Time-Variant Reliability Analysis of Unsaturated Soil Slopes Under Rainfall

Time-variant reliability analysis for a typical unsaturated soil slope is performed. Eight rainfall conditions are considered, and three slope models are set up for studying the influence of shear strength parameters, hydraulic conductivity parameters, rainfall intensity and duration on the reliability of the soil slope. Sensitivity analysis shows that when the saturated hydraulic conductivity (k _s) is very small, the variation of hydraulic conductivity has little effect on the reliability index (β). For saving the computation effort, only the shear strength parameters are needed in performing the reliability analysis in this condition. With the increase of k _s, the importance of hydraulic conductivity becomes large. The reliability index of the soil slope is changing with time (t), and the shape of β–t curves for different slope model is quite different for they depend on the value of k _s. When k _s is very small, β keeps decreasing for all the 18 simulation days. With the increase of k _s, β decreases to its minimum value at about the cessation day of rainfall events, and it then increases gradually due to the redistribution of suction in the soil slope.     

Static stress drop inferred from near-fault parameters for the 1999 Chi–Chi earthquake in Taiwan

In 2001, a special issue of the Bulletin of the Seismological Society of America (BSSA) featured seismological research for the 1999 Chi–Chi Taiwan earthquake. This study uses source parameters suggested by the first author in this special issue to estimate static stress drop associated with the Chi–Chi earthquake. The waveform simulation method was used to carefully examine these source parameters. The simulation results indicate that source parameters, inferred from near-fault observations, are well determined. According to the rupture area and slip, the static stress drops (Δσ_s) obtained were distributed between a small value of 47 bars near the epicentral region and a much larger value (>200 bars) to the north. Similar trends in dynamic stress drop (Δσ_d) were also recognized by the first author in his paper published in 2001 BSSA special issue. Comparing the Δσ_s with Δσ_d, satisfies the relation Δσ_s/Δσ_d ≈ 1. This relation suggests that fault motion is mostly spent releasing seismic wave energy during the rupture process of the Chi–Chi earthquake. The consistency between static and dynamic stress drops thus provides a measure of energy-moment (E_s/M₀) ratios, which range from 9.0 × 10⁻⁵ to 6.5 × 10⁻⁴. The average E_s/M₀ ratio estimated for the northern portions of the fault is 3.4 × 10⁻⁴, which is about 3 times that of the south. Such a high E_s/M₀ ratio can be interpreted as having low strength in the rupture for the northern portions of the fault, where the fault would release less energy per unit rupture surface to create the new rupture.     

Influence of source thickness on steady-state plume length

The impact of source thickness on steady-state plume length is studied using modifications of the analytical expressions provided in Liedl et al. (2005, 2011) for 2D and 3D scenarios. For comparison, 2D and 3D numerical experiments were performed, and the following three important conclusions were obtained: first, the modified expressions overestimate the plume length only up to a factor of 2 when the source thickness (M _s ) is at least 50 % of the aquifer depth (M). Second, overestimates do not exceed plume length by a factor of 10 (2D scenario) or 5 (3D scenario) for 25 % < M _s /M < 50 %. Third, numerical techniques are recommended for M _s  < 25 %. In addition, it was observed that the degradation from the top dominates for M _s /M > 50 %. As far as the numerical experiments are concerned, it is important to note that the employed finite element approach was applied to the transformed transport equation provided in both Liedl et al. works. This transformation, which can also be applied to more complex scenarios than those studied here, eliminates reaction terms from the model equations and therefore largely facilitates numerical computations.     

Pile Head Cyclic Lateral Loading of Single Pile

This paper presents an elastic continuum model using an extended nonlinear Davies and Budhu equations, which enables the nonlinear behavior of the soil around the long elastic pile to be modeled using a simple expression of pile-head stiffness method. The calculated results were validated with the measured full-scale dynamic field tests data conducted in Auckland residual clay. An idealized soil profile and soil stiffness under small strain (i.e. shear modulus, G _s and shear wave velocity, V _s of the soil) determined from in situ testing was used to model the single pile tests results. The predictions of these extended equations are also confirmed by using the three-dimensional finite-element OpenSeesPL (Lu et al. in OpenSeesPL 3D lateral pile-ground interaction: user manual, University of California, San Diego, 2010). A soil stiffness reduction factor, G _s /G _s,max of 0.36 was introduced to the proposed method and model. It was found to give a reasonable prediction for a single pile subjected to dynamic lateral loading. The reduction in soil stiffness found from the experiment arises from the cumulative effects of pile–soil separation as well as a change in the soil properties subjected to cyclic load. In summary, if the proposed method and model are accurately verified and properly used, then they are capable of producing realistic predictions. Both models provide good modelling tools to replicate the full-scale dynamic test results.     

Relationship between hydrogeological parameters for data-scarce regions: the case of the Araripe sedimentary basin, Brazil

This paper applies and validates a method for generating spatially distributed hydraulic conductivity (k) based on the specific capacity (Q _s) for data-scarce regions. This method has been applied to the Araripe sedimentary basin, Brazil, and consists of four steps: (1) selection of (32) wells for which both k and Q _s data are available; (2) estimation of k as a function of Q _s for the (128) wells for which only specific capacity data are available; (3) spatial distribution of k using the kriging geostatistical tool; (4) validation of the method, using (17) representative wells with k measured data. The equation relating k and Q _s showed a statistically significant linear relationship (R = 0.93), from which a database has been generated using kriging with the spherical model. The results showed a calibration coefficient of Nash and Sutcliffe (NS) of 0.54 and moderate spatial dependence ratio of 69 %. The validation process provided only a moderate efficiency (NS = 0.22), possibly due to the geological complexity of the focus system. Despite its limitations, the method indicates the possibility of application of ordinary kriging to generate reliable data from auxiliary variables, especially for the water management of data-scarce areas.     

The role of geological heterogeneity and variability in water infiltration on non-aqueous phase liquid migration

This study investigates the influence of two factors—geological heterogeneity and variability in water infiltration—on non-aqueous phase liquid (NAPL) migration in the unsaturated zone. NAPL migration under three-phase flow conditions resulting from a ground surface spill is modeled for multiple heterogeneous realizations of a porous medium with various water infiltration scenarios. Increased water infiltration before the spill has two counteracting effects: NAPL relative permeability (k _rn) increases with increasing water saturation (S _w) for a given NAPL saturation, while higher S _w in the soil near the NAPL source zone leads to less NAPL mass infiltration. It is found that the former effect is overwhelmed by the latter effect, the net effect being that with longer infiltration durations before the spill, both the infiltrated NAPL mass and the depth of the front migration decrease. Simulation results also show strong effect of the medium heterogeneity. Results suggest that total infiltrated mass, front depth and plume spread increase with an increasing standard deviation of log-permeability. Also variability in modeling results among realizations is largely impacted by the log-permeability standard deviation. Spatial correlation in permeability also strongly influences NAPL infiltration. An increase in the isotropic correlation length from 0.75 to 1.5 m leads to a decrease in total infiltrated mass, plume migration depth as well as vertical spread. Lateral spread in this case is not shown to be affected by the correlation length.     

The 57Fe Mössbauer parameters of pyrite and marcasite with different provenances

Eighteen pyrite and twelve marcasite samples which have different provenances have been investigated to determine the systematics of the influence of mineralogical and geological factors on the ⁵⁷Fe Mössbauer spectra at 298 K. The following results have been obtained: there is no ambiguity in distinguishing single phase pyrite from single phase marcasite by means of ⁵⁷Fe Mössbauer spectroscopy at 298 K. At 298 K the average electric quadrupole splitting, 〈ΔE_Q〉, and average isomer shift, 〈δ〉, with respect to Fe metal, are 0.6110 ± 0.0030 mm s^?1 and 0.313 ± 0.008 mm s^?1, respectively, for the 18 pyrites; 〈ΔE_Q〉 = 0.5030 ± 0.0070 mm s^?1 and 〈δ〉 = 0.2770 ± 0.0020 mm s^?1 for the 12 marcasites. At 77 K, ΔE_Q is 0.624 mm s^?1 for pyrite and 0.508 mm s^?1 for marcasite. In distinguishing pyrites from marcasites, spectra obtained at 77 K are not warranted.The Mössbauer parameters of pyrite and marcasite exhibit appreciable variations, which bear no simple relationship to the geological environment in which they occur but appear to be selectively influenced by impurities, especially arsenic, in the pyrite lattice. Quantitative and qualitative determinations of pyrite/marcasite mechanical mixtures are straightforward at 298 K and 77 K but do require least-squares computer fittings and are limited to accuracies ranging from ±5 to ±15 per cent by uncertainties in the parameter values of the pure phases. The methodology and results of this investigation are directly applicable to coals for which the presence and relative amounts of pyrite and marcasite could be of considerable genetic significance.     

Possible roles of the Zipingpu Reservoir in triggering the 2008 Wenchuan earthquake

To better understand the role the Zipingpu Reservoir may have played in triggering the 2008 M_s8 (M_w7.9) Wenchuan earthquake in China, this study evaluates changes of Coulomb failure stress (ΔCFS) and assesses their role in local seismicity and their potential impact on the Wenchuan earthquake. In addition, key aspects associated with reservoir-triggered earthquake (RTS), including mechanisms of stress triggering and permeability of fault zones, is briefly reviewed. ΔCFS was calculated at the faults involved in the Wenchuan earthquake due to the combined effects of gravitational loading and pore-pressure diffusion from the impoundment history of the reservoir. ΔCFS on the major source fault is larger than 0.1 MPa in the upper 10 km below the reservoir and reached a few tens of kPa at the focal depth. Such levels of ΔCFS are large enough to modulate the secular stress buildup of a few kPa/yr in the Longmen-shan thrust zone. Based on detailed analysis of numerical results and local seismicity, the author suggests that it is not proper to rule out the possibility of the Wenchuan earthquake being a RTS only based on very limited knowledge from a few cases of historical RTS so far.     

Empirical modeling of plate load test moduli of soil via gene expression programming

New empirical models were developed to predict the soil deformation moduli using gene expression programming (GEP). The principal soil deformation parameters formulated were secant (E_s) and reloading (E_r) moduli. The proposed models relate E_s and E_r obtained from plate load-settlement curves to the basic soil physical properties. The best GEP models were selected after developing and controlling several models with different combinations of the influencing parameters. The experimental database used for developing the models was established upon a series of plate load tests conducted on different soil types at depths of 1–24 m. To verify the applicability of the derived models, they were employed to estimate the soil moduli of a part of test results that were not included in the analysis. The external validation of the models was further verified using several statistical criteria recommended by researchers. A sensitivity analysis was carried out to determine the contributions of the parameters affecting E_s and E_r. The proposed models give precise estimates of the soil deformation moduli. The E_s prediction model provides considerably better results in comparison with the model developed for E_r. The simplified formulation for E_s significantly outperforms the empirical equations found in the literature. The derived models can reliably be employed for pre-design purposes.     

Partitioning of divalent transition elements between octahedral sheets of trioctahedral smectites and water

Using trioctahedral smectites synthesized at low temperature (25 and 75°C). partition coefficients have been determined for M²⁺ transition metals (Mn, Fe, Co, Ni, Cu, Zn) between octahedral sheets of smectites and water. These coefficients D_(M²⁺?Mg) = (M²⁺)/(Mg) solid/(M²⁺)/(Mg) liquid have high values near 10⁴ for Cu, 1000 for Ni, Co, Zn, 300 for Fe and 30 for Mn. All transition metals are strongly stabilized in the magnesian solid phase, even Mn which leads to noncrystallized products. Within the range of experimental uncertainties, it is found that tetrahedral substitution of Si by Al and differences in temperature (from 25 to 75°C) have no influence on partition coefficients. Experimental data are closely related to thermodynamic properties of the cations and on this basis other partition coefficients can be calculated, for the (M²⁺ ? Fe²⁺) pair for instance. The behaviour of transition metals is explained using crystal field theory.     

Estimation of maximum magnitude (M max ): Impending large earthquakes in northeast region,India

In the present study, the cumulative seismic energy released by earthquakes (M _w ≥ 5) for a period of 1897 to 2009 is analyzed for northeast (NE) India. For this purpose, a homogenized earthquake catalogue in moment magnitude (M _w ) has been prepared. Based on the geology, tectonics and seismicity, the study region is divided into three source zones namely, 1: Arakan-Yoma Zone (AYZ), 2: Himalayan Zone (HZ) and 3: Shillong Plateau Zone (SPZ). The maximum magnitude (M _max ) for each source zone is estimated using Tsuboi’s energy blocked model. As per the energy blocked model, the supply of energy for potential earthquakes in an area is remarkably uniform with respect to time and the difference between the supply energy and cumulative energy released for a span of time, is a good indicator of energy blocked and can be utilized for the estimation of maximum magnitude (M _max ) earthquakes. The proposed process provides a more consistent model of gradual accumulation of strain and non-uniform release through large earthquakes can be applied in the assessment of seismic hazard. Energy blocked for source zone 1, zone 2 and zone 3 regions is 1.35×10¹⁷ Joules, 4.25×10¹⁷ Joules and 7.25×10¹⁷ Joules respectively and will act as a supply for potential earthquakes in due course of time. The estimated M _max for each source zone AYZ, HZ, and SPZ are 8.2, 8.6, and 8.7 respectively. M _max obtained from this model is well comparable with the results of previous workers from NE region.     

Soil CO2 efflux along an elevation gradient in Qinghai spruce forests in the upper reaches of the Heihe River,northwest China

This study was conducted in six plots along an elevation gradient in the Qinghai spruce (Picea crassifolia Kom.) forest ecosystem of the Qilian Mountains, northwest China. Soil CO₂ efflux over bare soil (R _s) and moss covered soil (R _s+m) were investigated from June to September in 2010 and 2011 by means of an automated soil CO₂ flux system (LI-8100). The results showed that R _s ranged from 1.51 to 3.96 (mean 2.64 ± 0.72) μmol m^?2 s^?1 for 2010, and from 1.41 to 4.09 (mean 2.55 ± 0.70) μmol m^?2 s^?1 for 2011. The daily change trend of R _s resembled that of air temperature (T _a), and there was a hysteresis between R _s and soil temperature (T _s). The seasonal variations of R _s at lowlands (i.e., Plot 1, Plot 2 and Plot 3) were driven by soil moisture and temperature (T _a and T _s), while that at highlands (i.e., Plot 4, Plot 5 and Plot 6) were obviously affected by temperature. There were higher values at Plot 2 and Plot 6, which were caused by the interaction between soil moisture and temperature. In addition, soil CO₂ efflux over moss covered soil (R _s+m) was 8.83 % less than that over bare soil (R _s), indicating that moss was another factor affecting R _s. It was concluded that R _s had temporal and spatial variations and was mainly controlled by temperature and soil moisture; the main determinants differed at different elevations; moss could reduce R _s.     

Opaque mineralogy and magnetic investigation of some basaltic occurrences, Sinai, Egypt

Ore microscopic investigation of the Fe?CTi oxide minerals was carried out on samples from three Oligo-Miocene basaltic occurrences from Sinai, Egypt. These occurrences are Gebel Maghara (north Sinai), Rageibet Naama (central Sinai), and Wadi Matulla (west Sinai). The results and correlations of magnetic parameters such as NRM intensity and susceptibility, coercive force H _c, and the ratio M _r/M _s, H _c and Q value, the ratio M _r/M _s, saturation magnetization M _s, and K are discussed in light of opaque mineralogical studies. It has been found that the variations in the magnetic properties of the basaltic occurrences are strongly dependent on the crystallite size and nature and style of exsolution textures and fabrics. The latter are controlled by the cooling conditions, being most sensitive to the partial pressure of oxygen in the melt.     

Stability of a long unsupported circular tunnel in soils with seismic forces

By using the lower-bound finite element limit analysis, the stability of a long unsupported circular tunnel has been examined with an inclusion of seismic body forces. The numerical results have been presented in terms of a non-dimensional stability number (γH/c) which is plotted as a function of horizontal seismic earth pressure coefficient (k _h) for different combinations of H/D and ?; where (1) H is the depth of the crest of the tunnel from ground surface, (2) D is the diameter of the tunnel, (3) k _h is the earthquake acceleration coefficient and (4) γ, c and ? define unit weight, cohesion and internal friction angle of soil mass, respectively. The stability numbers have been found to decrease continuously with an increase in k _h. With an inclusion of k _h, the plastic zone around the periphery of the tunnel becomes asymmetric. As compared to the results reported in the literature, the present analysis provides a little lower estimate of the stability numbers. The numerical results obtained would be useful for examining the stability of unsupported tunnel under seismic forces.     

Late-Quaternary Slip Rate and Seismic Activity of the Xianshuihe Fault Zone in Southwest China

The Xianshuihe fault zone is a seismo-genetic fault zone of left-lateral slip in Southwest China. Since 1725, a total of 59 Ms ≥ 5.0 earthquakes have occurred along this fault zone, including 18 Ms 6.0–6.9 and eight Ms ≥ 7.0 earthquakes. The seismic risk of the Xianshuihe fault zone is a large and realistic threat to the western Sichuan economic corridor. Based on previous studies, we carried out field geological survey and remote sensing interpretation in the fault zone. In addition, geophysical surveys, trenching and age-dating were conducted in the key parts to better understand the geometry, spatial distribution and activity of the fault zone. We infer to divide the fault zone into two parts: the northwest part and the southeast part, with total eight segments. Their Late Quaternary slip rates vary in a range of 11.5 mm/a –(3±1) mm/a. The seismic activities of the Xianshuihe fault zone are frequent and strong, periodical, and reoccurred. Combining the spatial and temporal distribution of the historical earthquakes, the seismic hazard of the Xianshuihe fault zone has been predicted by using the relationship between magnitude and frequency of earthquakes caused by different fault segments. The prediction results show that the segment between Daofu and Qianning has a possibility of Ms ≥ 7.0 earthquakes, while the segment between Shimian and Luding is likely to have earthquakes of about Ms 7.0. It is suggested to establish a GPS or In SAR-based real-time monitoring network of surface displacement to cover the Xianshuihe fault zone, and an early warning system of earthquakes and post seismic geohazards to cover the major residential areas.     

Physical properties of calcium aluminates from vibrational spectroscopy

Heat capacity (C_V) and entropy (S) as a function of temperature were calculated for phases in the CaO-Al₂O₃ system from vibrational spectra using a quasi-harmonic model. Calculated values of C_V at 298 K for the calcium aluminates may have uncertainties as small as ±1%, based on comparison with published calorimetric data for CaO, Al₂O₃, and CaAl₂O₄. For hibonite (CaAl₁₂O₁₉), we predict C_P as 519.3 J/mol-K and S as 391.7 J/mol-K, at 298 K. For grossite (CaAl₄O₇), calculated values of C_P as 195.9 J/mol-K and of S as 172.0 J/mol-K are slightly smaller than the available calorimetric data at 298 K, consistent with calorimetric data having been obtained from samples containing ∼10 wt% hibonite impurities. Thermal conductivity at 298 K (k₀) is predicted from peak widths of the vibrational modes using the damped harmonic oscillator model of a phonon gas. Calculations of k₀ for CaO and Al₂O₃ differ from the measurements by 17% and 5%, respectively. The discrepancy for lime is larger due to uncertainties in its peak widths. This comparison suggests that our results for the calcium aluminates should be more accurate than conventional measurements of k₀ which are commonly uncertain by ∼25%.     

Yielding and shear behaviour of cement-treated dredged materials

The mechanical behaviour of three cement-treated dredged materials (DM) was studied in the laboratory by isotropic compression and undrained triaxial tests. The intrinsic properties of the untreated and reconstituted soil were used as a reference framework to interpret the effect of cementation on the mechanical behaviour of the cement-treated DM. The isotropic compression line of the reconstituted soil is termed the intrinsic normal compression line (INCL). It is found that the isotropic compression lines of the cement-treated DM lie above the INCL, i.e. the void ratio of the cement-treated soil is higher than that of the reconstituted soil for a given confining pressure. The yield stress measured from the isotropic compression tests increases with increasing cement content and curing time. The pre-yield and post-yield shear responses of the cement-treated DM are different. Pre-yield soil specimens show a tendency to dilate, but post-yield soil specimens show a tendency to contract. Failure envelopes of the cement treated DM lie above that of the reconstituted DM. Linear Mohr–Coulomb failure envelopes were observed for the range of applied stress used in the study. The cohesion intercept increases with increasing cement content and curing time. The strength enhancement of the cement-treated DM is the result of the structures developed during cementation process. Based on a recently proposed soil water transfer model, the change in normalised bound water content, (Δm_bw)_N, is used to evaluate the combined effects of cement content and curing period on the mechanical behaviour of the cement-treated DM. It is found that there exists a threshold value of (Δm_bw)_N, beyond which the yield stress and cohesion intercept increases nonlinearly with increasing (Δm_bw)_N. The threshold value is equal to 0.37 for the three DM used in the study.     

Probabilistic evaluation of primary consolidation settlement of Songdo New City by using kriged estimates of geologic profiles

The uncertainty in the spatial distributions of consolidation settlement (s _c) and time (t _p) for Songdo New City is evaluated by using a probabilistic procedure. Ordinary kriging and three theoretical semivariogram models are used to estimate the spatial distributions of geo-layers which affect s _c and t _p in this study. The spatial map of mean (μ) and standard deviation (σ) for s _c and t _p are determined by using a first-order second moment method based on the evaluated statistics and probability density functions (PDFs) of soil properties. It is shown that the coefficients of variation (COVs) of the compression ratio [C _c/(1 + e ₀)] and the coefficient of consolidation (c _v) are the most influential factors on the uncertainties of s _c and t _p, respectively. The μ and σ of the s _c and t _p, as well as the probability that s _c exceeds 100 cm [P(s _c > 100 cm)] and the probability that t _p exceeds 36 months [P(t _p > 36 months)] in Sect. 1, are observed to be larger than those of other sections because the thickness of the consolidating layer in Sect. 1 is the largest in the entire study area. The area requiring additional fill after the consolidation appears to increase as the COV of C _c/(1 + e ₀) increases and as the probabilistic design criterion (α) decreases. It is also shown that the area requiring the prefabricated vertical drains installation increases as the COV of c _v increases and as the α decreases. The design procedure presented in this paper could be used in the decision making process for the design of geotechnical structures at coastal reclamation area.     

Tectonic structures across the East African Rift based on the source parameters of the 20 May 1990 M7.2 Sudan earthquake

Earthquakes in Kenya are common along the Kenya Rift Valley because of the slow divergent movement of the rift and hydrothermal processes in the geothermal fields. This implies slow but continuous radiation of seismic energy, which relieves stress in the subsurface rocks. On the contrary, the NW-SE trending rift/fault zones such as the Aswa-Nyangia fault zone and the Muglad-Anza-Lamu rift zone are the likely sites of major earthquakes in Kenya and the East African region. These rift/fault zones have been the sites of a number of strong earthquakes in the past such as the M _w = 7.2 southern Sudan earthquake of 20 May 1990 and aftershocks of M _w = 6.5 and 7.1 on 24 May 1990, the 1937 M _s = 6.1 earthquake north of Lake Turkana close to the Kenya-Ethiopian border, and the 1913 M _s = 6.0 Turkana earthquake, among others. Source parameters of the 20 May 1990 southern Sudan earthquake show that this earthquake consists of only one event on a fault having strike, dip, and rake of 315°, 84°, and ?3°. The fault plane is characterized by a left-lateral strike slip fault mechanism. The focal depth for this earthquake is 12.1 km, seismic moment M _o = 7.65 × 10¹⁹ Nm, and moment magnitude, M _w = 7.19 (?7.2). The fault rupture started 15 s earlier and lasted for 17 s along a fault plane having dimensions of ?60 km × 40 km. The average fault dislocation is 1.1 m, and the stress drop, ?σ, is 1.63 MPa. The distribution of historical earthquakes (M _w ≥ 5) from southern Sudan through central Kenya generally shows a NW-SE alignment of epicenters. On a local scale in Kenya, the NW–SE alignment of epicenters is characterized by earthquakes of local magnitude M _l ≤ 4.0, except the 1928 Subukia earthquake (M _s = 6.9) in central Kenya. This NW–SE alignment of epicenters is consistent with the trend of the Aswa-Nyangia Fault Zone, from southern Sudan through central Kenya and further southwards into the Indian Ocean. We therefore conclude that the NW–SE trending rift/fault zones are sites of strong earthquakes likely to pose the greatest earthquake hazard in Kenya and the East African region in general.     

Connections between surface complexation and geometric models of mineral dissolution investigated for rhodochrosite

Mineral dissolution rates have been rationalized in the literature by surface complexation models (SCM) and morphological and geometric models (GM), and reconciliation of these conceptually different yet separately highly successful models is an important goal. In the current work, morphological alterations of the surface are observed in real time at the microscopic level by atomic force microscopy (AFM) while dissolution rates are simultaneously measured at the macroscopic level by utilizing the AFM fluid cell as a classic flow-through reactor. Rhodochrosite dissolution is studied from pH = 2 to 11 at 298 K, and quantitative agreement is found between the dissolution rates determined from microscopic and macroscopic observations. Application of a SCM model for the interpretation of the kinetic data indicates that the surface concentration of >CO₃H regulates dissolution for pH < 7 while the surface concentration of >MnOH₂⁺ regulates dissolution for pH > 7. A GM model explains well the microscopic observations, from which it is apparent that dissolution occurs at steps associated with anisotropic pit expansion. On the basis of the observations, we combine the SCM and GM models to propose a step-site surface complexation model (SSCM), in which the dissolution rates are quantitatively related to the surface chemical speciation of steps. The governing SSCM equation is as follows: R = χ_1/2(k_co + k_ca)[>CO₃H] + χ_1/2(k_mo + k_ma)[>MnOH₂⁺ ], where R is the dissolution rate (mol m⁻² s⁻¹), 2χ_1/2 is the fraction of surface sites located at steps, [>CO₃H] and [>MnOH₂⁺ ] are surface concentrations (mol m⁻²), and k_co, k_ca, k_mo, and k_ma are the respective dissolution rate coefficients (s⁻¹) for the >CO₃H and the >MnOH₂⁺ surface species on obtuse and acute steps. We find k_co = 2.7 s⁻¹, k_ca = 2.1 × 10⁻¹ s⁻¹, k_mo = 4.1 × 10⁻² s⁻¹, k_ma = 3.7 × 10⁻² s⁻¹, and χ_1/2 = 0.015 ± 0.005. The rate coefficients quantify the net result of complex surface step processes, including double-kink initiation and single-kink propagation. We propose that the SSCM model may have general applicability for dissolution far from equilibrium of flat mineral surfaces of ionic crystals, at least those that dissolve by step retreat.