Mechanisms of Pore Pressure-stress Coupling which Can Adversely Affect Stress Measurements Conducted in Deep Tunnels

— Rock-stress measurements performed in boreholes drilled from a tunnel at a depth of 800 m indicate that the minimum stress has been reduced from pre-excavation levels by drawdown in pore pressure. The disturbance to the ambient stresses extends well beyond two tunnel diameters. A model is developed to explain the inferred strong coupling between the pore pressure and minimum stress in the rock mass around the tunnel. The model includes the effects of poro-elasticity of the intact rock and the stiffness of the fractures. For the field situation under study where the fractures are unusually complaint, both poro-elasticity and fracture compliance could be important contributors to the coupling. Changes in pore pressure are shown to produce reductions in minimum stress that are at least 50% of the drop in pore pressure and probably higher. In more general situations, the poro-elastic component is likely to be the more significant of the two mechanisms and alone accounts for a coupling factor of 50%. In this context, the importance of fractures in crystalline conditions probably lies more in their promotion of penetrative drainage than their contribution to coupling coefficient. The results highlight the importance of establishing the extent and distribution of pore pressure drawdown about galleries from which stress measurements are to be conducted.     

Pore water pressure increment model for saturated Nanjing fine sand subject to cyclic loading

Three groups of dynamic triaxial tests were performed for saturated Nanjing fine sand subjected to uniform cyclic loading. The tested curves of the excess pore water pressure (EPWP) ratio variation with the ratio of the number of cycles are provided. The concept of the EPWP increment ratio is introduced and two new concepts of the effective dynamic shear stress ratio and the log decrement of effective stress are defined. It is found that the development of the EPWP increment ratio can be divided into three stages: descending, stable and ascending. Furthermore, at the stable and ascending stages, a satisfactory linear relationship is obtained between the accumulative EPWP increment ratio and natural logarithm of the effective dynamic shear stress ratio. Accordingly, the EPWP increment ratio at the number of cycles N has been deduced that is proportional to the log decrement of effective stress at the cycle number N-1, but is independent of the cyclic stress amplitude. Based on the analysis, a new EPWP increment model for saturated Nanjing fine sand is developed from tested data fitting, which provides a better prediction of the curves of EPWP generation, the number of cycles required for initial liquefaction and the liquefaction resistance.     

Understanding mass fluvial erosion along a bank profile: using PEEP technology for quantifying retreat lengths and identifying event timing

This study provides fundamental examination of mass fluvial erosion along a stream bank by identifying event timing, quantifying retreat lengths, and providing ranges of incipient shear stress for hydraulically driven erosion. Mass fluvial erosion is defined here as the detachment of thin soil layers or conglomerates from the bank face under higher hydraulic shear stresses relative to surface fluvial erosion, or the entrainment of individual grains or aggregates under lower hydraulic shear stresses. We explore the relationship between the two regimes in a representative, US Midwestern stream with semi‐cohesive bank soils, namely Clear Creek, IA. Photo‐Electronic Erosion Pins (PEEPs) provide, for the first time, in situ measurements of mass fluvial erosion retreat lengths during a season. The PEEPs were installed at identical locations where surface fluvial erosion measurements exist for identifying the transition point between the two regimes. This transition is postulated to occur when the applied shear stress surpasses a second threshold, namely the critical shear stress for mass fluvial erosion. We hypothesize that the regimes are intricately related and surface fluvial erosion can facilitate mass fluvial erosion. Selective entrainment of unbound/exposed, mostly silt‐sized particles at low shear stresses over sand‐sized sediment can armor the bank surface, limiting the removal of the underlying soil. The armoring here is enhanced by cementation from the presence of optimal levels of sand and clay. Select studies show that fluvial erosion strength can increase several‐fold when appropriate amounts of sand and clay are mixed and cement together. Hence, soil layers or conglomerates are entrained with higher flows. The critical shear stress for mass fluvial erosion was found to be an order of magnitude higher than that of surface fluvial erosion, and proceeded with higher (approximately 2–4 times) erodibility. The results were well represented by a mechanistic detachment model that captures the two regimes. Copyright © 2017 John Wiley & Sons, Ltd.     

The stratospheric quasi-biennial oscillation observed in the semidiurnal ground pressure data

Ground pressure observations made at Macao (22^○N, 113^○E) from 1953 to 1991 are analyzed and compared with the stratospheric quasi-biennial oscillation (QBO) data obtained during the same interval. The periods of the two phenomena and their time evolution are found to be close to each other. Furthermore, the time series of the stratospheric winds and the S2(p) QBO signature are highly correlated, thus confirming earlier analysis. On this basis, pressure measurements obtained at Batavia (now Djakarta: 6^○S, 107^○E) from 1870 to 1944 are used to trace back the QBO phenomenon before the advent of systematic stratospheric balloon measurements. The inferred period, which varies between 25 and 32 months, suggests that the QBO has been present in the atmosphere at least since 1870.     

Intracrustal origin of Arenal basaltic andesite in the light of solid–melt interactions and related compositional buffering

The origin of Arenal basaltic andesite can be explained in terms of fractional crystallization of a parental high-alumina basalt (HAB), which assimilates crustal rocks during its storage, ascent and evolution. Contamination of this melt by Tertiary calc-alkalic intrusives (quartz–diorite and granite, with ⁸⁷Sr/⁸⁶Sr ratios ranging 0.70381–0.70397, nearly identical with those of the Arenal lavas) occurs at upper crustal levels, following the interaction of ascending basaltic magma masses with gabbroic–anorthositic layers. Fragments of these layers are found as inclusions within Arenal lavas and tephra and may show reaction rims (1–5 mm thick, consisting of augite, hypersthene, bytownitic–anorthitic plagioclase, and granular titanomagnetite) at the gabbro–lava interface. These reaction rims indicate that complete `assimilation' was prevented since the temperature of the host basaltic magma was not high enough to melt the gabbroic materials (whose mineral phases are nearly identical to the early formed liquidus phases in the differentiating HAB). Olivine gabbros crystallized at pressure of about 5–6 kbar and equilibrated with the parental HAB at pressures of 3–6 kbar (both under anhydrous and hydrous conditions), and temperatures ranging 1000–1100°C. In particular, `deeper' interactions between the mafic inclusions and the hydrous basaltic melt (i.e., with about 3.5 wt.% H₂O) are likely to occur at 5.4 (±0.4) kbar and temperatures approaching 1100°C. The olivine gabbros are thus interpreted as cumulates which represent crystallized portions of earlier Arenal-type basalts. Some of the gabbros have been `mildly' tectonized and recrystallized to give mafic granulites that may exhibit a distinct foliation. Below Arenal volcano a zoned magma chamber evolved prior the last eruptive cycle: three distinct andesitic magma layers were produced by simple AFC of a high-alumina basalt (HAB) with assimilation of Tertiary quartz–dioritic and granitic rocks. Early erupted 1968 tephra and 1969 lavas (which represent the first two layers of the upper part of a zoned magma chamber) were produced by simple AFC, with fractionation of plagioclase, pyroxene and magnetite and concomitant assimilation of quartz–dioritic rocks. Assimilation rates were constant (r<sub>1</sub>=0.33) for a relative mass of magma remaining of 0.77–0.80, respectively. Lavas erupted around 1974 are less differentiated and represent the `primitive andesitic magma type' residing within the middle–lower part of the chamber. These lavas were also produced by simple AFC: assimilation rates and the relative mass of magma remaining increased of about 10%, respectively (r₁=0.36, and F=0.89). Ba enrichment of the above lavas is related to selective assimilation of Ba from Tertiary granitic rocks. Lava eruption occurred as a dynamic response to the intrusion of a new magma into the old reservoir. This process caused the instability of the zoned magma column inducing syneruptive mixing between portions of two contiguous magma layers (both within the column itself and at lower levels where the new basalt was intruded into the reservoir). Syneruptive mixing (mingling) within the middle–upper part of the chamber involved fractions of earlier gabbroic cumulitic materials (lavas erupted around 1970). On the contrary, within the lower part of the chamber, mixing between the intruded HAB and the residing andesitic melt was followed by simple fractional crystallization (FC) of the hybrid magma layer (lavas erupted in 1978–1980). By that time the original magma chamber was completely evacuated. Lavas erupted in 1982/1984 were thus modelled by means of `open system' AFCRE (i.e., AFC with continuous recharge of a fractionating magma batch during eruption): in this case assimilation rates were r₁=0.33 and F=0.86. Recharge rates are slightly higher than extrusion rates and may reflect differences in density (between extruded and injected magmas), together with dynamic fluctuations of these parameters during eruption. Ba and LREE (La, Ce) enrichments of these lavas can be related to selective assimilation of Tertiary granitic and quartz–dioritic rocks. Calculated contents for Zr, Y and other REE are in acceptable agreement with the observed values. It is concluded that simple AFC occurs between two distinct eruption cycles and is typical of a period of repose or mild and decreasing volcanic activity. On the contrary, magma mixing, eventually followed by fractional crystallization (FC) of the hybrid magma layer, occurs during an ongoing eruption. Open-system AFCRE is only operative when the original magma chamber has been totally replenished by the new basaltic magma, and seems a prelude to the progressive ceasing of a major eruptive cycle.     

Preliminary stress measurements in central California using the hydraulic fracturing technique

Use of the hydraulic fracturing technique for determiningin situ stress is reviewed, and stress measurements in wells near the towns of Livermore, San Ardo, and Menlo Park, California are described in detail. In the Livermore well, four measurements at depths between 110 and 155 m indicate that the least principal compressive stress is horizontal and increases from 1.62 to 2.66 MPa. The apparent direction of maximum compression is N 70° E (±40°). At the San Ardo site the least principal stress is that due to the overburden weight. At depths of 240.2 and 270.7 m the minimum and maximum horizontal stresses are estimated to be 11.4 and 22.5 MPa, and 12.0 (±1.1) and 15.8 (±3.3) MPa, respectively. From an impression of the fracture at 240.2 m, the direction of maximum compression appears to be about N 15° E. The rock in the Menlo Park well is too highly fractured to yield a reliable measurement of the horizontal stresses. The data indicate, however, that the least principal stress is vertical (due to the overburden weight) to a depth of 250 m.     

Variations in shear wave splitting during aftershocks of the Luquan earthquake in Yunnan Province

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Theoretical study of slope effects in resistivity surveys and applications

When electric soundings are made over an irregular terrain, topographic effects can influence the values of apparent resistivity and lead to erroneous 1D interpretation. A 3D finite-element method has been applied to study the topographical effect of a slope on Schlumberger soundings parallel to the strike. When the resistivity survey is performed at the top of the slope, the apparent resistivity values can be two times higher than in the flat-earth case, depending on the angle (α) and height (H) of the slope, and on the distance (X) between the sounding and the slope top. The results are presented as nondimensional curves which can be used for evaluating topographic anomalies for any value of the parameters α, H and X. It is numerically shown that the topographic effects can be removed from measurements on horizontally layered structures with an irregular earth surface. Real measurements were performed in different geological conditions over an irregular terrain. The correction method based on the nondimensional curves has been applied to the data and has enabled the determination of the correct layered ground configuration using 1D interpretation.     

Stresses produced by a normal load moving over a transversely isotropic layer of ice lying on a rigid foundation

Summary In this paper, the problem of a normal load moving over the surface of a layer of ice, lying on a rigid foundation, has been considered. FollowingHearmon, the ice is taken to be transversely isotropic. Two cases have been considered-in the first case, the rigid foundation is taken to be smooth, and in the second case, it is taken to be in welded contact with the layer of ice. Expressions have been obtained in both cases for the stresses at any point of the layer. From detailed numerical calculations, it has been found that the value of the normal stress at a point directly below the moving load falls of approximately as that of 1/z with increase in the depthz below the surface. On calculating the normal stress at the boundary between the layer of ice and the foundation, it is found that the normal stress falls off rapidly as we move away along the boundary from the point directly below the load.     

Comparison of the results obtained from different techniques such as overcoring, hydrofracturing, breakouts and focal mechanism solutions

In China, a lot of data derived from focal mechanism solutions, and especially, from overcoring and hydrofracturing stress measurements, as well as borehole breakouts carried out for various aims have contributed to understanding of the state of the crustal stress. We conducted everin situ stress measurements in a borehole with different methods, for the sake of comparison of various measuring techniques. Furthermore, we carried out measurements in different borehole with one or two kinds of techniques. All the observations taken out in these ways showed little variations. So we believe that the data obtained by the techniques can be used to study the tectonic stress field of certain region and thein situ state of the crustal stress. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 149–155, 1992.     

Spatial variations in surface sediment structure in riffle–pool sequences: a preliminary test of the Differential Sediment Entrainment Hypothesis (DSEH)

Riffle–pool sequences are maintained through the preferential entrainment of sediment grains from pools rather than riffles. This preferential entrainment has been attributed to a reversal in the magnitude of velocity and shear stress under high flows; however the Differential Sediment Entrainment Hypothesis (DSEH) postulates that differential entrainment can instead result from spatial sedimentological contrasts. Here we use a novel suite of in situ grain‐scale field measurements from a riffle–pool sequence to parameterize a physically‐based model of grain entrainment. Field measurements include pivoting angles, lift forces and high resolution digital elevation models (DEMs) acquired using terrestrial laser scanning, from which particle exposure, protrusion and surface roughness were derived. The entrainment model results show that grains in pools have a lower critical entrainment shear stress than grains in either pool exits or riffles. This is because pool grains have looser packing, hence greater exposure and lower pivoting angles. Conversely, riffle and pool exit grains have denser packing, lower exposure and higher pivoting angles. A cohesive matrix further stabilizes pool exit grains. The resulting predictions of critical entrainment shear stress for grains in different subunits are compared with spatial patterns of bed shear stress derived from a two‐dimensional computational fluid dynamics (CFD) model of the reach. The CFD model predicts that, under bankfull conditions, pools experience lower shear stresses than riffles and pool exits. However, the difference in sediment entrainment shear stress is sufficiently large that sediment in pools is still more likely to be entrained than sediment in pool exits or riffles, resulting in differential entrainment under bankfull flows. Significantly, this differential entrainment does not require a reversal in flow velocities or shear stress, suggesting that sedimentological contrasts alone may be sufficient for the maintenance of riffle–pool sequences. This finding has implications for the prediction of sediment transport and the morphological evolution of gravel‐bed rivers. Copyright © 2012 John Wiley & Sons, Ltd.     

Basic characteristics of recent tectonic stress field in southwest China

Direction and structure characteristics of 58 tectonic stress tensors have been determined in 41 surveyed areas (points) in the southwestern district of China through a calculation method for inversion of tectonic stress tensors from sliding direction of faults, and, in combination with seismic mechanism solution andin-situ stress measurements, the following characteristics of the recent tectonic stress fields in the southwestern district of China have been defined: (1) the stress fields in this district have remained stable since the end of early to mid-Pleistocene; (2) the effect of such tectonic stresses is mainly horizontal; (3) the orientation of the maximum principal stress axis shows a trend of regular rotation from north to south, i. e. from NEE-SWW in northern Songpan and Longmen Shan areas to sub-EW in the central part of western Sichuan, and further to NNW-SWW or sub-SN in Yunnan; (4) the regional tectonic stress fields are of distinct division character; (5) there is well concordance between the main direction and type of stress structures in the stress tate both in deep and shallow parts of the crust. In addition, studies of staged tectonic stress tensors preliminarily show that in early Quaternary the southwestern district was mainly affected by lateral compression of Indian plate, under which the regional tectonic stress fields mainly display NE-sub-EW compression. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 407–417, 1993.     

Current measurements and spectral analyses in the upper 450 m and deep layers of the northeastern South China Sea

On the basis of the current measurements from the moored Long Ranger ADCP in the upper 450 m layer and the deep current measurements at 2000 and 2300 m from the moored cur-rent meters with the time series data of about 7 months at the mooring station in the northeastern South China Sea, the spectral analyses and calculation have been made. The major results are as follows: (ⅰ) From the progressive vector diagrams of the observed daily currents at the water lev-els from 50 m to 400 m, its temporal variation of velocity rotated counterclockwise in most of the observing time. This agrees basically with the result from the qualitative analysis of the sea surface height data, which was obtained from TOPEX/ERS-2 altimeter data by CCAR. The daily and monthly average velocities are both the largest in November, next in October and minimum in Au-gust. (ⅱ) At the 2000 and 2300 m levels, the daily and monthly average velocities are both the largest in January, next in September and minimum in August. From the seasonal change of cur-rents, the current velocity is the strongest in winter (January-March), next in autumn, and weak in summer. (ⅲ) There exists the variation of tidal current with the change of depth. In the upper layer, the height of diurnal peak is higher than that of semidiurnal peak. However, the semidiurnal peak is higher than the diurnal peak at the levels from 200 m to 400 m. In the layers above 450 m the clockwise component is dominant in their fluctuations. In the layers below 1500 m the diurnal peak is again higher than the semidiurnal peak. (ⅳ) There is the prominent periodic fluctuation of more than two months in the layer from 50 m to 2300 m. The period of this prominent peak is 75 d and its fluctuation is counterclockwise in the upper 450 m layers, and is 68 d and 69 d at the depths of 2000 and 2300 m, respectively, and the counterclockwise component is dominant in their fluctua-tions. (ⅴ) There are the variations of periods fluctuating with the change of depth in the upper 450 m layers. For example, when f＞0, there are the prominent fluctuations of about 22 d and 15 d pe-riods at the 50 and 100 m levels. However, there are no such periods at the layer from 200 m to 400 m, where only the fluctuation of about 13 d period occurs. (ⅵ) There are the fluctuations with periods of more than one month, 23 d and 15 d at the 2000 m and 2300 m levels. (ⅶ) In the layer from 50 m to 2300 m there are the following prominent peaks: ⅰ) the fluctuation in the period range of about 4-8 d, which occurs in the weather process; ⅱ) the fluctuation with inertial period, the fluctuation is clockwise; and ⅲ) the fluctuations with short periods of about 8 h and 6 h. (ⅷ) From the cross spectral estimates between two time series, it is shown that there are significant coherence peaks with the periods of more than two months (T = 68.3 d) and more than one month between the two time series of currents at 2000 m and 2300 m depths, and also those with periods of about half a month (15.5 d), 2 d and so on between two time series of currents at 100 m and 2300 m depths.     

Microbial Quality in Coastal Waters of Dardanelles in Relation to the Pollution Sources and Transport Pathways

The coastal water quality of Çanakkale Dardanelles (Turkey) was assessed based on bacteriological data and physical–chemical parameters. Total coliform (TC), fecal coliform (FC), and enterococci (ENT) bacteria along with physicochemical parameters were measured monthly up to a year at 12 different sampling sites located through both coastal lines of the strait. The fecal bacteria were abounded at several sampling sites such as B1, B3, G3, and G4 due to direct wastewater discharges and septic leakages or overloading. Storm water runoff and sediment resuspension were important pathways for the transport of coliform and ENT bacteria to the Dardanelles, as the region receives high precipitation and strong winds for most part of the year. The values of pH, temperature, and salinity were in typical ranges for the studied area. The microbiological and physicochemical data were correlated individually and in combination. The best fit correlations for bacterial data were attained between TC and FC or TC and ENT (R = 0.67 or ?0.68), while those for the combined data were obtained for TC with temperature (R = 0.94) and TC with salinity (R = ? 0.70).     

Eruptive activity at Mount St Helens,Washington, USA, 1984–1988: a gas geochemistry perspective

The results from two different types of gas measurement, telemetered in situ monitoring of reducing gases on the dome and airborne measurements of sulfur dioxide emission rates in the plume by correlation spectrometry, suggest that the combination of these two methods is particularly effective in detecting periods of enhanced degassing that intermittently punctuate the normal background leakage of gaseous effluent from Mount St Helens to the atmosphere. Gas events were recorded before lava extrusion for each of the four dome-building episodes at Mount St Helens since mid-1984. For two of the episodes, precursory reducing gas peaks were detected, whereas during three of the episodes, COSPEC measurements recorded precursory degassing of sulfur dioxide. During one episode (October 1986), both reducing gas monitoring and SO₂ emission rate measurements simultaneously detected a large gas release several hours before lava extrusion. Had both types of gas measurements been operational during each of the dome-building episodes, it is thought that both would have recorded precursory signals for all four episodes. Evidence from the data presented herein suggests that increased degassing at Mount St Helens becomes detectable when fresh upward-moving magma is between 2 km and a few hundred meters below the base of the dome and between about 60 and 12 hours before the surface extrusion of lava.     

Central Europe: Active or residual tectonic stresses

The regional stress field in the Western Alps and their northern foreland has been investigated byin situ stress determinations. More than 600 strain relief measurements were made with resistance strain gages in boreholes carried out in mines, tunnels and quarries. The stresses calculated and data obtained from other papers were used to get a detailed idea of the stress conditions in Central Europe.The measurements confirm a continuous flux of compressive stress from the Alps to the northern foreland east of the Rhinegraben. The largest stresses are observed in the Central Alps, the lowest in the Rhinegraben rift system. The horizontal stresses exceed at nearly all places the vertical ones. Evidently the excess of horizontal stress is generated by active plate tectonics in the Alps. A tectonic model to explain the observed stress pattern is presented.     

Biosorption of Procion Red MX 5B by Bacillus subtilis and Its Extracellular Polysaccharide: Effect of Immobilization

Bacillus subtilis and its extracellular polysaccharide (EPS) were used in free form as well as immobilized form as biosorbent for the removal of an anionic dye Procion Red MX 5B. Low pH was favourable for biosorption. Immobilization resulted in reduced biosorption of the dye. The presence of functional groups responsible for the high adsorption capacity in free cells (FC) and EPS was confirmed by FTIR analysis. High Q_max and b values were noted in the case of FC and free EPS in contrast to immobilized cells and EPS. The kinetics data showed that the adsorption system followed pseudo‐first‐order reaction at low dye concentration. Desorption of the dye was found to be 100% in 1 N NaOH. In the case of immobilized biomass and EPS the alginate was found to be unstable under high alkaline conditions of NaOH.     

Some preliminary results of the geomagnetic survey of the northern part of the Federal Republic of Germany in 1982

Conclusion As forF, further improvements can be hardly expected; that applies to both technique of measurement and reduction routine.The effort of reduction according to additional stations is considerable. On principle, the effort can be cut down, if future surveys will be conducted during years of the quiet sun, i. e., minimum particle radiation, again — as was the case in 1965.0 and 1935.0. Then, obviously, in most cases a correction derived from the deviations of hourly means against daily means (Voppel, Wienert [1974]) of the reference observatories (WNG and FUR) may be sufficient, provided that the measurements are carried out not between the early morning and the late afternoon. At noon, both longitude and latitude influences become maximum and most complicated, as was revealed by a statistic investigation (Voppel, Wienert [1974]) and also by an isolated case (Schulz, Beblo [1984]). Only measurements carried out during disturbed intervals and during strong Sq variations are to be reduced according to the nearest of a few additional high-quality variation stations.What is valid for the reduction ofF, that is valid for the other components, because theF variations were calculated fromH andZ variations. From this follows that the residuals ofD and particularly ofI to a great extent are due to uncertainties of measurement. Therefore, in the future, efforts must be focused upon a reliable reproduction of the standards of these components at secular points. However, as has been emphasized in the beginning, only the next survey can clarify as to what extent the probe theodolite contributes to the uncertainty of measurement.     

The Assessment of Damage Around Critical Engineering Structures Using Induced Seismicity and Ultrasonic Techniques

—?Two large-diameter boreholes have been excavated vertically from the floor of a tunnel at the Äspö Hard Rock Laboratory, Sweden. The two deposition holes will have simulated high-level radioactive waste canisters installed in them in an experiment undertaken to test the retrievability of waste from a proposed repository. Induced seismicity and other acoustic monitoring techniques have been used to investigate the Excavation Damaged Zone (EDZ) around the two holes. High-frequency acoustic emission (AE) monitoring has been used to delineate regions of stress-induced microfracturing on the millimetre scale. This has been shown to locate in clusters around the perimeter of the deposition hole at azimuths orthogonal to the far-field maximum principal stress. Three-dimensional velocity surveys have been conducted along ray paths that pass through the damaged region and through a stress-disturbed zone around the excavation. Induced microfracturing and stress disturbance have been observed as sharp decreases in velocity as the excavation proceeds through the rock mass. The combination of the high-resolution velocity measurements and the AE source locations has allowed the linking of the velocity measurements to a volume of excavation damaged rock. This has provided a quantitative estimate of the effect of the EDZ on the rock mass.     

Effect of micro‐inhomogeneity on the effective stress coefficients and undrained bulk modulus of a poroelastic medium: a double spherical shell model

Although most rocks are complex multi‐mineralic aggregates, quantitative interpretation workflows usually ignore this complexity and employ Gassmann equation and effective stress laws that assume a micro‐homogeneous (mono‐mineralic) rock. Even though the Gassmann theory and effective stress concepts have been generalized to micro‐inhomogeneous rocks, they are seldom if at all used in practice because they require a greater number of parameters, which are difficult to measure or infer from data. Furthermore, the magnitude of the effect of micro‐heterogeneity on fluid substitution and on effective stress coefficients is poorly understood. In particular, it is an open question whether deviations of the experimentally measurements of the effective stress coefficients for drained and undrained elastic moduli from theoretical predictions can be explained by the effect of micro‐heterogeneity. In an attempt to bridge this gap, we consider an idealized model of a micro‐inhomogeneous medium: a Hashin assemblage of double spherical shells. Each shell consists of a spherical pore surrounded by two concentric spherical layers of two different isotropic minerals. By analyzing the exact solution of this problem, we show that the results are exactly consistent with the equations of Brown and Korringa (which represent an extension of Gassmann's equation to micro‐inhomogeneous media). We also show that the effective stress coefficients for bulk volume α, for porosity n_? and for drained and undrained moduli are quite sensitive to the degree of heterogeneity (contrast between the moduli of the two mineral components). For instance, while for micro‐homogeneous rocks the theory gives n_? = 1, for strongly micro‐inhomogenous rocks, n_? may span a range of values from –∞ to ∞ (depending on the contrast between moduli of inner and outer shells). Furthermore, the effective stress coefficient for pore volume (Biot–Willis coefficient) α can be smaller than the porosity ?. Further studies are required to understand the applicability of the results to realistic rock geometries.