. (9) indicate about 1380 m to 2956 m in the Rajmahal Barakar River.

4.4 Sediment load parameter (F)

So important is the type of sediment load in determining fluvial morphology that Schumm has proposed classifying alluvial river channels on the basis of the ratio of suspended load to bed-load and introduced the term bed-load, mixed load and suspended load channels ([27], p. 1579, Table 1). Although the ratio of suspended load to bed load is not determined directly but directly related to the percentage of silt and clay in the channel perimeter. And to calculate the percent silt-clay in the channel perimeter (M), following relationship is used:

$$\mathrm{M}=\left({{\mathrm{S}}_{\mathrm{a}}}^{\ast }{\mathit{W}}_{\mathrm{c}}\right)+\left({{\mathrm{S}}_{\mathrm{b}}}^{\ast }{\mathit{D}}_{\mathrm{c}}\right)/{\mathit{W}}_{\mathrm{c}}+{\mathit{D}}_{\mathrm{c}}$$E10

Where M = Sediment load parameter, W_c = Bankfull channel width, D_c = Bankfull channel depth, S_a = percent silt-clay in channel alluvium, and S_b = percent silt-clay in the bank alluvium. Detailed petrographic and geochemical studies in recent years have revealed that much of the clay size fraction of Barakar sandstones is authigenetic and secondly digenesis may completely alter the original silt-clay matrix may cause unknown error in estimation of M derived from Eq. (10), hence not used in present study. It is also possible to estimate M for the Barakar sandstone indirectly from Schumm’s following equation:

$$\mathrm{F}=255{\mathrm{M}}^{-1.08}$$E11

Where F (width/depth ratio) = W c/Dc, and W_c = bankfull channel width, Dc = bankfull channel depth, and M = sediment load parameter. Substituting the estimated values of Wc and Dc, Eq. (11) indicates that Barakar River had a sediment load parameter of 3.07 and 3.52 for the Brahmini and Pachwara sub basin and between 5.41–6.92 in the northern sub basin of Chuperbhita and Hurra. Values from tables ([27], p. 1579, Table 1) indicate range in M, between 5 and 20 for mixed load rivers and less than 5 for bed load Rivers. Furthermore, the assessment of percentage of total load as bed load is estimated by using ref. [27] formula:

$$55/\mathrm{M}$$

where M denotes sediment load parameter.

By substituting values for M, the bed load comes out to be 17.74, 15.62, 10.14 and 7.94 respectively for Brahmini, Pachwara, Chuperbhita and Hurra sub basin respectively. Calculated values of M and percentage of total load as bed load in this study fall within the range of those established values for bed load rivers in the southern part (Brahmini and Pachwara sub basins) and mixed load rivers in northern part (Chuperbhita and Hurra sub basin).

4.5 Width of channel belt (W_cb)

There are a number of empirical relationships between channel width and channel belt width, for example, from ref. [25] (Eq. (12)) and [1] (Eq. (13)).

$${\mathit{W}}_{\mathrm{cb}}=59.9{{\mathit{D}}_{\mathrm{c}}}^{1.80}$$E12

$${\mathit{W}}_{\mathrm{c}}={\left({\mathit{W}}_{\mathrm{cb}}/6.89\right)}^{1.01}$$E13

Taking the mean bankfull channel depth of 15.00 m–11.78 m gives a range of channel-belt widths from 6780 m–2205 m. The value in these calculations is that they give a range of possible channel and channel-belt sizes that compare favorably with outcrop observations where the Barakar channels are confined, or where channel margin are observable.

Sedimentological descriptions of the fluvial deposits of the study area show a predominance of dune-scale cross-stratified, pebbly, coarse to medium grained sandstone, fining upward into fine grained sandstone and shale, shaly coal and thick coal seams characterized by asymmetrical fining upward cycles [11]. The abundant shale and fine clastics deposited in the floodplain demonstrate that the Barakar Rivers carried a significant shaly load in suspension, as well as a sandy bed load moving primarily as dune-scale bedform.

4.6 Paleo-channel slope (Sc)

Slope affects river plan form (i.e. braiding is favored by steeper slope and meandering by gentler slope) and facies boundaries [13, 28]. Paleoslope in ancient river system is calculated using physics-based methods, such as Shield’s [29] threshold for bed-load movement, especially where grain size, channel depth and channel width of a paleo-river are known [4, 16]. Paleoslope is estimated using grain size and density of sediment grains following the empirical equation [22, 29];

$${{\mathrm{\tau }}^{\ast }}_{\mathrm{bf}50}=\left({\mathit{D}}_{\mathrm{c}}\mathit{Sc}\right)/\left({\mathit{RD}}_{50}\right)$$

on re-arranging we get

$$\mathit{Sc}={{\mathrm{\tau }}^{\ast }}_{\mathrm{bf}50}{\mathit{RD}}_{50}/{\mathit{D}}_{\mathrm{c}}$$E14

Where Sc is the paleoslope, τ^*_bf50 is the bankfull Shields number for dimensionless shear stress, Dc is the mean bankfull channel flow depth, R is the submerged dimensionless density of sand-gravel sediment (ρ_s–ρ_w), ρ_s = the grain density (assumed to be quartz, with density of 2.65 g/cm³), ρ_w = the fluid density; and D₅₀ is the median grain size, τ^*_bf50 is assumed to be 1.86 [22]. When working with ancient fluvial systems, D_c is measureable from outcrop or estimated by empirical formula (Eqs. (7) and (8)), and D₅₀ for this study was estimated from observations of rocks in outcrop using magnifying lens 10× and/or from grain size analysis. When previously determined values of channel depth and median grain size are substituted, Eq. (13) indicate that paleochannel slope or gradient was about 0.000162 for Brahmini sub basin and decreased to 0.000116 in northern Hurra sub basin as sedimentation progressed in the area.

Another estimate of the paleoslope of the Early Permian Barakar River can be derived using the model [23] of which is based on Bayesian regression analysis relating paleoslope to bankfull channel depth, Dc, and median grain size D₅₀ that takes the form:

$$\mathrm{Log}{\mathrm{S}}_{\mathrm{c}}={\mathrm{\alpha }}_0+{\mathrm{\alpha }}_{1}log{\mathit{D}}_{50}+{\mathrm{\alpha }}_{2}log{\mathit{D}}_{\mathrm{c}}$$E15

Where α_0, α₁, and α₂ are empirical constant parameters with associated uncertainties are given by −02.08 for α₀, 0.254 for α₁, and − 1.09 for α₂ respectively [30] (Table 1). Empirical paleoslope reconstruction, such as the one applied here for the Barakar rivers; typically involve approximately an order-of-magnitude variation fitted to Trampush’s model. Ultimately, this may have a significant control on the uncertainty of any quantitative estimation of past flow conditions. The sediment grain sizes of the Brahmini and Pachwara channel rages from very coarse to coarse grained sand (≈ 0.72–0.57 mm) with the fine grained sand (≈ 0.25 mm). The grain sizes of remaining two sub basins (Chuperbhita and Hurra) yielded a D₅₀ grain size value between 0.45 to 0.35 mm, categorized as medium to fine grained sandstone. By substituting values for D₅₀ (0.72, 0.57, 0.45 and 0.35 mm), D_c (13.63–9.28 m) in Eq. (15), the channel paleoslope is calculated to between 0.000176 and 0.000138.

Additional approximation of the paleoslope can be derived using the Manning equation for the open channel flow systems. This same relationship has been used to determine the paleochannel slope in many ancient fluvial rivers [5, 8].

$${\mathrm{V}}_{\mathrm{c}}=1.486\left({\mathrm{R}}^{2/3}{{\mathrm{S}}_{\mathrm{c}}}^{1/2}\right)/\mathit{n}$$E16

In this equation, V_c is the average flow velocity, R is the hydraulic radius, approximately equal to the channel depth, D_c, S_c is the channel paleoslope, and n is the Manning roughness coefficient (For metric calculations (CGS), 1.486 is replaced by 1 because Manning equation employed FPS system). Rearranging Eq. (16) and putting R = D_c and 1 in place of 1.486, the formula becomes:

$${\mathrm{Sc}}^{\mathrm{½}}=\mathit{n}{\mathrm{V}}_{\mathrm{c}}/{\mathrm{D}}_{\mathrm{c}}$$E17

Paleoslope of the Barakar channels estimated using Eq. (17) ranges from 0.00038 to 0.00065 (Table 1), which suggests a low paleoslope comparable to slope ranges for the Amazon, Mississippi and Niger Rivers (slope range 0.00002–0.0005; 21). The estimated moderately high paleoslope from Eqs. (15)–(17) for the Brahmini and Pachwara sub basins are an order of magnitude equivalent to the estimated slope of the low sinuosity channel, whereas, estimated lower slope for Chuperbhita and Hurra sub basin channels agrees with the dominant fine clastics observed in the sand body. These values are within the low end of the range of values recorded from modern, humid-tropical climate, fluvial systems that transported mixed load sediments.

5. Flow dynamics

5.1 Boundary shear stress (τ_b)

The boundary shear stress (τ_b) acting on the bed of the channel can be calculated as:

$${\mathrm{\tau }}_{\mathrm{b}}=\mathrm{\rho }\mathrm{g}{\mathrm{D}}_{\mathrm{c}}{\mathrm{S}}_{\mathrm{c}}$$E18

where τ_b = the boundary shear stress, ρ = the fluid density, g = gravitational acceleration, D_c = averaged channel flow depth, and S_c is averaged water-surface paleoslope. Both field and laboratory experiments have shown that initial motion of bed materials in coarse-medium grained rivers typically occurs at a transport stage between 1 and 3 [31]. This relationship between the flow and its container can be applied to all natural channels with some error and has been recently applied in ancient fluvial deposits [32] of the Sharon Formation, USA, ref. [33] for the Parthenon Sandstone USA. Using previous estimates of Dc and Sc in Eq. (16) the boundary shear stress is estimated to be in between 10.68–5.24 N/m² for the Barakar Rivers in Rajmahal Gondwana master basin.

The critical shear stress (τ_cr) represents the necessary boundary shear to move the bed-load materials, based upon their grain size, grain shape, effective density, and roughness. Therefore, the formulation to express critical shear stress (τ_cr) for non-cohesive sand is provided by Shield [29] and is given as:

$${\mathrm{\tau }}_{\mathrm{cr}}={\mathrm{\tau }}^{\ast }\left({\mathrm{\rho }}_{\mathrm{s}}–{\mathrm{\rho }}_{\mathrm{w}}\right)\mathrm{g}{\mathrm{D}}_{50}$$E19

Where τ_cr = the critical shear stress; τ* = the Shield number for the given particle non-dimensional critical shear stress; ρ_s = the grain density (assumed to be quartz with a density of 2650 kg/cm³; ρ_w = fluid density 1000 kg/m³; g = the acceleration due to gravity in m/sec² and D₅₀ = median particle size in meter. Critical shear stress is calculated from solving Eq. (19) when the transport stage was set to initial motion i.e., 1, using paleohydrological data for bankfull depth, and grain size data which comes out in between 0.169–0.204 N/m² or Pa.

Sediment mobility for a given particle size occurs when the boundary shear stress exceed the critical shear stress, in other words τ_b > τ_cr. This relationship has been observed in the Barakar sandstones of present study.

5.2 Paleoflow velocity (V_c)

Under the assumption of steady, uniform (i.e. constant channel depth) flow in a channel that has a rigid boundary (i.e. flow conditions up to bed motion), the threshold mean velocity, V_t, can be computed based on resistance coefficients and channel geometry by two commonly and widely used methods. The first employs the Manning roughness coefficient, n:

$${\mathrm{V}}_{\mathrm{c}}=\left({\mathrm{R}}^{0.67}{\mathrm{Sc}}^{0.50}\right)/\mathit{n}$$E20

And the second uses the Darcy-Weisbach friction factor, f:

$${\mathrm{V}}_{\mathrm{c}}={\left[\left(8\mathrm{g}\mathrm{R}\mathrm{Sc}/\mathit{f}\right)\right]}^{0.50}$$E21

Where R is the hydraulic radius is approximately equal to the depth D_c, Sc is the channel slope and n is the Manning roughness coefficient. The threshold mean flow velocity is a function of the size of bed particles that have been on the way, as evident in the equation for determining the resistance coefficient n and f below [Eqs. (21) and (22)].

Unlike the Manning empirical equation, the Darcy-Weisbach equation uses a dimensionless friction factor, has a sound theoretical basis, and exact accounts for the acceleration from gravity; moreover, the relative bed roughness does not influence the exponents of hydraulic radius and channel slope. For these reasons, the Darcy-Weisbach equation is preferred over the Manning approach as discussed [34]. Many algebraic manipulations has been used to calculate Manning roughness (n) and Darcy-Weisbach friction factor (f) and then various relationships have been proposed between resistance coefficients (n, f) and sediment grain size [35] as:

$$\mathit{n}=0.039{{\mathrm{D}}_{50}}^{0.167}$$E22

Ref. [34] derived a roughness coefficient encompassed a range of straight, braided and meandering, bed sediment sizes (sand and gravel), and river sizes (small scale to large river), as well as perennial rivers:

$${\left(8/\mathit{f}\right)}^{0.50}=2.2{\left({\mathit{D}}_{\mathrm{c}}/{\mathrm{D}}_{50}\right)}^{-0.055}{\mathrm{Sc}}^{-0.275}$$E23

Paleoflow velocities in the Barakar Rivers can be estimated using the method [36]. Their method is based on specific bed forms (e.g. ripples and dunes) are stable within specific ranges of grain size, flow velocity (Figure 2).

Figure 2.

Fine and coarse-medium grained bedform phase diagrams [37]. Inferred range of velocity for Hurra coal basin is 80–125 cm/sec. Pachwara coal basin is 60–150 cm/sec. Chuperbhita coal basin 58–160 cm/sec. Brahmini coal basin 150–200 cm/sec.

According to ref. [14] the height of a dune is strongly dependent on flow depth, therefore dune-scale cross sets is particularly useful in determining both flow velocity and water depth. If above assertion is correct than a flow velocity of between 65 and 160 cm/sec is estimated based on grain size (fine sand to coarse sand) using bed forms, grain size, and water depth and flow velocity plot [36]. Using this Eq. (23), the roughness coefficient (f) comes out to be between 0.0372–0.0334 (Table 1).

5.3 Rouse number (Z)

To determine dominant mode of sediment transport, the non-dimensional scale parameter Rouse number, Z, was calculated as

$$\mathrm{Z}={\mathit{W}}_{\mathrm{s}}/\mathrm{\beta \kappa }{\mathrm{U}}_{\ast }$$E24

Where β is a constant taken as 1, and κ is the von Karman constant, taken as 0.40, U_* is the boundary shear velocity, and sediment settling velocity, W_s, was calculated as a function of grain size following [38] as;

$$\mathit{W}\mathrm{s}=\mathrm{R}\mathrm{g}{{\mathrm{D}}_{50}}^2/{\mathrm{C}}_1\mathrm{v}+{\left(0.75{\mathrm{C}}_2\mathrm{R}\mathrm{g}{{\mathrm{D}}_{50}}^3\right)}^2$$E25

Where g is the Earth’s gravitational acceleration, D₅₀ is the median diameter of a particle, v is the kinematic viscosity of water (1 × 10⁻⁶ for water at 20^o C and C₁ = 18 and C₂ = 1 are constants associated with grain sphericity and roundness. And boundary shear velocity U_* determined as.

$${\mathrm{U}}_{\ast }=\surd {\mathrm{\tau }}_{\mathrm{b}}/{\mathrm{\rho }}_{\mathrm{w}}$$

Where τ_b is the boundary shear of the fluid and ρ _w is the mass density of the fluid. With Z, dominant mode of sediment transport in alluvial system is typically bed load for Z > 2.5, 50% suspended load (i.e. mixed load) for 1.2 < Z < 2.5. Setting previously estimated values of R, Ws (sediment fall velocity), D₅₀, and kinematic viscosity of water, Eq. (24) indicates that the Rouse Number (Z) was about 3.58 and 3.46 for the Brahmini and Pachwara and decreased to 2.01 and 1.71 in the northern Chuperbhita and Hurra sub-basins. These estimated values for Z is characteristic of a bed load channel in the southern part and mixed load (50% suspended load) for the northern part of the Rajmahal Gondwana master basin. These estimated values are in agreement with Schumm sediment load parameter (M) calculated by Eq. (11) suggests convincingly that the southern part of the basin predominantly deposited by bed load channels whereas the northern part mostly deposited by mixed load channel.

5.4 Reynolds particle number (R_ep)

To collaborate inferred sediment transport modes, the particle Reynolds particle number, R_ep, was additionally calculated as:

$${Re}_{\mathrm{p}}=\surd \mathrm{R}\mathrm{g}{\mathrm{D}}_{50}{\mathrm{D}}_{50}/\mathit{v}$$

And plotted R_ep as a function of τ*, following [39] (Figure 3). This plot enable field results to be contrasted with data that are typical of either bed load, mixed load and suspended load sediments [39], and to identify where these data are positioned among characteristics flow regimes (no sediment transport, ripples and dunes, upper plane beds) following ref. [40]. Using the statistical package VCALC the value of Reynolds number (R_ep) comes out to be 79.957 and 49.415 for the coalfields of southern part and decreasing to 29.573 to 16.975 in the coalfields of northern part of Rajmahal Gondwana master basin and corresponding sediment fall velocity in the range 0.1110–0.0485 m/sec. When these calculated values are plotted in Figure 3 indicate that mostly Barakar sediments were deposited in dunes and ripple flow attributes corroborating outcrop field study.

Figure 3.

The graphic plots of Reynolds particle number (Rep) as a function of Shield stress (τ*) for all coalfields. For comparison, this plot includes secondary data originally compiled by ref. [39].

5.5 Froude number (F_r)

The validity of paleoflow bankfull depth and paleo-velocity estimates was assessed by ensuring that the Froude number, Fr, mathematically written as:

$${\mathrm{F}}_{\mathrm{r}}={\mathrm{V}}_{\mathrm{c}}/\surd \mathrm{g}{\mathit{D}}_{\mathrm{c}}$$E26

Where Vc = water flow velocity, D_c = Bankfull channel depth, and g = acceleration due to gravity (approximately half of the present during Permian times, i.e. 4.9 m/sec². The Froude number is a dimensionless parameter that describes different flow regimen of an open channel flow and is a ratio of inertial and gravitational forces. In open channel flow, the nature of the flow (supercritical or subcritical) depends upon whether the Froude number is greater than or less than unity. When previously determined values of D_c and V_c are substituted, Eq. (26) indicates that Froude number was in between 0.149 and 0.208 indicating the flow was tranquil (subcritical) and of lower flow regimen as substantiated by the profuse development of small and large scale bedforms in the sandstone bodies. Subcritical flow (F_r < 1) is also consistent with field observations of normal fluvial cross beds in paleochannel deposits, whereas antidunes (not observed in study area) form in cohesion-less sedimentary beds under supercritical flow (F_r > 1) conditions ([13], p.120). Subcritical flow was considered acceptable for this study based on observed bedforms at the outcrop site and because of it is the most common type of flow in natural streams. The maximum Froude value calculated by putting respective values in Eq. (26) was 0.267, consistent with subcritical flow in all Gondwana sub-basin of Rajmahal basins.

5.6 Channel sinuosity (S_ch)

The channel sinuosity (S_ch) can be indirectly estimated from width and depth of channel and ref. [33] has convincingly developed relationship between them in following regression equation:

$${\mathrm{S}}_{\mathrm{ch}}=3.5{\left({\mathit{W}}_{\mathrm{c}}/{\mathit{D}}_{\mathrm{c}}\right)}^{-0.20}$$E27

Where W_c is the bankfull width and D_c is the Bankfull channel depth.

When previously estimated values of Wc and D_c are substituted, Eq. (27) indicates that the channel sinuosity was about 1.361 for Brahmini sub basin and progressively increased to 1.632 for the Hurra sub basin through 1.517 for the Pachwara sub basin.

Additional estimates of channel sinuosity can be indirectly from dispersion of paleocurrent directions obtained from the pooled orientation data between channel sinuosity and consistency ratio (L) [41] as

$$\mathrm{Log}{\mathrm{S}}_{\mathrm{ch}}=3.68–0.0684\mathrm{L}+0.00032{\mathrm{L}}^2$$E28

The consistency ratio (L) is concentration measure of orientation vectors and is (magnitude of vector mean/Number of observation) * 100. Paleocurrent analysis of the Barakar sandstone in four sub basins of Rajmahal suggests consistency ratio (L) 82% for the Brahmini, 77% for the Chuperbhita, 74% for the Pachwara and 71% for Hurra respectively. Setting the values of L in Eq. (28) the channel sinuosity comes out to be 1.383, 1.570, 1.663 and 1.728 which signifies low sinuous (braided) for the southern part and moderately sinuous (meandering) in the northern part of the basin. Both Eqs. (27) and (28) yield similar values suggesting that the channel sinuosity increases as the sedimentation progressed from southern to northern part of the Rajmahal Gondwana master basin.

Very recently [37] presents following equation which can be used to estimate the maximum channel sinuosity P _(max) of the depositing river:

$${\mathrm{P}}_{\left(max\right)}={1.22}^{\ast }{\left(900/\surd 10{{\mathrm{D}}_{50}}^{0.42}\right)}^{0.09}$$E29

By substituting value for D₅₀ (0.40 mm), the maximum channel sinuosity P_(max) of the Barakar River in the study area is calculated to be 1.955.

6. Additional parameters

6.1 Paleodischarge (Q_w)

Channel dimensions and paleoslope along with flow velocity permit paleo channel reconstruction using bankfull channel width derived from regression equations and Gibling’s scaling factor so as to account variability in channel cross sectional area due to depositional environment as used [6, 42]. A more robust method of estimating paleo-discharge is based on Bagnold’s continuity equation as:

$${\mathrm{Q}}_{\mathrm{w}}={\mathrm{V}}_{\mathrm{c}}\mathrm{A}$$E30

$${\mathrm{Q}}_{\mathrm{w}}={\mathrm{W}}_{\mathrm{c}}{\mathrm{D}}_{\mathrm{c}}{\mathrm{V}}_{\mathrm{c}}$$E31

Where Q_w is the discharge and A is the cross-sectional area, which is the product of channel bankfull width (Wc) and channel depth (D_c). V_c is paleoflow velocity was estimated by bedform phase diagram and Darcy Weisbach friction coefficient equation to estimate flow velocity under the assumption that the dominant bedform reflects dominant bed load transport condition during flooding event as described elsewhere. Given bankfull width (W_c), bankfull depth (D_c) and V_c = average flow velocity, Eq. (30) yields a calculated paleo-discharge of 22,070 m³ for Brahmini sub basin, 12,865 m³ for Pachwara, 5880 m³ for Chuperbhita and 4510 m³ for Hurra sub basin (Table 1).

Ref. [43] Related bankfull channel width (W_c) and maximum flow depth (Dc) to bankfull discharge defined as Q_2.33 based on data collected by ref. [44] for semiarid and sub-humid stable alluvial channels in USA and Australia:

$${\mathrm{Q}}_{2.33}=2.66{{\mathrm{W}}_{\mathrm{c}}}^{0.9}{{\mathrm{D}}_{\mathrm{c}}}^{0.68}$$E32

On the other hand [45] demonstrate that peak annual flood fluvial discharge is related to drainage basin area (D_A) by the equation:

$$\mathrm{Log}{\mathrm{Q}}_{\text{flood}}=2.084-0.070log{{\mathrm{D}}_{\mathrm{A}}}^2+0.865log{\mathrm{D}}_{\mathrm{A}}$$E33

Where Q _flood is the discharge with a recurrence interval of 2.33 years and D_A is the drainage basin area. Using previously estimates of (D_A) in this Eq. (33) the mean annual flood is estimated to be about 170,600 m³/sec for Brahmini sub basin, 112,200 m³/sec for Pachwara sub basin, 65,460 m³/sec for Chuperbhita sub basin and 48,640 m³/sec for Hurra sub basin of Rajmahal Gondwana basin, although there is an order of magnitude uncertainty in this calculation. It is emphasized that this value would not apply year round, would primarily reflect only times of high seasonal yearly discharge. Ref. [45] suggest on the basis of data compiled by them that Q_flood/Q_average ratios can range over 4 orders of magnitude, from 10 to 10,000. If this is correct than this ratio suggests that average discharge for Barakar Rivers could be as high as 17,060 m³/sec but as low as 17 m³/sec. It appears to be that the estimated average discharge of Barakar River compares well with the average discharge of many Indian continental rivers, for example Tapti (6317 m³/sec), Godavari (3505 m³/sec), and Indus (6600 m³/sec).

Ref. [44] used regional hydraulic geometry curves to estimate the discharge of a number of ancient river system based on drainage area. These relationships are developed from analysis of rivers from different climatic and tectonics area. Ref. [4] point out that application to an ancient river system requires some knowledge of the climatic conditions prevailing at that time. The data for this approach require estimates of bankfull channel depth, which can be estimated from empirical relationship as outlined above. Ref. [44] provide hydraulic geometry curves derived using power-law relationships of the form:

$${\mathrm{D}}_{\mathrm{A}}=\mathrm{a}{\mathrm{A}}^{\mathrm{b}}$$E34

$${\mathrm{Q}}_{\mathrm{w}}=\mathrm{a}{\mathrm{A}}^{\mathrm{b}}$$E35

Combining Eqs. (33) and (34) we have

$${\mathrm{D}}_{\mathrm{A}}={\mathrm{Q}}_{\mathrm{w}}$$E36

The Eq. (36) strengthen the views expressed by several workers that in humid and semi-humid regions that area of the drainage basin is approximately equal to the mean annual discharge(Q_w) as recently suggested by workers quoted above. If this is true of the Barakar river system of the study area, the drainage area was about 22,070 km² to 4510 km². This relationship was used in an attempt to estimate paleoflow parameters of the streams in different parts of world [5, 46, 47].

6.2 Drainage area (D_A)

Drainage basin area is an important component of hydrological analysis which controls sediment supply from provenance to sedimentary basin. Ref. [47] is of the opinion that key information of drainage can be obtained from fluvial deposits, as which are mainly transported from the provenance by fluvial channels. In recent years, a number of studies have investigated river data such as river channel dimensions, bankfull discharge and drainage area generally follow power laws in which bankfull thickness is positively correlated with the drainage area [28, 48]. The power law equations has been used to predict the drainage area of ancient Middle Triassic fluvial deposits of southwest Utah [44], ref. [47] measured bankfull channel-belt thickness of Early Miocene in the Gulf Of Mexico Basin to estimate the drainage areas. Whereas [49, 50] reconstructed drainage basin and sediment routing for the Cretaceous and Paleocene of Gulf of Mexico and Middle Jurassic of northern Qaidam Basin, northwest China respectively by using fluvial scaling relationship. The power law relationship is as:

$${\mathit{D}}_{\mathrm{A}}=249.0{{\mathrm{D}}_{\mathrm{c}}}^{2.44}$$E37

Where D_c = bankfull channel-belt thickness (bankfull thickness) and D_A = Drainage area. Using this Eq. (37), the drainage area comes out to be 107.4 × 10³ km², 86.5 × 10³ km², 60.52 × 10³ km² and 42.2 × 10³ km² respectively for the Brahmini, Pachwara Chuperbhita, and Hurra coal basins of Rajmahal Gondwana basin.

Ref. [51] estimate a rivers drainage area based on a power-law relationship between drainage area and peak discharge by the equation:

$${\mathrm{Q}}_{\mathrm{w}}=k{D_A}^m$$E38

Where Q_w is water discharge in m³/sec, D_A is catchment area (drainage area) in km², k constant equal to 0.075 and an m exponent of 0.80. Subsequent work by ref. [52] has shown that, the constant and exponent variables of power law relationship (38) change based on different climatic zones as shown in ref. [52] (Table 1). As humid climate have been visualized by many workers during deposition of Barakar formation thereby the k constant equal to 0.0161 and exponent m of 0.9839 have been used. Putting these values in Eq. (38)

$${\mathrm{D}}_{\mathrm{A}}=0.0161{{\mathrm{Q}}_{\mathrm{w}}}^{0.9839}$$E39

Where D_A = drainage area and Q_w = mean annual discharge. Substituting the estimated values of Q_w in the above power equation the drainage area was approximately 136.2 × 10³ sq. km in Brahmini coal basin and decreased to 28.5 × 10³ sq. km to Hurra coal basin as sedimentation progressed in Rajmahal master Gondwana basin.

Barakar sandstone (Permian) drainage networks appear to have been broadly similar in scale to modern intra-basinal rivers draining active mountain belts and the continental-scale drainages, like the Ganga (India-861.4 × 10³ km²), the Indus (India-321.2 × 10³ km²), Brahmaputra (Bangladesh-194.4 × 10³ km²), the Po (Italy- 70.0 × 10³ km²), and the Rhone (France- 96.2 × 10³ km²).

6.3 Stream length (L)

The length of a stream refers to the total length of stream channels in the drainage basin and therefore has units with dimension (L). Theories postulated shows that drainage area and stream length are related in a power function ([53], for references therein). If works done by these workers are correct, a power relation equation can be then derived which would be in form:

$$\mathrm{L}=\mathrm{a}{\left({\mathrm{D}}_{\mathrm{A}}\right)}^{\mathrm{b}}$$E40

Where L = stream length, D_A = drainage area and a, b are constants. Ref. [54] derived the values of constants as: a = 1.109 and b = 0.545 while studying relationship between drainage basin area and length of stream for River Gongola, Nigeria. Substituting the constant values in Eq. (40) we have power relation as;

$$\mathrm{L}=1.109{\left({\mathrm{D}}_{\mathrm{A}}\right)}^{0.545}$$E41

When previously determined value of D_A from Eq. (37) is substituted, Eq. (41) indicates that the length of the Late Paleozoic Barakar River was about 703 km in Brahmini sub basin and gradually decreasing as channel sinuosity increases through Chuperbhita sub basin (525 km) to Hurra sub basin to about 427 km in Rajmahal Gondwana master basin.

7. Paleo-dimensions, flow dynamics and paleogeography

The quantitative parameters of Early Permian Barakar River in Rajmahal Gondwana basin of eastern India suggest systematic changes in paleo-dimensions and flow dynamics. The Brahmini sub basin in the south was 10.91–14.96 m deep and 817–2956 m wide, carried coarse to medium grained sand (>700 microns) and flowed over a steep northward paleoslope of 6.5 to 16.2 × 10⁻⁴ through the alluvial plain; the channel belt width ranging between 6310 and 6780 m and drained an area of 136 × 103 to 107 × 10³ square km. Shields stress, inversion estimates consistently show higher difference in paleoslope (i.e. higher slopes up dip and lower slopes down dip) relative to paleoslope derived from ref. [30] is, perhaps, due to the Trampush’s method using a continuous function to estimate slope. Reconstructed Rouse numbers, (Z), indicate that dominant transport modes of bed material varied in space and time (Table 1). The proximal field sites consistently exhibit high Z values (between 3.58–3.46), indicating predominant bed load transport. Sediment load parameter value is characteristic of a bed load channel where the bed load forms about formed only about 17.74%, whose mean annual discharge was 22,070 m³/sec, and mean annual flood was about 170,600 m³/sec. These quantitative estimates along with sinuosity value of 1.361–1.383 characterize low sinuosity braided stream channels (Figure 3). The Flow characteristics remained in the upper part of the lower flow regime (Froude number = 0.208) and flows tend to be dominated by laminar flow because the estimated value of Reynolds number (R_ep) is low (Table 1); the flow velocity between 1.57 and 1.89 m/sec caused coarse to medium grained sand to be in a dune configuration. The power equations suggest that the bedform length varies from 34.21–25.52 m and corresponding dune height is 1.363 m, comparable in magnitude with large dunes.

As the Barakar River entered in Pachwara basin in the north, the length is reduced to 631 km which drained an area of 81,000 to 86,536 square km; it had a mean annual discharge of 12,865 m³/sec and a mean annual flood of about 112,200 m³/sec. The river was about 697 m wide and its depth in between 9.64–13.87 m. This multithread stream with sinuosity of 1.517 carried 15.62 percentage of bed load flowed on a moderate slope of about 0.000144 with flow velocity between 1.35 and 1.77 m/sec. It is evident that the upper part of the lower flow regime caused the medium-coarse grained sand to be in a dune configuration attains a height of 1.247 m and bedform length in between 23.27–31.40 m (large dunes). Calculated high values of Rouse number, Z, indicates that dominant transport modes of bed material and in Pachwara sub basin implying that bed load remains the most important transport mode. A greater width/depth ratio and moderate sinuosity streams are known to transport little silt and clay in their channel perimeter. The trunk Barakar River in this sub basin with modal coarse-medium sand transported its load as bed load at the threshold of motion. Critical stream power in this basin decreases to 0.152 Pa to carry coarser sediments (D₅₀ = 0.57 mm) and produce lower amount of sediment flux a common phenomenon in many modern natural rivers. This sub basin shows low paleoslope between 0.000052–0.000152 indicating that river channels carry more wash load relative to total load which, in turn, would imply less boundary shear stress (8.66 Pa) in these river channels. Further north in Chuperbhita sub basin, its length is decreased again to about 525 km, flowed down the paleoslope from southwest to northeast having drainage area of about 60,512–37,000 km². The mean annual discharge was about 5880 m³/sec during normal period and up to 65,450 m³/sec during periodic flood. Consequently, the water velocity of 1.12 m/sec through most time but increased to 3.01 m/sec during flood and clast flow stages, respectively. The quantitative parameters provide evidence for a relative decline in the channel depth (8.58–12.56 m), width (534 m) and channel belt width (3240–4305 m) and meander lengths of 7230 m, and increase in channel sinuosity up to 1.62–1.66, implying a decline in the slope of the Chuperbhita sub basin as compared with the southerly sub basins (Pachwara and Brahmini). The river channel in this sub basin flowed over a gently sloping surface (0.000139–0.000045) with relatively lower flow velocity of 1.12 m/sec. Indeed, there is an increase in the channel sinuosity owing to an increase in fine clastics and decrease in the stream power as indicated by boundary shear stress and critical shear stress. The sediments so transported are medium to fine sand with more of fine clastics. These changes in the channel parameters together with a decrease in the bed load percentage (10.14) and Rouse number (2.01) are indications of sinuous stream. The hydrodynamic characters (Froude number = 0.174, Reynolds particle number = 29.573) indicated that the flow in the stream channel was tranquil and river flow was in the lower flow regime, which, in turn, gave rise fine- to medium grained sand to be in large and medium scale bed configuration of relatively lower height of 1.073 m and bedform length in between 26.97–18.36 m as compared to southern sub basins.

In the extreme north in Hurra sub basin, its length is further reduced to 427 km and drained an area to the north and northeast of 42,257–28,000 km². The average water depth and channel width was 7.25 m, 408 m and increased up to 10.87 and 1380 m, respectively during annual periodic flood. Consequently, the mean annual discharge that was 3890 m³/sec during normal period may jump up to 48,640 m³/sec during periodic flood. The water velocity is 0.92 m/sec during normal period and up to 2.84 m/sec during flood season. The stream power is reduced so as the sediment load parameter (M) 6.92 and Rouse Number (Z) further decreased to 1.71, suggestive of the mixed load remains the dominant transport mode of the streams. These narrow streams with meander wavelength of 6576 m swept over a depositional surface sloping at the rate of 116–176 cm/km in northeasterly direction. However, the flow in the stream channel was tranquil and in the upper part of lower flow regimen as indicated by the flow dynamics (Froude number = 0.149, Reynolds particle number = 16.75) which, in turn, facilities development of cross-bedded units in the fine- to medium grained sandstones. These dune bed configurations so developed attains relatively lower height of 0.928 m and bedform length in between 23.33–14.16 m as compared to southern sub basins. The stream channel sinuosity increased up to 1.632–1.728, owing to an increase in the fine clastics, implying a further decline in the paleoslope. However, low sinuous Barakar River, like those of the Brahmini, Pachwara and Chuperbhita became moderately sinuous (? Meandering) streams equivalent to ‘mixed load channels’, which might be due to intra-basin differential subsidence. To corroborate inferred sediment transport modes, the graphic plots of Reynolds particle number, R_ep as a function of Shield stress, τ* (Figure 3), are typical for bed load channel in the Brahmini and Pachwara in the south, whereas the mixed load realm for Chuperbhita and Hurra sub basins in the north. Down-dip, all data straddle the bounds between stability fields for ripples and dunes, which imply unidirectional flow and high to moderate sediment transport rates (both mixed transport and bed load transport).

Early studies have postulated northerly outlet of Permian rivers in this part of Peninsular India based on regional stratigraphic and sedimentary framework and paleocurrent studies [55, 56]. In addition, newly identified isolated sub basins of Lower and Upper Gondwana litho-units in the sub-surface in Purnea of India and Bogra in western Bangladesh constitute north-south oriented larger Purnea-Rajmahal-Bogra Gondwana Graben [57, 58]. The southerly provenance of subsurface Gondwana rocks in the northern part of Bangladesh, further, justify the northerly sediment transport in this part of eastern India [59]. Figure 4 illustrates paleogeography of eastern Peninsular India within the framework of eastern Gondwanaland. It is suggested that about 2260 km Long Early Permian River flowed northward from the Fox Ridge and had its outlet towards the cratonic shore zone close to the Himalayan foothills in the north [60].

Figure 4.

Paleogeographic reconstruction during early Permian of eastern peninsular India. Solid arrow indicated the outlet of Barakar River.

8. Conclusions

In light of paleo-dimensions and flow dynamics of Early Permian Barakar river of Rajmahal Gondwana sub-basin of eastern India it concluded that:

1. About 2270 km long Early Permian Barakar river of Rajmahal sub-basin of eastern India drained an area of 107,000 to 86,500 sq. km and flowed northward on a steeper slope of 6.5 to 16.2 × 10⁻⁴ with a variable flow velocity (157–135 cm/sec) from Fox Ridge; the channel sinuosity was 1.361. The rivers sub-channels were at least 817 m–700 m wide and 13 m deep. Bed load was moderately high and about 17.74–15.60 of the total load of this river, whose mean annual discharge was 12,800–22,000 m³/sec during normal period and rose to 112,200–170,000 m³/sec. These parameters suggest that the stream pattern was multithread (braided) in Brahmini and Pachwara sub-basins in the south. It indicates that the depositing bed load river became mixed- and suspended load within 2260 km in the downstream direction

2. Further northward in Chuperbhita and Hurra sub basins, the river record a decline in paleo-dimensions and flow dynamics such as channel width, channel depth, channel slope, sediment load, discharge and increase in channel sinuosity. Although only 8 to 10 percent of the total river load was bed load; the flow velocity of 92 and 152 cm/sec in the upper part of the lower flow regime caused the fine to medium grained sand to be in dune bed configuration. In the Chuperbhita and Hurra sub basins, it was about 500 km long, drained 42,000 to 62,000 km² area to the north and northeast. The gentle slope and abundance of fine clastics suggest slow deposition by single thread river. These paleo dimensions and flow dynamics estimates, indeed, correlate well with the corresponding differences in the lithic- fill of the northern and southern sub basins.

To sum up, the results are merely reasonable approximations that fit the stratigraphic and geologic context in which fluvial facies of the Barakar sandstone deposited in Rajmahal Gondwana sub basin of eastern India.

Symbols and abbreviations

D₅₀

mean particle diameter

ρ_w

fluid water density

H _m

mean dune height

ρs

grain density

S _m

Mean cross bed thickness

τ_b

boundary shear stress

D_c

river bankfull channel depth

τ_cr

critical shear stress

D*

maximum channel bankfull depth

g

acceleration due to gravity

W_c

bankfull channel width

f

Darcy-Weisbach friction factor

M

Manning roughness coefficient

L_b

bedform length

Z

Rouse number

M

sediment load parameter

Fr

Froude number

S_a

% silt- clay in channel alluvium

Rep

Reynolds particle number

S_b

% silt-clay in bank alluvium

Q w

water discharge

F

bankfull width/bankfull depth ratio

Q flood

flood discharge

W_cb

bankfull width of channel belt

D_A

drainage area

Sc

paleochannel slope

A

area of cross section

R

hydraulic radius

V_c

paleoflow velocity

S _ch

channel sinuosity

L

concentration parameter