Alteration of the Callovo–Oxfordian clay from Meuse-Haute Marne underground laboratory (France) by alkaline solution. I. A XRD and CEC study

The reaction of the clay fraction of the Callovo–Oxfordian hard shale formation hosting the French underground laboratory site, with high pH NaOH, KOH and Ca(OH)₂ solutions has been investigated through closed system experiments at 60, 90 and 120 °C over 6, 24 and 168 h. The mineralogical composition of the run samples has been determined using X-ray diffraction (XRD) of randomly oriented powders showing the formation of different species of zeolites (analcime, chabazite, phillipsite) and Ca silicates (tobermorite, katoite). The phyllosilicates were studied using XRD of oriented preparations and cation exchange capacity measurements. Detrital or diagenetic mica and chlorite in the <2 μm fraction remain unchanged. On the contrary, the smectite and random illite–smectite mixed layer minerals are strongly reactive. The expandable layers of montmorillonite type are selectively dissolved while beidellitic ones survive or are transitionally formed.     

Deformation of shock-loaded andalusite studied with X-ray diffraction techniques

The structural deformation of an andalusite single crystal, shockloaded up to 400 kb with shock wave direction approximately parallel to c, was investigated by means of X-ray powder (Guinier) and single crystal techniques (Weissenberg, precession). Exposure to the dynamic pressure revealed a fracturing of the crystal into lattice blocks, with a mean size >1,000 Å. No change of the lattice constants could be observed after pressure release. From the streaks of X-ray reflection spots measured within the hk0, h0l, 0kl, and hhl planes the shock-induced lattice deformation is interpreted in terms of rotational gliding and/or microfracturing. The distortion mode is highly structure controlled. It follows preferrably two different structural motion systems: (1) Gliding parallel to (001) occurs, which produces lamellae parallel to (001), mainly arranged in two sublattices with common c-axis. The stacking sequence of lamellae along c is irregular. The lamellae-type structure may also result from an orientated transformation into a high pressure phase of lower symmetry and subsequent inversion into the original phase after pressure release. (2) Gliding parallel to (100) occurs. In this case the deformation mode is asymmetrical with respect to the undistorted crystal. The common direction b of the (001) and (100) deformation planes is probably the main direction of the shock-induced lattice deformation.     

Modeling the composition of the pore water in a clay-rock geological formation (Callovo-Oxfordian, France)

The interstitial water contained in the microporosity of highly compact clay-rich media does not obey the classical condition usually used to derive the ionic composition of a solution. This is because the requirement for global electroneutrality of a charged microporous body (one having a significant fraction of pores with dimensions of the same order of size as the diffuse double layer) implies that the net charge density of the pore water must balance the deficiency (or the excess) of electrical charge carried by the solid matrix. In order to determine the solution composition in the micropores of a clay-rock, we first generalize the Donnan equilibrium conditions for the case of a multi-ionic electrolyte, with partitioning of the charge compensating counterions between the Stern and the diffuse layers A material-specific geochemical equilibrium model, incorporating an electrical triple layer model for adsorption reactions, is used to calculate the partition coefficient for the compensating ion charge (i.e., the fraction of charge in the Stern layer). This is then used to calculate the osmotic pressure and ionic composition of the pore water in the micropores. The material considered in this study is the argillite clay-rock sampled from the Callovo-Oxfordian geological formation under consideration in France for a deep geological disposal facility for radioactive waste.     

Deformation twinning and residual stress in calcite studied with synchrotron polychromatic X-ray microdiffraction

Microstructures of deformed calcite in marble from the Bergell Alps are studied by using a microfocused polychromatic synchrotron X-ray beam. The high spatial resolution, together with orientation and strain resolutions, reveals twin plane orientation, multiple twin lamellae, and strain distributions associated with the twins. Single and multiple mechanical twins on e = { 01[`1] 8 } e = \left\{ {01\overline{1} 8} \right\} systems are confirmed. Residual stresses are derived from the strain tensor that is derived from Laue diffraction patterns. Average lattice strains from several hundred to over one thousand microstrains are detected in a deformed marble from the Bergell Alps. Such strains suggest 60–120 MPa residual stresses. A detailed study of strain components shows that shear stresses on twin planes are completely released.     

High-pressure behaviour of germanate olivines studied by X-ray diffraction and X-ray absorption spectroscopy

Germanate olivines Mg₂GeO₄, Ca₂GeO₄ and CaMgGeO₄ have been studied by high-pressure X-ray Diffraction and high-pressure X-ray Absorption Spectroscopy. The three compounds were compressed, in the 0–30 GPa pressure range, at room temperature in a diamond-anvil cell, silicon oil being used as the pressure transmitting medium. Values of K₀ are 166 ± 15, 117 ± 15 and 152 ± 14 GPa for Mg₂GeO₄, Ca₂GeO₄ and CaMgGeO₄ respectively. These olivines all exhibit compression anisotropy, the a axis being the least compressible. Crystal to crystal phase transitions have been observed in Mg₂GeO₄ and Ca₂GeO₄ above 12 GPa and 6 Gpa respectively. The nature of these structural changes remains unclear yet. The onset of amorphization has been observed in Mg₂GeO₄ and Ca₂GeO₄ at pressures above about 22 and 11 GPa respectively. These phase transitions and amorphization processes do not involve any detectable increase in the coordination number of germanium atoms. At higher pressure (P >23 GPa), we report the onset of a transition from a phase with fourfold coordinated germanium to a phase with higher germanium coordination number in CaMgGeO₄.     

Comparison of neutron and X-ray diffraction in texture analysis of deformed carbonate rocks

The paper compares pole figure determinations with neutron diffraction and X-ray diffraction on experimentally deformed carbonate rocks, a coarse grained marble and fine grained limestone. Neutron diffraction enables determination of complete pole figures on a single spherical specimen and is advantageous for coarse grained materials. Results obtained with both diffraction techniques agree satisfactorily, although uncertainties introduced by counting statistics are more serious for neutrons than for X-rays. Continuous detectors add new possibilities which are still little explored.     

X-ray imaging of uranium in individual fluid inclusions

The spatial distribution of major (K, Ca, Mn, Fe) and trace elements (Ti, Cr, Cu, As, Br, Rb, Sr, Zr, Pb, Th, U) were determined in individual fluid inclusions from quartz veins of the Streltsov uranium deposit, Russia, using synchrotron radiation X-ray fluorescence (SXRF). The analyses were performed on the beamline ID-22 Micro-FID (Fluorescence, Imaging, Diffraction) of the European Synchrotron Research Facility (ESRF, Grenoble, France). Fluorescence X-ray maps of single fluid inclusions show a relatively homogeneous distribution of most elements throughout the inclusion, whereas Fe and, to a lesser extent, Sr display highly localized count rates. This observation argues for the presence of minute, optically invisible, compounds that are precipitated inside the inclusion. Simple model calculations indicate that relatively diluted solutions (10–100 ppm U) trapped at geologically relevant temperatures (e.g. 250 °C) would precipitate submicron sized particles. These particles would be highly reactive to the photon flux but not necessarily visible under the microscope. These results indicate that third-generation synchrotron light source can be a powerful technique to study the physical processes undergone by the fluid. When combined with chemical data, this technique can help to clarify fluid transport properties in natural systems.     

河床透-阻型岩溶塌陷形成机理

由岩溶引发的地面塌陷具有灾害性大,隐蔽性高等特点,为了对其进行有效预报及治理,以某岩溶塌陷强烈发育地区为研究对象,提出采用等值反磁通瞬变电磁法（Opposing Coils Transient Electromagnetics Method,OCTEM）与工程地质钻探相结合的方法,对地层界面进行地球物理方法探测,由覆盖层埋深、电阻率大小、等值线变化等因素确定地层产状,并通过物探反演图及钻孔信息进行验证。结果表明,在岩溶塌陷强烈发育地段,等值反磁通瞬变电磁法可以有效查明地下溶蚀发育情况,在周围环境因素干扰强等常规物探方法无法开展的情况下,可以达到较好的应用效果。等值反磁通瞬变电磁法在岩溶、地面塌陷等地质灾害发育地区提供了有效的预测,为相似情况下的研究分析工作提供理论及实践基础。     

Organic–mineral interactions in marine sediments studied using density fractionation and X-ray photoelectron spectroscopy

Interactions between organic matter (OM) and minerals are important for the preservation of organic material in marine sediments. Recent evidence suggests that these interactions may not be due to protection of the organic matter via simple sorption to minerals, but rather that the organic matter is acting as a glue between mineral particles resulting in aggregate formation. Density fractionation into multiple density intervals is a powerful approach for looking at the patchy nature of organic matter distribution (Bock, M.J., Mayer, L.M., 2000. Mesodensity organo-clay associations in a near-shore sediment. Marine Geology 163, 65–75), because isolates with varying organic matter loadings can be obtained. The aggregate surfaces can be examined using X-ray photoelectron spectroscopy (XPS), because this technique is restricted to the top 10 nm of the sample surface. XPS gives quantitative information on all the elements on the surface (except H and He) and, in addition, gives information on the chemical bonding of carbon and nitrogen. We used these techniques, along with more standard geochemical tools (CHN, surface area and amino acid analyses), to study a sediment sample of high organic matter content from the oxygen deficient zone off the western coast of Mexico. We found that amino acid composition indicates that the fractions get progressively more degraded as density increases, while the fraction of carbon bonded to oxygen suggests that the oxidation state of the organic matter is similar for all fractions. In addition, the comparison of surface carbon concentrations from XPS and OC:SA suggests that the OM is located in discrete spots on the surface and that as density increases (OC:SA decreases) the organic matter decreases in thickness while retaining the same proportional areal extent.     

Thermal expansion and high temperature structure evolution of zoisite by single-crystal X-ray and neutron diffraction

The thermo-elastic behaviour and the temperature-induced structure evolution of a natural Fe-free zoisite have been investigated by in situ single-crystal X-ray and neutron diffraction. Neither discontinuities in volume expansion nor changes in symmetry have been observed up to 1,023 K. Zoisite shows a negative thermal expansion along [100] at T > 700 K, while a continuous positive expansion occurs on the (100) plane. Two different regimes in the anisotropic thermal behaviour of zoisite can be distinguished (i.e. at T < 700 K and T > 700 K), corresponding to an increase in the volumetric thermal expansion at T > 700 K. The structure evolution with temperature has been described by a series of X-ray and neutron refinements at different temperatures. In particular, the M(3) polyhedra show a significant octahedral flattening and expansion in the equatorial plane with T. All [SiO₄] tetrahedra show a regularization with increasing T. The neutron refinements show no change in the configuration of the hydrogen bonding at least up to 873 K. The effects of the T-induced main deformation mechanisms on the anisotropic elastic behaviour of zoisite are discussed. A comparison with the thermal behaviour of epidote has been carried out.     

Cation exchange processes and human activities in unconfined aquifers

During the 1999–2002 water years, a hydrogeological research project was carried out on the unconfined aquifer of Trifilia in the Peloponnese. Seawater intrusion due to overpumping, and intensive use of fertilizers caused the groundwater quality degradation that is a typical case for the coastal aquifers in Greece. Isopiezometric maps along with ion distribution balances, ion distribution maps and factor analysis indicate the existence of three zones of groundwater quality. In the first zone of saline water, a cation exchange process between the Ca²⁺ of sediments and the Na⁺ of groundwater contribute to the formation of the water type Na⁺-Ca²⁺-Cl^–. In the second zone, which is considered as a transition zone, dominate the Ca²⁺-Na⁺-HCO₃^–-Cl^– water type. In the third zone of Ca²⁺-HCO₃^–-SO₄^2– water type, relationships among Ca²⁺, SO₄^2–, NO₃^– and NH₄ can be attributed to the dissociation of ammonium nitrate and sulfate fertilizers on one hand, and Ca²⁺ derivation from cation exchange processes between water, rocks and clay minerals, such as smectite and illite, on the other.     

Pristine and reacted surfaces of pyrrhotite and arsenopyrite as studied by X-ray absorption near-edge structure spectroscopy

Fe L-, S L-, and O K-edge X-ray absorption spectra of natural monoclinic and hexagonal pyrrhotites, Fe_1-xS, and arsenopyrite, FeAsS, have been measured and compared with the spectra of minerals oxidized in air and treated in aqueous acidic solutions, as well as with the previous XPS studies. The Fe L-edge X-ray absorption near-edge structure (XANES) of vacuum-cleaved pyrrhotites showed the presence of, aside from high-spin Fe²⁺, small quantity of Fe³⁺, which was higher for a monoclinic mineral. The spectra of the essentially metal-depleted surfaces produced by the non-oxidative and oxidative acidic leaching of pyrrhotites exhibit substantially enhanced contributions of Fe³⁺ and a form of high-spin Fe²⁺ with the energy of the 3d orbitals increased by 0.3–0.8 eV; low-spin Fe²⁺ was not confidently distinguished, owing probably to its rapid oxidation. The changes in the S L-edge spectra reflect the emergence of Fe³⁺ and reduced density of S s–Fe 4s antibonding states. The Fe L-edge XANES of arsenopyrite shows almost unsplit e_g band of singlet Fe²⁺ along with minor contributions attributable to high-spin Fe²⁺ and Fe³⁺. Iron retains the low-spin state in the sulphur-excessive layer formed by the oxidative leaching in 0.4 M ferric chloride and ferric sulphate acidic solutions. The S L-edge XANES of arsenopyrite leached in the ferric chloride, but not ferric sulphate, solution has considerably decreased pre-edge maxima, indicating the lesser admixture of S s states to Fe 3d orbitals in the reacted surface layer. The ferric nitrate treatment produces Fe³⁺ species and sulphur in oxidation state between +2 and +4.     

The uptake and solubility of water in quartz at elevated pressure and temperature

The uptake of water in quartz at 1.5 GPa total pressure, 1173 K and high water fugacity, over times up to 24 h, has been investigated using a newly developed assembly to prevent microcracking. It is found that the uptake is small, and below the detectability of the presently used technique of infrared spectroscopy and serial sectioning. This observation reflects either a low value for the diffusivity or the solubility or a combination of both, and is in agreement with the observations of Kronenberg et al. (1986) and Rovetta et al. (1986). It brings into question the interpretation of the early experiments on water weakening by Griggs and Blacic (1964) and the recent estimates of the solubility and diffusivity by Mackwell and Paterson (1985). Rults of a combined T.E.M., light-scattering and infrared-spectroscopy investigation of ‘wet’ synthetic quartz before and after heating at 0.1, 300 and 1500 MPa total pressure and 1173 K, strongly suggest that the water in ‘wet’ quartz is mainly in the form of H₂O in inclusions, consistent with the solubility being low, possibly less than 100 H/10⁶Si. From these observations, water-containing inclusions appear to play a major role in the plasticity of quartz, while any role of water in solid solution remains to be clarified.     

Three-dimensional petrographical investigations on borehole rock samples: a comparison between X-ray computed- and neutron tomography

Technical difficulties associated with excavation works in tectonized geological settings are frequent. They comprise instantaneous and/or delayed convergence, sudden collapse of gallery roof and/or walls, outpouring of fault-filling materials and water inflows. These phenomena have a negative impact on construction sites and their safety. In order to optimize project success, preliminary studies on the reliability of rock material found on site are needed. This implies in situ investigations (surface mapping, prospective drilling, waterflow survey, etc.) as well as laboratory investigations on rock samples (permeability determination, moisture and water content, mineralogy, petrography, geochemistry, mechanical deformation tests, etc.). A set of multiple parameters are then recorded which permit better insight on site conditions and probable behavior during excavation. Because rock formations are by nature heterogeneous, many uncertainties remain when extrapolating large-scale behavior of the rock mass from analyses of samples order of magnitudes smaller. Indirect large-scale field investigations (e.g. geophysical prospecting) could help to better constrain the relationships between lithologies at depth. At a much smaller scale, indirect analytical methods are becoming more widely used for material investigations. We discuss in this paper X-ray computed tomography (XRCT) and neutron tomography (NT), showing promising results for 3D petrographical investigations of the internal structure of opaque materials. Both techniques record contrasts inside a sample, which can be interpreted and quantified in terms of heterogeneity. This approach has the advantage of combining genetic parameters (physico-chemical rock composition) with geometric parameters resulting from alteration or deformation processes (texture and structure). A critical analysis of such 3D analyses together with the results of mechanical tests could improve predictions of short- and long-term behavior of a rock unit. Indirect methods have the advantage of being non-destructive. However, as it is the case with large-scale geophysical surveying, XRCT and NT are affected by several error factors inherent to the interaction of a radiation modality (X-ray or neutron beam) with the atomic structure of the investigated materials. Recorded signals are therefore in particular cases not artifact-free and need to be corrected in a subsequent stage of data processing.     

Seasonal water uptake near trees: a numerical and experimental study

Issues related to the numerical simulation of moisture migration patterns in the unsaturated zone and in the vicinity of mature trees are explored in this paper. The research is based on the use of Richard's equation for unsaturated moisture flow incorporating a sink term. A numerical solution has been achieved via the finite-element method for spatial discretization along with a finite-difference time-marching scheme. An axisymmetric solution is developed to represent water uptake near an established tree. The approach adopted utilizes radial symmetry and assumes a linear distribution of water extraction rates with both depth and radius. The model has been validated by direct comparison with field measurements recorded (by others) for a mature lime tree located on a boulder clay subsoil. Non-linear hydraulic properties have been obtained from independent published data. A good correlation between field data and simulated results has been achieved. The simulation covers a full annual cycle starting from field capacity in winter, extending through a full spring–summer drying period and subsequent autumn recharge. It is believed that this is the first attempt to simulate the behaviour of an established tree over such a time-scale. This relatively straightforward approach is thought to be suitable for development and application to a range of geo-engineering problems (e.g. slope stability, shrinkage/heave prediction, etc).     

The use of X-ray tomography in the study of water repellents and consolidants

To reduce the weathering rate of natural building stones, a wide variety of water repellents and consolidants are commercially available. Although a lot of research is performed on these products, it remains difficult to determine which product is appropriate to use for a certain type of building stone. Each type of building stone has its own petrographic characteristics (mineralogy, texture, …), leading to typical physical and technical properties which influence its rate of decay. The localisation of the products inside a stone type is not only depending on the properties of the products themselves, but also linked to the texture and structure of the stone. The impregnation depth of the products strongly influences their efficiency and is therefore a key issue in the determination if a product is functional for a certain type of stone. X-ray micro-CT has recently been introduced as a non-destructive material evaluation technique for engineering and geology purposes. The fact that micro-CT can provide information about the internal structure and properties of natural building stones, is a major advantage in the study of their conservation. Firmly linked with more classical research techniques, this non-destructive technique offers an extra dimension to the cultural heritage research.In this paper, non-destructive X-ray computed micro-tomography (micro-CT) turns out to be a powerful tool as it can visualise the presence of water repellents and consolidants inside the stone and can help to detect the influence that these treatments exert on porosity and pore-size distribution. For the visualization of the product its atomic number and density and the amount of product inside the natural building stone is crucial. Besides the contrast in attenuation, the resolution of the micro-CT also needs to be taken into account to obtain a good contrast between stone and product. By doping with 3-bromopropyltrimethoxysilane, more contrast occurs between the stone material and the conservation product. When the amount of product inside the samples is very low and the product is homogeneously spread inside the sample, the doped product is difficult to distinguish from the stone material due to the resolution of the micro-CT. When the amount of doped product inside the stone material reaches a certain threshold value, the dope will appear in the 2D cross-sections derived from micro-CT, creating a good visualization of the products inside the stone samples.     

Coordination chemistry and hydrolysis of Fe(III) in a peat humic acid studied by X-ray absorption spectroscopy

The speciation of iron (Fe) in soils, sediments and surface waters is highly dependent on chemical interactions with natural organic matter (NOM). However, the molecular structure and hydrolysis of the Fe species formed in association with NOM is still poorly described. In this study extended X-ray absorption fine structure (EXAFS) spectroscopy was used to determine the coordination chemistry and hydrolysis of Fe(III) in solution of a peat humic acid (5010-49,200 μg Fe g⁻¹ dry weight, pH 3.0-7.2). Data were analyzed by both conventional EXAFS data fitting and by wavelet transforms in order to facilitate the identification of the nature of backscattering atoms. Our results show that Fe occurs predominantly in the oxidized form as ferric ions and that the speciation varies with pH and Fe concentration. At low Fe concentrations (5010-9920 μg g⁻¹; pH 3.0-7.2) mononuclear Fe(III)-NOM complexes completely dominates the speciation. The determined bond distances for the Fe(III)-NOM complexes are similar to distances obtained for Fe(III) complexed by desferrioxamine B and oxalate indicating the formation of a five-membered chelate ring structure. At higher Fe concentrations (49,200 μg g⁻¹; pH 4.2-6.9) we detect a mixture of mononuclear Fe(III)-NOM complexes and polymeric Fe(III) (hydr)oxides with an increasing amount of Fe(III) (hydr)oxides at higher pH. However, even at pH 6.9 and a Fe concentration of 49,200 μg g⁻¹ our data indicates that a substantial amount of the total Fe (>50%) is in the form of organic complexes. Thus, in environments with significant amounts of organic matter organic Fe complexes will be of great importance for the geochemistry of Fe. Furthermore, the formation of five-membered chelate ring structures is in line with the strong complexation and limited hydrolytic polymerization of Fe(III) in our samples and also agrees with EXAFS derived structures of Fe(III) in organic soils.     

Biostratigraphy and ammonites of the Middle Oxfordian to lowermost Upper Kimmeridgian in northern Central Siberia

The Middle Oxfordian to lowermost Upper Kimmeridgian ammonite faunas from northern Central Siberia (Nordvik, Chernokhrebetnaya, and Levaya Boyarka sections) are discussed, giving the basis for distinguishing the ammonite zones based on cardioceratid ammonites of the genus Amoeboceras (Boreal zonation), and, within the Kimmeridgian Stage, faunas–for distinguishing zones based on the aulacostephanid ammonites (Subboreal zonation). The succession of Boreal ammonites is essentially the same as in other areas of the Arctic and NW Europe, but the Subboreal ammonites differ somewhat from those known from NW Europe and Greenland. The Siberian aulacostephanid zones—the Involuta Zone and the Evoluta Zone—are correlated with the Baylei Zone (without its lowermost portion), and the Cymodoce Zone/lowermost part of the Mutabilis Zone (the Askepta Subzone) from NW Europe. The uniform character of the Boreal ammonite faunas in the Arctic makes possible a discussion on their phylogeny during the Late Oxfordian and Kimmeridgian: the succession of particular groups of Amoeboceras species referred to successive subgenera is revealed by the occurrence of well differentiated assemblages of typical normal-sized macro and microconchs, intermittently marked by the occurrence of assemblages of paedomorphic “small-sized microconchs” appearing at some levels preceeding marked evolutionary modifications. Some comments on the paleontology of separate groups of ammonites are also given. These include a discussion on the occurrence of Middle Oxfordian ammonites of the genus Cardioceras in the Nordvik section in relation to the critical review of the paper of Rogov and Wierzbowski (2009) by Nikitenko et al. (2011). The discussion shows that the oldest deposits in the section belong to the Middle Oxfordian, which results in the necessity for some changes in the foraminiferal zonal scheme of Nikitenko et al. (2011). The ammonites of the Pictonia involuta group are distinguished as the new subgenus Mesezhnikovia Wierzbowski and Rogov.     

Estimating specific yield and transmissivity with magnetic resonance sounding in an unconfined sandstone aquifer (Niger)

The unconfined aquifer of the Continental Terminal in Niger was investigated by magnetic resonance sounding (MRS) and by 14 pumping tests in order to improve calibration of MRS outputs at field scale. The reliability of the standard relationship used for estimating aquifer transmissivity by MRS was checked; it was found that the parametric factor can be estimated with an uncertainty ≤150% by a single point of calibration. The MRS water content (θ _MRS) was shown to be positively correlated with the specific yield (Sy), and θ _MRS always displayed higher values than Sy. A conceptual model was subsequently developed, based on estimated changes of the total porosity, Sy, and the specific retention Sr as a function of the median grain size. The resulting relationship between θ _MRS and Sy showed a reasonably good fit with the experimental dataset, considering the inherent heterogeneity of the aquifer matrix (residual error is ～60%). Interpreted in terms of aquifer parameters, MRS data suggest a log-normal distribution of the permeability and a one-sided Gaussian distribution of Sy. These results demonstrate the efficiency of the MRS method for fast and low-cost prospection of hydraulic parameters for large unconfined aquifers.     

Steady flow rate to a partially penetrating well with seepage face in an unconfined aquifer

The flow rate to fully screened, partially penetrating wells in an unconfined aquifer is numerically simulated using MODFLOW 2000, taking into account the flow from the seepage face and decrease in saturated thickness of the aquifer towards the well. A simple three-step method is developed to find the top of the seepage face and hence the seepage-face length. The method is verified by comparing it with the results of previous predictive methods. The results show that the component of flow through the seepage face can supply a major portion of the total pumping rate. Variations in flow rate as a function of the penetration degree, elevation of the water level in the well and the distance to the far constant head boundary are investigated and expressed in terms of dimensionless curves and equations. These curves and equations can be used to design the degree of penetration for which the allowable steady pumping rate is attained for a given elevation of water level in the well. The designed degree of penetration or flow rate will assure the sustainability of the aquifer storage, and can be used as a management criterion for issuing drilling well permits by groundwater protection authorities.