Revisiting the effect of foundation embedment on elastic settlement: A new approach

The effect of foundation embedment on settlement calculation is a widely researched topic in which there is no scientific consensus regarding the magnitude of settlement reduction. In this paper, a non-linear three dimensional Finite Element analysis has been performed with the aim of evaluating the aforementioned effect. For this purpose, 1800 models were run considering different variables, such as the depth and dimensions of the foundation and the Young’s modulus and Poisson’s ratio of the soil. The settlements from models with foundations at surface level and at depth were then compared and the relationship between them established. The statistical analysis of this data allowed two new expressions, with a mean maximum error of 1.80%, for the embedment influence factor of a foundation to be proposed and these to be compared with commonly used corrections. The proposed equations were validated by comparing the settlements calculated with the proposed influence factors and the true settlements measured in several real foundations. From the comprehensive study of all modelled cases, an improved approach, when compared to those proposed by other authors, for the calculation of the true elastic settlements of an embedded foundation is proposed.     

Equation of state, elasticity, and shear strength of pyrite under high pressure

 Physical properties including the equation of state, elasticity, and shear strength of pyrite have been measured by a series of X-ray diffraction in diamond-anvil cells at pressures up to 50 GPa. A Birch–Murnaghan equation of state fit to the quasihydrostatic pressure–volume data obtained from laboratory X-ray source/film techniques yields a quasihydrostatic bulk modulus K _0T =133.5 (±5.2) GPa and bulk modulus first pressure derivative K ^′ _0T =5.73 (±0.58). The apparent equation of state is found to be strongly dependent on the stress conditions in the sample. The stress dependency of the high-pressure properties is examined with anisotropic elasticity theory from subsequent measurements of energy-dispersive radial diffraction experiments in the diamond-anvil cell. The calculated values of K _0T depend largely upon the angle ψ between the diffracting plane normal and the maximum stress axis. The uniaxial stress component in the sample, t=σ₃−σ₁, varies with pressure as t=−3.11+0.43P between 10 and 30 GPa. The pressure derivatives of the elastic moduli dC ₁₁/dP=5.76 (±0.15), dC ₁₂/dP=1.41 (±0.11) and dC ₄₄/dP=1.92 (±0.06) are obtained from the diffraction data assuming previously reported zero-pressure ultrasonic data (C ₁₁=382 GPa, C ₁₂=31 GPa, and C ₄₄=109 GPa). Received: 21 December 2000 / Accepted: 11 July 2001     

High-temperature elasticity of magnesioferrite spinel

The elastic moduli of magnesioferrite spinel, MgFe₂O₄, and their temperature dependence have been determined for the first time by ultrasonic measurements on a polycrystalline specimen. The measurements were carried out at 300 MPa and to 700°C in a gas-medium high-pressure apparatus. On heating, both the elastic bulk (K _S) and shear (G) moduli decrease linearly to 350°C. By combining with extant thermal-expansion data, the values for the room-temperature K _S and G, and their temperature derivatives are as follows: K ₀ = 176.3(7) GPa, G ₀ = 80.1(2) GPa, (∂K _S/∂T) _P = −0.032(3) GPa K⁻¹ and (∂G/∂T) _P = −0.012(1) GPa K⁻¹. Between 350 and 400°C, there are abrupt increases of 1.4% in both of the elastic moduli; these closely coincide with the magnetic Curie transition that was observed by thermal analyses at about 360°C.     

Texture development and elastic stresses in magnesiowűstite at high pressure

Cubic magnesiowűstite has been deformed in a diamond anvil cell at room temperature. We present results for (Mg_0.4Fe_0.6)O, (Mg_0.25Fe_0.75)O, and (Mg_0.1Fe_0.9)O up to 37, 16, and 18 GPa, respectively. The diffraction images, obtained with the radial diffraction technique, are analyzed using both single peak intensities and a Rietveld method. For all samples, we observe a [100] fiber texture but the texture strength decreases with increasing iron content. This texture pattern is consistent with {110}〈1-10〉 slip. The images were also analyzed for stress, elastic strains, and elastic anisotropy. In general, the stress measured in magnesiowűstite samples is lower than previously measured on MgO. The elastic anisotropy deduced from the X-ray measurements shows a broad agreement with models based on measurements with other techniques.     

Time dependent piezomagnetic fields in viscoelastic medium

We investigated time dependent piezomagnetic fields due to volcanic sources embedded in a viscoelastic, homogeneous half-space. Especially in volcanic areas, the presence of inhomogeneous materials and high temperatures produce a lower effective viscosity of the Earth's crust that calls for considering anelastic properties of the medium. Piezomagnetic properties are carried by grains of titano-magnetite, which occupy only a small fraction of ordinary rock volume and are supposed to be elastic, while the non-magnetic surrounding matrix is assumed to be viscoelastic. From all the possible rheological models, we investigated two cases in which the bulk modulus is purely elastic and the shear modulus relaxes as: (i) a Maxwell solid and (ii) a standard linear solid (SLS). We applied the Correspondence Principle to the analytical elastic solutions for pressurized spherical sources and dislocation sources in order to determine the time dependent piezomagnetic fields in a viscoelastic medium. The piezomagnetic field completely vanishes after the relaxation process for a Maxwell rheology, whereas it is found to decrease over time and reach some finite offset value for a SLS rheology. These different behaviours provide helpful hints in understanding the temporal evolution of piezomagnetic anomalies in volcanic regions.     

Evidence of seismic deformation of the paved floor of the decumanus at Tindari (NE, Sicily)

Most of the ancient town of Tindari (NE, Sicily) was settled on a plateau the most surficial layer of which was made of unconsolidated material. Ongoing excavations at the archaeological site at Tindari uncovered a large portion of the decumanus which suffered deformations preliminarily assigned to coseismic effects.
An analysis of the local dynamic response through the simulation of strong seismic shaking to the bedrock and modelling of spectral ratios of the bedrock-soft soil was carried out to verify the susceptibility of superficial terrains of the promontory to coseismic deformations. To perform this simulation the finite element method (FEM) was used. Four accelerometric recordings of three earthquakes of medium-high magnitude, recorded on rocky sites, were chosen to simulate the seismic shaking, using a constitutive law for the materials composing the promontory layers both of linear-elastic type and of elastoplastic type.
The analysis of the linear-elastic field allowed the definition of the frequencies for which the spectral ratios of the accelerations recorded the highest amplifications; in particular the frequency range 31.5–37.2 Hz can be combined with deformation of the paved floor of the decumanus. The analysis in the elastoplastic field highlighted the zones of promontory more susceptible to suffer plasticization process. The results show that the topmost layer of the decumanus is the most susceptible to suffer plasticization. Therefore, the performed analysis lends greater support to the hypothesis that the deformations were produced by seismic shaking.     

里海沿岸地壳和上地幔弹性参数的3D模型分析

为了解决应力和应变三维模拟问题,研讨了建立里海沿岸地壳和上地幔弹性参数信息数据库的结果及里海沿岸盆地的地球动力学模型。创建了研究区资料信息数据库,得到了研制地壳应力应变状态的计算法。     

Single-crystal elastic properties of chondrodite: implications for water in the upper mantle

Chondrodite, a member of the humite group of minerals, forms by hydration of olivine and is stable over a range of temperatures and pressures that includes a portion of the uppermost mantle. We have measured the single crystal elastic properties of a natural chondrodite specimen at ambient conditions using Brillouin spectroscopy. The isotropic aggregate bulk (K) and shear (μ) moduli calculated from the single-crystal elastic moduli, C_ij, are: K_S=118.4(16) GPa and μ=75.6(7) GPa. A comparison of the structures and elasticity of olivine and chondrodite indicate that the replacement of O with (OH,F) in M²⁺O₆ octahedra has a small effect on the elasticity of humite-group minerals. The slightly diminished elastic moduli of humite-group minerals (as compared to olivine) are likely caused by a smaller ratio of strong structural elements (SiO₄ tetrahedra) to weaker octahedra, and perhaps a more flexible geometry of edge-sharing MO₄(O,OH,F)₂ octahedra. In contrast to the humite-olivine group minerals, the incorporation of water into garnets and spineloids leads to a more substantial decrease in the elastic properties of these minerals. This contrasting behavior is due to formation of O₄H₄ tetrahedra and vacant hydroxyl-bearing octahedra in the garnets and spineloids, respectively. Therefore, the mechanism of incorporation of H/OH into mineral phases, not only degree of hydration, should be taken into account when estimating the effect of water on the elastic properties of minerals. The bulk elastic wave velocities of chondrodite and olivine are very similar. If humite-like incorporation of OH is predominant in the upper mantle, then the reaction of OH with olivine will have a minor or possibly no detectable effect on seismic velocities. Thus, it may be difficult to distinguish chondrodite-bearing rocks from “anhydrous” mantle on the basis of seismically determined velocities for the Earth. Received: 25 February 1998 / Revised, accepted: 18 August 1998     

Rock physics modelling based on depositional and burial history of Barents Sea sandstones

Understanding how physical properties and seismic signatures of present day rocks are related to ancient geological processes is important for enhanced reservoir characterization. In this paper, we have studied this relationship for the Kobbe Formation sandstone in the Barents Sea. These rocks show anomalous low shear velocities and high V_P/V_S ratios, which does not agree well with conventional rock physics models for moderately to well consolidated sandstones. These sandstones have been buried relatively deeply and subsequently uplifted 1–2 km. We compared well log data of the Kobbe sandstone with velocity–depth trends modelled by integrating basin modelling principles and rock physics. We found that more accurate velocity predictions were obtained when first honouring mechanical and chemical compaction during burial, followed by generation of micro-cracks during uplift. We suspect that these micro-cracks are formed as overburden is eroded, leading to changes in the subsurface stress-field. Moreover, the Kobbe Formation is typically heterogeneous and characterized by structural clays and mica that can reduce the rigidity of grain contacts. By accounting for depositional and burial history, our velocity predictions become more consistent with geophysical observables. Our approach yields more robust velocity predictions, which are important in prospect risking and net erosion estimates.