SANICLAY: simple anisotropic clay plasticity model

SANICLAY is a new simple anisotropic clay plasticity model that builds on a modification of an earlier model with an associated flow rule, in order to include simulations of softening response under undrained compression following K_o consolidation. Non‐associativity is introduced by adopting a yield surface different than the plastic potential surface. Besides, the isotropic hardening of the yield surface both surfaces evolve according to a combined distortional and rotational hardening rule, simulating the evolving anisotropy. Although built on the general premises of critical state soil mechanics, the model induces a critical state line in the void ratio–mean effective stress space, which is a function of anisotropy. To ease interpretation, the model formulation is presented firstly in the triaxial stress space and subsequently, its multiaxial generalization is developed systematically, in a form appropriate for implementation in numerical codes. The SANICLAY is shown to provide successful simulation of both undrained and drained rate‐independent behaviour of normally consolidated sensitive clays, and to a satisfactory degree of accuracy of overconsolidated clays. The new model requires merely three constants more than those of the modified Cam clay model, all of which are easily calibrated from well‐established laboratory tests following a meticulously presented procedure. Copyright © 2006 John Wiley & Sons, Ltd.     

The Ms = 6.2, June 15, 1995 Aigion earthquake (Greece): evidence for low angle normal faulting in the Corinth rift

We present the results of a multidisciplinary study of the M_s = 6.2, 1995, June 15, Aigion earthquake (Gulf of Corinth, Greece). In order to constrain the rupture geometry, we used all available data from seismology (local, regional and teleseismic records of the mainshock and of aftershocks), geodesy (GPS and SAR interferometry), and tectonics. Part of these data were obtained during a postseismic field study consisting of the surveying of 24 GPS points, the temporary installation of 20 digital seismometers, and a detailed field investigation for surface fault break. The Aigion fault was the only fault onland which showed detectable breaks (< 4 cm). We relocated the mainshock hypocenter at 10 km in depth, 38 ° 21.7 N, 22 ° 12.0 E, about 15 km NNE to the damaged city of Aigion. The modeling of teleseismic P and SH waves provides a seismic moment M_o = 3.4 10¹⁸ N.m, a well constrained focal mechanism (strike 277 °, dip 33 °, rake – 77°), at a centroidal depth of 7.2 km, consistent with the NEIC and the revised Harvard determinations. It thus involved almost pure normal faulting in agreement with the tectonics of the Gulf. The horizontal GPS displacements corrected for the opening of the gulf (1.5 cm/year) show a well-resolved 7 cm northward motion above the hypocenter, which eliminates the possibility of a steep, south-dipping fault plane. Fitting the S-wave polarization at SERG, 10 km from the epicenter, with a 33° northward dipping plane implies a hypocentral depth greater than 10 km. The north dipping fault plane provides a poor fit to the GPS data at the southern points when a homogeneous elastic half-space is considered: the best fit geodetic model is obtained for a fault shallower by 2 km, assuming the same dip. We show with a two-dimensional model that this depth difference is probably due to the distorting effect of the shallow, low-rigidity sediments of the gulf and of its edges. The best-fit fault model, with dimensions 9 km E–W and 15 km along dip, and a 0.87 m uniform slip, fits InSAR data covering the time of the earthquake. The fault is located about 10 km east-northeast to the Aigion fault, whose surface breaks thus appears as secondary features. The rupture lasted 4 to 5 s, propagating southward and upward on a fault probably outcropping offshore, near the southern edge of the gulf. In the shallowest 4 km, the slip – if any – has not exceeded about 30 cm. This geometry implies a large directivity effect in Aigion, in agreement with the accelerogram aig which shows a short duration (2 s) and a large amplitude (0.5 g) of the direct S acceleration. This unusual low-angle normal faulting may have been favoured by a low-friction, high pore pressure fault zone, or by a rotation of the stress directions due to the possible dip towards the south of the brittle-ductile transition zone. This fault cannot be responsible for the long term topography of the rift, which is controlled by larger normal faults with larger dip angles, implying either a seldom, or a more recently started activity of such low angle faults in the central part of the rift.     

Earthquake generation in Cyprus revealed by the evolving stress field

Strong earthquake occurrence (M ≥ 6.0) onshore and offshore the Cyprus Island constitutes significant seismic hazard because they occur close to populated areas. Seismicity is weak south of the Island along the Cyprean Arc and strong events are aligned along the Paphos transform fault and Larnaka thrust fault zone that were already known and the Lemessos thrust fault zone that defined in the present study. By combining the past history of strong (M ≥ 6.0) events and the long-term tectonic loading on these major fault zones, the evolution of the stress field from 1896 until the present is derived. Although uncertainties exist in the location, magnitude and fault geometries of the early earthquakes included in our stress evolutionary model, the resulting stress field provides an explanation of later earthquake triggering. It was evidenced that the locations of all the strong events were preceded by a static stress change that encouraged failure. The current state of the evolved stress field may provide evidence for the future seismic hazard. Areas of positive static stress changes were identified in the southwestern offshore area that can be considered as possible sites of future seismic activity.     

The Mw = 6.0, 7 September 1999 Athens Earthquake

On 7 September 1999 at 11:56 GMT a destructive earthquake (M_w = 6.0) occurred close to Athens (Greece). The rupture process is examined using data from the Cornet local permanent network, as well as teleseismic recordings. Data recorded by a temporary seismological network were analyzed to study the aftershock sequence. The mainshock was relocated at 38.105°N, 23.565°E, about 20 km northwest of Athens. Four foreshocks were also relocated close to the mainshock. The modeling of teleseismic P and SH waves provides a well-constrained focal mechanism of the mainshock (strike = 105°, dip = 55° and rake = -80°) at a depth of 8 km and a seismic moment M₀ = 1.010²⁵ dyn·cm. The obtained fault plane solution represents normal faulting indicating an almost north-south extension. More than 3500 aftershocks were located, 1813 of which present RMS < 0.1 s and ERH, ERZ < 1.0 km. Two main clusters were distinguished, while the depth distribution is concentrated between 2 and 11 km. Over 1000 fault plane solutions of aftershocks were constrained, the majority of which also correspond to N–S extension. No surface breaks were observed but the fault plane solution of the mainshock is in agreement with the tectonics of the area and with the focal mechanisms obtained by aftershocks. The hypocenter of the mainshock is located on the deep western edge of the fault plane. The relocated epicenter coincides with the fringe that represents the highest deformation observed on the differential interferometric image. The calculated source duration is 5 sec, while the estimated dimensions of the fault are 15 km length and 10 km width. The source process is characterized by unilateral eastward rupture propagation, towards the city of Athens. An evident stop phase observed in the recordings of the Cornet local stations is interpreted as a barrier caused by the Aegaleo Mountain.     

A critical state interpretation for the cyclic liquefaction resistance of silty sands

Contrary to many laboratory investigations, common empirical correlations from in situ tests consider that the increase in the percentage of fines leads to an increase of the cyclic liquefaction resistance of sands. This paper draws upon the integrated Critical State Soil Mechanics framework in order to study this seemingly not univocal effect. Firstly the effect of fines on the Critical State Line (CSL) is studied through a statistical analysis of a large data set of published monotonic triaxial tests. The results show that increasing the content of non-plastic fines practically leads to a clockwise rotation of the CSL in (e–ln p) space. The implication of this effect on cyclic liquefaction resistance is subsequently evaluated with the aid of a properly calibrated critical state elasto-plastic constitutive model, as well as a large number of published experimental results and in situ empirical correlations. Both sets of data show clearly that a fines content, less than about 30% by weight, may prove beneficial at relatively small effective stresses (p₀<50–70 kPa), such as the in situ stresses prevailing in most liquefaction case studies, and detrimental at larger confining stresses, i.e. the stresses usually considered in laboratory tests. To the extent of these findings, a correction factor is proposed for the practical evaluation of liquefaction resistance in terms of the fines content and the mean effective confining stress.     

Explicit integration of bounding surface model for the analysis of earthquake soil liquefaction

This paper presents a new plasticity model developed for the simulation of monotonic and cyclic loading of non‐cohesive soils and its implementation to the commercial finite‐difference code FLAC, using its User‐Defined‐Model (UDM) capability. The new model incorporates the framework of Critical State Soil Mechanics, while it relies upon bounding surface plasticity with a vanished elastic region to simulate the non‐linear soil response. Stress integration of constitutive relations is performed using a recently proposed explicit scheme with automatic error control and substepping, which so far has been employed in the literature only for constitutive models aiming at monotonic loading. The overall accuracy of this scheme is evaluated at element level by simulating cyclic loading along complex stress paths and by using iso‐error maps for paths involving change of the Lode angle. The performance of the new constitutive model and its stress integration scheme in complex boundary value problems involving earthquake‐induced liquefaction is evaluated, in terms of accuracy and computational cost, via a number of parametric analyses inspired by the successful simulation of the VELACS centrifuge Model Test No. 2 studying the lateral spreading response of a liquefied sand layer. Copyright © 2009 John Wiley & Sons, Ltd.     

Travel time residuals in southeastern Europe

The Pn travel time relative residuals, in respect to a crustal model of the Aegean area, have been determined for 103 permanent seismological stations in southeastern Europe, western Turkey and the Middle East. The values of these residuals are considered to depend mainly on the crustal thickness beneath the seismological stations. Based on these values seven regions with different crustal thickness, varying between 31 Km and 42 Km, have been defined. The crust in these regions is continental. A region with very high negative residuals has been defined in the Middle East (Egypt, Israel, Lebanon). These negative residuals are attributed to different crustal structure of the eastern Mediterranean (oceanic crust with an extra thick sedimentary layer) and not the crustal thickness at the station sites.Independently from the interpretation, these Pn residuals can be used successfully to considerably improve (up to 2 Km) the determination of the earthquake foci locations.     

Rupture zones in the area of the 17.08.99 Izmit (NW Turkey) large earthquake (Mw 7.4) and stress changes caused by its generation

The M_w 7.4 Izmit earthquake of 17 August 1999 struck a part ofthe North Anatolian fault in the area of Izmit Bay (NW Turkey). Historicalinformation shows that the fault which moved during the generation of thisearthquake consists of two fault segments moved during the generation oflarge (M 7) earthquakes in 1719 and 1754, respectively. Since then onlythe central part (between Izmit and Lake Sapanca) of this fault ruptured bythe generation of a smaller shock (M = 6.6) in 1878.The spatial stress variations based on the calculation of changes in theCoulomb Failure Function (CFF) associated with this earthquake aresupported by the distribution of strong aftershock foci. Large positive valuesof CFF to the east and west of the mainshock epicenter are inagreement with the notion that secondary faults were triggered there by thegeneration of the main event. Large positive values of CFF are alsoobserved in the adjacent western fault segment where the 1766 event wasgenerated, evidencing the occurrence of the next strong earthquake in thissegment.     

Multi‐variable relations for soil effects on seismic ground motion

Soil effects on peak ground acceleration, velocity and elastic response spectra (5% damping) are expressed by simple approximate relations in terms of five key parameters: (a) the fundamental vibration period of the non‐linear soil, T_S, (b) the period of a bedrock site of equal thickness, T_b, (c) the predominant excitation period, Te, (d) the peak seismic acceleration at outcropping bedrock, a, and (e) the number of significant excitation cycles, n. Furthermore, another relation is proposed for the estimation of T_S in terms of the soil thickness H, the average shear wave velocity of the soil V?_S,o and a. The aforementioned parameters were first identified through a simplified analytical simulation of the site excitation. The multivariable approximate relations were then formulated via a statistical analysis of relevant data from more than 700 one‐dimensional equivalent‐linear seismic ground response analyses, for actual seismic excitations and natural soil conditions. Use of these relations to back‐calculate the numerical results in the database gives an estimate of their error margin, which is found to be relatively small and unbiased. The proposed relations are also independently verified through a detailed comparison with strong motion recordings from seven well‐documented case studies: (a) two sites in the San Fernando valley during the Northridge earthquake, and (b) five different seismic events recorded at the SMART‐1 accelerometer array in Taiwan. It is deduced that the accuracy of the relations is comparable to that of the equivalent‐linear method. Hence, they can be readily used as a quick alternative for routine applications, as well as for spreadsheet computations (e.g. GIS‐aided seismic microzonation studies) where numerical methods are cumbersome to implement. Copyright © 2003 John Wiley & Sons, Ltd.     

Analysis of fault rupture propagation through uniform soil cover

This paper presents results from numerical simulations of the propagation of an active dip–slip fault rupture through a uniform soil layer covering the rigid bedrock. Following verification of the numerical methodology against field evidence, a parametric study is performed for loose and dense sand, for normally consolidated and overconsolidated clay, as well as for different fault dip angles (normal and reverse faults) and for different thicknesses of the soil cover. The soil is modeled as an elasto-plastic, strain-softening material that obeys the Mohr–Coulomb failure criterion. The study aims at establishing criteria for the approximate depiction of the location and the width of the zone with significant ground surface distortion, where the differential ground displacements induced by the fault rupture may threaten the integrity of man-mad structures.