Evaluation of Curve Fitting Techniques in Deriving p–y Curves for Laterally Loaded Piles

The p–y method is one of the most popular methods for the analysis and design of laterally loaded piles. The mathematical relationship it provides between the bending moment, which can be easily measured at strain gauges along the pile, and the soil resistance and lateral pile displacement, facilitates the construction of p–y curves. Numerical techniques are required to fit smooth continuous curves to the discrete bending moment data in order to improve the accuracy of subsequent differentiation and integration operations. Due to the lack of guidance on the optimum positioning of strain gauges and the reliability and accuracy of curve fitting methods, a unifying study, inclusive of small (0.61 m) and large (3.8 and 7.5 m) diameter piles in clay, was carried out using 18 strain gauge layouts and cubic spline, cubic to quintic B-spline and 3rd to 10th degree global polynomial techniques. Bending moment data was obtained using 3D finite element analysis. Through a comprehensive evaluation, the cubic and cubic B-spline methods were found to be consistently accurate in deriving p–y curves for both the small and large diameter piles.     

Analytical Behaviour of Bolt–Joint Intersection Under Lateral Loading Conditions

An analytical method is developed to provide a better understanding of bolt shearing across joint planes under lateral confinement. The study was undertaken in conjunction with a laboratory study of the double shearing of bolts in concrete. A review of various analytical methods is discussed, and the bending behaviour of the bolts is studied under both elastic and plastic conditions. Issues examined include; hinge point location, the effect of concrete strength on the bolt-bending behaviour; the influence of bolt axial loading and bolt diameter on the hinge point position with respect to sheared joint planes. It was found that the applied axial load on the bolt had a significant bearing on the location of the hinge points in different strength concrete, particularly at low strengths. The hinge point location is also influenced by the bolt diameter.     

Soil–Structure Interaction of Damped Infinite Beams on Extensible Geosynthetic Reinforced Earth Beds Under Moving Loads

In the present paper, soil-structure interaction analysis of an infinite beam resting on extensible geosynthetic reinforced earth beds has been carried out for an applied load moving with constant velocity. The viscous damping of the soil-foundation system has been given due consideration in the analytical procedure. The infinite beam has been treated as resting on a granular fill layer overlying the naturally occurring weak soil layer. Geosynthetic layer has been provided in the granular fill layer and has been considered as extensible. This extensible nature has been incorporated with the help of no slip and the compatibility conditions at the interface between reinforcing layer and the neighboring soil. These conditions help in eliminating the two interfacial shear stress parameters and in considering the tensile modulus of geosynthetic layer in the analysis. The influence of various parameters, like magnitude and velocity of applied moving load, viscous damping, relative stiffness of granular fill and tensile modulus of geosynthetic layer, on the response of soil-foundation system has been studied. It has been observed that all these parameters affect the response significantly, however, the effect of velocity of moving load and viscous damping has been found to be more significant especially at higher velocities.     

An Elastic Stress–Strain Relationship for Porous Rock Under Anisotropic Stress Conditions

A stress–strain relationship within porous rock under anisotropic stress conditions is required for modeling coupled hydromechanical processes associated with a number of practical applications. In this study, a three-dimensional stress–strain relationship is proposed for porous rock under elastic and anisotropic stress conditions. This relationship is a macroscopic-scale approximation that uses a natural-strain-based Hooke’s law to describe deformation within a fraction of pores and an engineering-strain-based Hooke’s law to describe deformation within the other part. This new relationship is evaluated using data from a number of uniaxial and triaxial tests published in the literature. Based on this new stress–strain relationship, we also develop constitutive relationships among stress, strain, and related stress-dependent hydraulic/mechanical properties (such as compressibility, shear modulus, and porosity). These relationships are demonstrated to be consistent with experimental observations.     

Soil–Water Characteristic Curves Obtained for a Colluvial and Lateritic Soil Profile Considering the Macro and Micro Porosity

This study aims to determine and to model the relationship of matric suction versus water content, known as soil?Cwater characteristic curve (SWCC), for a tropical soil profile at the southeastern Brazil. This soil profile consists of a colluvial, lateritic silty clay, with thickness of about 6.5?m. The filter paper and pressure plate techniques were used to determine the SWCC. Specimens were trimmed from the undisturbed soil samples collected along soil profile depth and submitted to drying paths. Impregnated thin-layer plates and a petrographic microscope were used to examine the structure and mineralogical composition of the soil samples. Mercury intrusion porosimetry tests were performed on some soil samples to obtain the frequency histogram of the pores. SWCC with bimodal pore-size distribution were obtained by the filter paper technique and SWCC with unimodal pore-size distribution were obtained by the pressure plate technique. The SWCC showed values of air-entry ranging from 1 to 3?kPa, depending on the technique used, resembling soils with macroporosity, as the lateritic soils. Combining both techniques, the SWCC could be fitted by a model that takes into consideration soils with macro and microporosity.     

P–T–t evolution of the Cycladic Blueschist Unit in Western Anatolia/Turkey: Geodynamic implications for the Aegean region

Eclogite and blueschist facies rocks occurring as a tectonic unit between the underlying Menderes Massif (MM) and the overlying Afyon Zone/Lycian Nappes and the Bornova Flysch Zone in western Anatolia represent the eastward continuation of the Cycladic Blueschist Unit (CBU) in Turkey. This high-P unit is attributed to the closure of the Pindos Ocean and consists of (a) a Triassic to Upper Cretaceous coherent series derived from passive continental margin sediments and (b) the tectonically overlying Upper Cretaceous Selçuk mélange with eclogite blocks embedded in a pelitic epidote-blueschist matrix. The coherent series has experienced epidote-blueschist facies metamorphism (490 ± 25°C/11.5 ± 1.5 kbar; 38 km depth). ⁴⁰Ar/³⁹Ar white mica and ²⁰⁶Pb/²³⁸U monazite dating of quartz metaconglomerate from coherent series yielded middle Eocene ages of 44 ± 0.3 and 40.1 ± 3.1 Ma for epidote-blueschist facies metamorphism, respectively. The epidote-blueschist facies metamorphism of the matrix of the Selçuk mélange culminates at 520 ± 15°C/13 ± 1.5 kbar, 43 km depth, and is dated at 57.5 ± 0.3–54.5 ± 0.1 Ma (⁴⁰Ar/³⁹Ar phengite). Eclogite facies metamorphism of the blocks (570 ± 30°C/18 ± 2 kbar, 60 km depth) is early Eocene and dated at 56.2 ± 1.5 Ma by ²⁰⁶Pb/²³⁸U zircon. Eclogites experienced a nearly isothermal retrogression (490 ± 40°C/~6 to 7 kbar) during their incorporation into the Selçuk mélange. The retrograde overprints of the coherent series (410 ± 15°C/7 ± 1.5 kbar from Dilek Peninsula and 485 ± 33°C/~6 to 7 kbar from Selçuk–Tire area) and the Selçuk mélange (510 ± 15°C/6 ± 1 kbar) are dated at 35.8 ± 0.5–34.3 ± 0.1 Ma by ⁴⁰Ar/³⁹Ar white mica and 31.6 ± 6.6 Ma by ²⁰⁶Pb/²³⁸U allanite dating methods, respectively. Regional geological constrains reveal that the contact between the MM and the CBU originally formed a lithosphere-scale transform fault zone. ⁴⁰Ar/³⁹Ar white mica age from the contact indicates that the CBU and the MM were tectonically juxtaposed under greenschist facies conditions during late Eocene, 35.1 ± 0.3 Ma.     

Metamorphic evolution of the Maud Belt: P–T–t path for high-grade gneisses in Gjelsvikfjella,Dronning Maud Land,East Antarctica

A metamorphic petrological study, in conjunction with recent precise geochronometric data, revealed a complex P–T–t path for high-grade gneisses in a hitherto poorly understood sector of the Mesoproterozoic Maud Belt in East Antarctica. The Maud Belt is an extensive high-grade, polydeformed, metamorphic belt, which records two significant tectono-thermal episodes, once towards the end of the Mesoproterozoic and again towards the late Neoproterozoic/Cambrian. In contrast to previous models, most of the metamorphic mineral assemblages are related to a Pan-African tectono-thermal overprint, with only very few relics of late Mesoproterozoic granulite-facies mineral assemblages (M₁) left in strain-protected domains. Petrological and mineral chemical evidence indicates a clockwise P–T–t path for the Pan-African orogeny. Peak metamorphic (M_2b) conditions recorded by most rocks in the area (T = 709–785 °C and P = 7.0–9.5 kbar) during the Pan-African orogeny were attained subsequent to decompression from probably eclogite-facies metamorphic conditions (M_2a).The new data acquired in this study, together with recent geochronological and geochemical data, permit the development of a geodynamic model for the Maud Belt that involves volcanic arc formation during the late Mesoproterozoic followed by extension at 1100 Ma and subsequent high-grade tectono-thermal reworking once during continent–continent collision at the end of the Mesoproterozoic (M₁; 1090–1030 Ma) and again during the Pan-African orogeny (M_2a, M_2b) between 565 and 530 Ma. Post-peak metamorphic K-metasomatism under amphibolite-facies conditions (M_2c) followed and is ascribed to post-orogenic bimodal magmatism between 500 and 480 Ma.     

Application of the content–area (C–A) fractal model and prediction–area (P–A) plot for mineral prospectivity modeling in the Luchun area of Yunnan Province,China

This method of assigning weights based on expert opinion introduces bias when we are evaluating the relative importance of evidence values. In this paper, we used a prediction–area (P–A) plot method and content–area (C–A) fractal model to estimate the weight of each evidence map. In this paper, we used the content region (C–A) fractal model to divide the evidence maps to the threshold of the corresponding dimensions. The P–A plot approach is an objective data-driven approach for evaluating map weights. Using geochemical layer and remote sensing, hydroxyl layers as weight evidence maps are the highlights of this study. We use the P–A method from which we can evaluate the predictive ability of each evidence map with respect to the known ore occurrences. We used the P–A plot for weighting each evidence map and choosing the appropriate threshold for predictor maps in the Luchun area of Yunnan Province, China. The method adopted in this paper can improve the prediction efficiency of ore prospecting.     

Zircon as the best mineral for P–T–time history of UHP metamorphism: A review on mineral inclusions and U–Pb SHRIMP ages of zircons from the Dabie–Sulu UHP rocks

Zircon is the best mineral to record the complex evolution history of ultrahigh-pressure (UHP) metamorphic rocks as mineralogical and geochemical tracers of UHP metamorphism are almost obliterated in matrix assemblages resulted from subsequent retrogression during exhumation. Zircons from Dabie–Sulu UHP rocks, including outcrop and core samples from drill holes ranging from 432 to 5158 m in depth contain abundant mineral inclusions of protolith, prograde, peak (UHP) and retrograde minerals in different domains; these minute inclusions were identified by laser Raman spectroscopy and/or electronic microprobe analysis. Systematic studies on inclusions in zircons from previous and present studies indicate that the Dabie–Sulu UHP terrane extends for >2000 km, is about 50 km wide, and has at least 10 km thick, probably the largest UHP terrane recognized in the world thus far. The internal structure of zircon revealed by cathodoluminescence (CL) imaging displays a distinct zonation, which comprises an inherited (magmatic or detrital) core, prograde, peak (UHP), and outmost retrograde domains, each with distinctive mineral inclusion assemblages. Low-pressure, igneous mineral inclusions are common in the inherited (magmatic or detrital) zircon cores. In contrast, quartz eclogite-facies inclusion assemblages occur in prograde domains, coesite eclogite-facies inclusion assemblages are preserved in UHP domains, and amphibolite-facies inclusion assemblages are enclosed in outmost retrograde rims. Parageneses and compositions of inclusion minerals preserved in distinct zircon domains were used to constrain the metamorphic P–T path of many Dabie–Sulu UHP rocks. The results indicate that Neoproterozoic supracrustal rocks together with minor mafic-ultramafic rocks were subjected to a prograde subduction-zone metamorphism at 570–690 °C and 1.7–2.1 GPa, and UHP metamorphism at 750–850 °C and 3.4–4.0 GPa, following by rapid decompression to amphibolite-facies retrograde metamorphism at 550–650 °C and 0.7–1.05 GPa. Sensitive high-resolution ion microprobe (SHRIMP) U–Pb spot analyses of the zoned zircons show four discrete and meaningful ages of the Dabie–Sulu metamorphic evolution: (1) Neoproterozoic protolith ages (800–750 Ma); (2) 246–244 Ma for early-stage quartz eclogite-facies prograde metamorphism; (3) 235–225 Ma for UHP metamorphism; and (4) 215–208 Ma for late-stage amphibolite-facies retrogression. This indicates that Neoproterozoic voluminous igneous protoliths of orthogneiss in response to the breakup of Rodinia supercontinent, together with various sedimentary rocks, and minor mafic-ultramafic intrusive and extrusive rocks, were subjected to coeval Triassic subduction to mantle depths and exhumation during the collision between the South China Block and North China Block. The estimated subduction and exhumation rates for the Dabie–Sulu UHP terrane would be up to 4.7–9.3 km Myr^?1 and 5.0–11.3 km Myr^?1, respectively. The zonal distribution of mineral inclusions and the preservation of index UHP minerals such as coesite imply that zircon is the best mineral container for each metamorphic stage, particular for supracrustal rocks as their metamorphic evolution and UHP evidence have been almost or completely obliterated. Similar conclusions have been documented elsewhere for other UHP terranes.     

Petrology and P–T history of the Wutai amphibolites: implications for tectonic evolution of the Wutai Complex,China

The Wutai Complex represents the best preserved granite-greenstone terrane in the North China Craton. The complex comprises a sequence of metamorphosed ultramafic to felsic volcanic rocks, variably deformed granitoid rocks, along with lesser amounts of siliciclastic and carbonate rocks and banded iron formations. Petrological evidence from the Wutai amphibolites indicates four metamorphic evolutionary stages. The M₁ assemblage is composed of plagioclase+quartz+actinolite+chlorite+epidote+biotite+rutile, preserved as mineral inclusions in garnet porphyroblasts. The metamorphic conditions for this assemblage cannot be quantitatively estimated. The M₂ stage is represented by garnet porphyroblasts in a matrix of quartz, plagioclase, amphibole, biotite, rutile and ilmenite. P–T conditions for this assemblage have been estimated using the program Tweequ at 10–12 kbar and 600–650°C. The M₃ assemblage is shown by amphibole+plagioclase±ilmenite symplectic coronas around embayed garnets and yields P–T conditions of 6.0–7.0 kbar and 600–650°C. M₄ is represented by chlorite and epidote rimming garnet, chlorite rimming amphibole and epidote replacing plagioclase under greenschist-facies conditions of 400–500°C and relatively lower pressures. Taken together, the qualitative P–T estimates from M₁ and M₄ and the quantitative P–T estimates from M₂ and M₃ define a clockwise P–T path for the Wutai amphibolites.The estimated P–T path from the four stages suggests that the Wutai Complex underwent initial burial and crustal thickening (M₁+M₂), subsequent isothermal exhumation (M₃), and finally cooling and retrogression (M₄). This tectonothermal path, along with those of the Fuping and Hengshan complexes, which bound the southeast and northwest margins, respectively, of the Wutai Complex, is considered to record the early Paleoproterozoic collision between the eastern and western segments of the North China craton.     

P–T history of garnet-websterites in the Sharyzhalgai complex,southwestern margin of Siberian craton: evidence for Paleoproterozoic high-pressure metamorphism

The Saramta massif in the Paleoproterozoic Sharyzhalgai complex, the southwestern margin of the Siberian craton, is mainly composed of spinel-peridotites with garnet-websterites; it is enclosed within granitic gneisses and migmatites with mafic intercalations of granulite-facies grade. The garnet-websterites occur as lenses or layers intercalated within spinel-harzburgite and spinel-lherzolite. They consist mainly of clinopyroxene (Cpx), garnet (Grt), and orthopyroxene (Opx): Grt often includes Cpx, Opx, and pargasite (Prg). Opx also occurs as kelyphite with plagioclase (Pl), spinel, olivine, Prg, and biotite. Relationships between textures and chemical compositions of these minerals suggest the following P–T stages: stage 1 (pre-peak), 0.9–1.5 GPa at 640–780 °C; stage 2 (peak), 2.3–3.0 GPa at 920–1030 °C as the minimum estimate; and stage 3 (post-peak), 750–830 °C at 0.5–0.9 GPa. Finally, the garnet-websterites are veined with lower amphibolite- to greenschist-facies minerals (stage 4).These results suggests that the Saramta massif was carried to depths of c. 100 km by subduction, and metamorphosed under eclogite-facies conditions in the Paleoproterozoic, despite the commonly held view that high geothermal gradients in those times would have prevented such deep subduction. Paleoproterozoic plate subduction at the southwestern margin of the Siberian craton might have caused subduction-zone magmatism and mantle metasomatism similar to those in the Phanerozoic.     

Metamorphic P–T–t–d evolution of (U)HP metabasites from the South Tianshan accretionary complex (NW China) — Implications for rock deformation during exhumation in a subduction channel

The late Carboniferous accretionary system of the South Tianshan orogen (North-Western China) underwent complex structural and polymetamorphic evolution. Combined petrological, geochronological and microstructural analysis of (ultra)high-pressure (UHP) metabasites (eclogites and blueschists) enclosed in metapelites show a relict coarse-grained eclogitic fabric S2 surrounded by a dominant fine-grained eclogite and blueschist facies retrograde fabric S2. The S2 fabric is reworked by upright folds F3 that are responsible for a major shortening of the whole accretionary system. For both the eclogite and blueschist, peak and retrograde P–T conditions have been thermodynamically constrained at 25–26 kbar and 425–500 °C and 10–13 kbar and 500−550 °C respectively, suggesting a shared exhumation history. The garnet-whole rock-amphibole isochron in the blueschist yielded Lu–Hf and Sm–Nd ages of 326.0 ± 2.9 Ma and 318.4 ± 3.9 Ma respectively, interpreted to date the prograde to peak metamorphic assemblage. The retrograde path of the eclogite is characterized by heterogeneous omphacite recrystallization into a mylonitic fine-grained matrix and crystallization of blue amphibole. Microstructures in both pristine porphyroclastic and recrystallized fine-grained domains in the eclogite indicate a gradual evolution from constriction-dominated (L>S-type) to flattening-dominated (S>L-type) type of deformation, increase of fabric intensity reflected by gradually growing M-indexes and the development of lattice preferred orientation (LPO) typical for dislocation creep under slightly hydrated conditions. Recrystallization of the matrix in the blueschist is homogeneous, which indicates a matrix dominated channel flow during exhumation. These LPOs evolutions suggest a significant mechanical coupling with the upper plate concomitant with oroclinal bending of the Kazakh orocline. Lock up of Kazakh orocline is responsible for further stress increase resulting in horizontal shortening of South Tianshan accretionary wedge and development of D3 upright folding and steepening of the whole sequence.     

Metamorphic P–T path of mafic granulites from Eastern Hebei: Implications for the Neoarchean tectonics of the Eastern Block,North China Craton

This study documents the metamorphic evolution of mafic granulites from the Eastern Hebei Complex in the Eastern Block of the North China Craton. Mafic granulites from Eastern Hebei occur as boudins or enclaves within Neoarchean high-grade TTG gneisses. Petrographic observations reveal three characteristic metamorphic mineral assemblages in the mafic granulites: the pre-peak hornblende + plagioclase + ilmenite + quartz + sphene assemblage (M₁) existing as mineral inclusions within coarse-grained peak assemblage (M₂) represented by garnet + clinopyroxene + orthopyroxene + plagioclase + hornblende + ilmenite + quartz, and post-peak assemblage (M₃) marked by garnet + quartz ± ilmenite symplectites surrounding the peak pyroxene and plagioclase. Based on pseudosection modeling calculated in the NCFMASHTO model system using the program THERMOCALC, P–T conditions of the pre-peak (M₁), peak (M₂) and post-peak (M₃) assemblages are constrained at 600–715 °C/6.0 kbar or below, 860–900 °C/9.6–10.3 kbar, and 790–810 °C/9.6–10.4 kbar, respectively. These P–T estimates, combined with their mineral compositions and reaction relations, define an anticlockwise P–T path incorporating isobaric cooling subsequent to the peak medium-pressure granulite-facies metamorphism for the mafic granulites from Eastern Hebei. Such an anticlockwise P–T path suggests that the end-Neoarchean metamorphism of the Eastern Hebei Complex correlated closely with underplating and intrusion of voluminous mantle-derived magmas. In conjunction with other geological considerations, a mantle-plume model is favored to interpret the Neoarchean tectonothermal evolution of the Eastern Hebei Complex and other metamorphic complexes in the Eastern Block. The prograde amphibolite-facies metamorphism (M₁) was initiated due to the upwelling of the relatively cooler mantle plume head, followed by the peak medium-pressure granulite-facies metamorphism (M₂) as triggered by the uprising hotter plume “tail”, and finally when plume activity ceased, the heated metamorphic crust experienced nearly isobaric cooling (M₃).     

Evidence for two burial/exhumation stages during the evolution of the Variscan belt,as exemplified by P–T–t–d paths of metabasites in distinct allochthonous units of the Maures massif (SE France)

This paper examines the metamorphic evolution of three juxtaposed units of the Maures massif (France) with respect to the tectonic processes related to the Variscan orogeny. All sampled rocks are metabasalts or metagabbros metamorphosed during Palaeozoic tectonic events. The inferred metamorphic evolution takes into account the relative chronology of mineral parageneses with respect to microstructures, the mineral chemistry of zoned amphiboles, and calculated P–T–t–d paths derived from each unit. Three successive and contrasting tectono-metamorphic events are clearly identified. The D₁ event is associated with coarse-grained amphiboles of an early S₁–L₁ fabric that recorded prograde/retrograde anticlockwise paths at high-grade amphibolite facies conditions (7–8 kbar/700–750 °C). The D₂ event is related to fine-grained amphiboles of the main S₂ foliation that recorded prograde/retrograde clockwise paths at MP–MT conditions (4–6 kbar/550–650 °C). The D₃ event corresponds to late post-S₂ amphiboles crosscutting the main foliation and recording retrograde clockwise paths at lower grade conditions (4–2 kbar/500–350 °C). The D₁ event results from Silurian–Devonian continental subduction and subsequent thrust tectonics during an early stage of the Variscan evolution, before the Carboniferous. The D₂ event is connected to the Visean continental collision, marked by nappe stacking (burial) then crustal folding and sinistral strike-slip shearing (exhumation). The D₃ event is an effect of the Namurian late-orogenic extension (late exhumation) that mostly affected the previously thickened whole central block. This paper demonstrates that the whole metamorphic history of the Maures massif consists of two successive stages of burial/exhumation at different metamorphic conditions during the Variscan mountain building. Similar stages of subduction-uplift then collision-uplift processes have also been recognised in others parts of the Variscan belt and in the Alpine orogen.