Rotation and strain of linear and planar structures in three-dimensional progressive deformation

Rotation and progressive strain have been studied for a sheet embedded in a matrix which undergoes rotational three-dimensional strain under constant volume conditions. The mathematics gives explicit information on the following features:

1. (1) The length and position (relative to a defined coordinate system) of the principal axes of the strain ellipsoid at any stage of the progressive deformation.

2. (2) The position and length of the principal axes in any plane intersecting the strain ellipsoid, also at any stage of the deformation.

3. (3) The position and length of passive markers which initially coincided with the principal axes in an intersecting plane. This is of consequence for the distinction between passively rotating structures and actively forming structures.

4. (4) The shear strain parallel to an intersecting plane or sheet, as indicated by the angular difference between the normal to an intersecting plane at any time and the marker at the same time which initially, however, was parallel to the normal. This layer-parallel shear causes boudins to rotate and the axial plane of buckles to tilt.

The relationships have been expressed quantitatively in the bulk of the paper and illustrated in diagrams. The analysis presented is basic for the study of the deformational behavior of competent sheets of rocks embedded in less competent ones.     

Trace element and isotopic studies of Permo-Carboniferous carbonate nodules from Talchir sediments of peninsular India: Environmental and provenance implications

Syngenetic carbonate nodules constitute an interesting feature of the glaciogene sediments of various Talchir basins in peninsular India. Petrographic, cathodoluminescence and sedimentary results suggest that many of these nodules contain primary carbonate precipitates whose geochemical signatures can be used for determining environment of deposition and provenance of the sediments and drainage source. Several nodules were collected from Gondwana basins of east-central India and analyzed for stable carbon and oxygen isotope ratios, REE and trace element composition, and Sr isotope ratio. The mean δ¹⁸O and δ¹³C values of the calcites in the nodules are — 19.5% and-9.7% (w.r.t. PDB) respectively suggesting a freshwater environment (probably lacustrine) for formation of these objects. Trace element ratios (Eu/Eu * and La/Yb) of the nodule samples show that the source of the sediments in the Damodar valley basin was the granites, gneisses and intrusives in the Chotanagpur region. The sediments in the Mahanadi valley were derived from granulites, charnockites and granites of the eastern ghat region. The Sr concentration of the carbonate phase of the nodules is low, ranging from 10–60 ng/g. The⁸⁷Sr/⁸⁶Sr ratios of the samples from the west Bokaro basin and Ramgarh basin vary from 0.735 to 0.748 (mean: 0.739) and from 0.726 to 0.733 (mean: 0.730) respectively. These values are consistent with our proposition that water of these basins drained through the granitic rocks of the Chotanagpur region. In contrast, the⁸⁷Sr/⁸⁶Sr ratios of the samples from the Talchir basin (Type area) of Mahanadi valley vary from 0.718 to 0.723 (mean: 0.719). These⁸⁷Sr/⁸⁶Sr ratios are close to those of the granulites in the adjoining eastern ghat belt suggesting that area as the drainage source.     

Patterns of deformed early lineations over later folds formed by buckling and flattening

The patterns of deformed early lineations (L₁) over later folds (F₂) can be classified into several morphological types depending on the nature of variation of L₁ F₂ over the folds. The field relations indicate that the folds under consideration are neither shear folds nor parallel folds modified by flattening. The lineation patterns are therefore interpreted in terms of an empirical model of simultaneous buckling and flattening in which it is assumed that (i) the central surface of the folded layer remains a sine curve in transverse profile, (ii) the ratio of rates of buckle shortening to homogeneous strain is proportional to sin 2a, with a as the dip angle and (iii) the progressive deformation is coaxial with the Z-axis of bulk strain parallel to the planar segments of the early folds. The model gives an insight into the relative importance of different physical factors which control the development of dissimilar lineation patterns. Not all lineation patterns are explicable by this simplified model. Thus complex patterns with variable L₁ F₂ along the fold axis may develop by a progressive rotation of the geometrically defined fold hinge through successive material lines. The theoretical results have been applied to interpret the lineation patterns in Central Rajasthan, India. It is concluded that L₁ was initially very close to the E-ESE trending subhorizontal Z-axis of bulk deformation during F₂-folding and that the X-axis was subhorizontal or gently plunging with a N-NNE trend.     

Reconnaissance report on geotechnical effects and structural damage caused by the 3 January 2017 Tripura earthquake,India

Natural Hazards - An earthquake of moment magnitude Mw 5.7 shook the northeastern region of India on 3 January 2017 at 14 h:39 min:0.5 s local time. The duration of the...     

Interaction of Aquifer and River‐Canal Network near Well Field

The article presents semi‐analytical mathematical models to asses (1) enhancements of seepage from a canal and (2) induced flow from a partially penetrating river in an unconfined aquifer consequent to groundwater withdrawal in a well field in the vicinity of the river and canal. The nonlinear exponential relation between seepage from a canal reach and hydraulic head in the aquifer beneath the canal reach is used for quantifying seepage from the canal reach. Hantush's (1967) basic solution for water table rise due to recharge from a rectangular spreading basin in absence of pumping well is used for generating unit pulse response function coefficients for water table rise in the aquifer. Duhamel's convolution theory and method of superposition are applied to obtain water table position due to pumping and recharge from different canal reaches. Hunt's (1999) basic solution for river depletion due to constant pumping from a well in the vicinity of a partially penetrating river is used to generate unit pulse response function coefficients. Applying convolution technique and superposition, treating the recharge from canal reaches as recharge through conceptual injection wells, river depletion consequent to variable pumping and recharge is quantified. The integrated model is applied to a case study in Haridwar (India). The well field consists of 22 pumping wells located in the vicinity of a perennial river and a canal network. The river bank filtrate portion consequent to pumping is quantified.     

Upper bound solutions of bearing capacity of strip footing by pseudo-dynamic approach

This paper presents the pseudo-dynamic analysis of seismic bearing capacity of a strip footing using upper bound limit analysis. However, in the literature, the pseudo-static approach was frequently used by several researchers to compute the seismic bearing capacity factor theoretically, where the real dynamic nature of the earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of bearing capacity factor N _γE are determined for different magnitudes of soil friction angle, soil amplification and seismic acceleration coefficients both in the horizontal and vertical directions. The results obtained from the present study are shown both graphically as well as in the tabular form. It is observed that the bearing capacity factor N _γE decreases significantly with the increase in seismic accelerations and amplification. The results are thoroughly compared with the existing values in the literature and the significance of the present methodology for designing the shallow footing is discussed.     

Precipitable water vapor estimation in India from GPS-derived zenith delays using radiosonde data

One of the most recent applications of global positioning system (GPS) is the estimation of precipitable water vapor (PWV). It requires proper modeling to extract PWV from zenith wet delay (ZWD). The existing global models take no account of latitudinal and seasonal variation of meteorological parameters in the atmosphere. In fact, they ignore the atmospheric conditions at a specific location. Therefore, site-specific PWV models have been developed for five stations spread over the Indian subcontinent, using 3-year (2006–2008) radiosonde data from each of these stations. Furthermore, a similar regional PWV model is also developed for the Indian region. The purpose of the developed site-specific as well as regional model was to convert ZWDs into PWV without using surface meteorological parameters. It has been found that the developed regional and site-specific PWV models show about mm-level accuracy in estimating PWV using derived ZWD from radiosonde as input. The developed site-specific, regional models were also used to extract PWV from GPS-derived ZWD at Bangalore and New Delhi. The accuracy of the developed site-specific and regional model is of the same level. The PWV accuracy obtained with the developed regional model is about 6.28, 6.6 mm in comparison to radiosonde PWV at Bangalore and New Delhi, respectively.