Frequency-independent impedances of soil-structure systems in horizontal and rocking modes

The frequency-independent foundation impedances, commonly used in soil-structure dynamic interaction problems, are developed for a circular footing resting on a homogeneous halfspace. As they ignore the structure attached to the foundation, the error introduced in the structural response may be 50 per cent or more in the neighbourhood of the fundamental frequency of the soil-structure system. The present study proposes a new method developed for most dynamic soil-structure interaction problems. The key idea is to retain for the frequency-independent impedances values computed for the fundamental frequency of the soil-structure system; thus these values include the dynamic characteristics of the whole soil-structure system and lead to a satisfactory approximation of the exact solution over a wide frequency range. The method is developed here for the horizontal and rocking modes of a structure with a circular base resting on a homogeneous halfspace. Numerical applications are given for a simple linear oscillator in order to make possible a thorough parametric study. The response of some idealized building-foundation systems to harmonic excitation or to a seismic input is next examined in order to illustrate the efficiency of the proposed model.     

Dynamic amplification factors for a system with multiple-degrees-of-freedom

It is well-known that the responses of a structure are different when subjected to a static load or a sudden step load. The dynamic amplification factor (DAF), which is defined as the ratio of the amplitude of the vibratory response to the static response, is normally used to depict the dynamic effect. For a single-degree-of-freedom system (SDOF) subjected to a sudden dynamic load, the maximum value of DAF is 2. Many design guidelines therefore use 2 as an upper bound to consider the dynamic effect. For a civil engineering structure, which is normally a multiple-degrees-of-freedom (MDOF) system, the DAF may exceed 2 in certain circumstances. The adoption of 2 as the upper bond as suggested by the design guidelines therefore may lead to unsafe structural design. Very limited studies systematically investigate the DAF of a MDOF system. This study theoretically investigates the DAF of a MDOF system when it is subjected to a step load based on the fundamental theory of structural dynamics. The condition on which the DAF may exceed 2 is defined. Two numerical examples and one experimental study of a cable-stayed bridge subjected to sudden cable loss are presented to illustrate the problem.     

Computing three-dimensional gravitational fields with equivalent sources

Existing techniques for computing the gravitational field due to a homogeneous polyhedron all transform the required volume integral, expressing the field due to a volume distribution of mass, into a surface integral, expressing the potential due to a surface mass distribution over the boundary of the source body. An alternative representation is also possible and results in a surface integral expressing the potential due to a variable-strength double layer located on the polyhedral source boundary. Manipulation of this integral ultimately allows the gravitational field component in an arbitrary direction to be expressed as a weighted sum of the potentials due to two basic source distributions. These are a uniform-strength double layer located on all faces and a uniform-strength line source located along all edges. The derivatives of the gravitational field components can also be expressed in a similar form as can the magnetic field components due to a homogeneous magnetic polyhedron. It follows that the present approach can be used to generate a universal program capable of modelling all the commonly used potential field responses due to 3D bodies of arbitrary shape.     

Some consequences of the differences in seismic properties in old and young continental plates for isostatic compensation

We present a short review of seismological data and show that a difference of upper mantle structure is clearly resolved between old and young continental plates. An Archean plate is approximately 1 second faster than a Paleozoic plate for P waves. Such a change in plate structure implies that the density of an Archean lithosphere should be greater than the density of a Paleozoic lithosphere, if they have the same chemical composition. Applying isostasy, we would expect a Precambrian plate to sink and its surface to stand at a level 8 km beneath that of a Paleozoic plate. We first check that the weight of a crustal column is not smaller for a Precambrian crust than for a Paleozoic crust. Explosion seismology data show that isostatic equilibrium is nearly achieved in the crust. Therefore a compensating mechanism has to be acting in the subcrustal lithosphere. Two hypotheses are presented. Provided that the chemical composition of the lower lithosphere does not vary with time, a simple condition for a continental plate not to sink when aging, would be that the density of the lower lithosphere be ?0.1 g/cm³ smaller than the density of the asthenosphere. Another condition that would prevent plates to sink would be a lowering of the density of the lower lithosphere with age due for example to a variation of its chemical composition and to a reduction in the mean atomic weight. Both hypotheses imply that isostatic equilibrium of old continental plates is maintained by a geochemical mechanism. Although thermal evolution is a key factor for explaining the evolution of continents, it has to be complemented by a hypothesis on the change of the chemistry of the lower continental lithosphere with respect to the asthenosphere and/or with respect to age.     

Wind-forced continental shelf waves from a geographical origin

The response of a barotropic coastal ocean on a step-shaped continental shelf to a traveling sinusoidal wind stress forcing is predicted theoretically using a frictional force proportional to the alongshore current velocity. This theory is compared to a small set of observations from the northeast coast of Australia where a sudden widening of the continental shelf provides a geographical origin. The comparison is accomplished by means of frequency response functions relating alongshore wind stress with alongshore velocity. Amplitudes of the response functions are predicted to increase with alongshore distance equatorward and also to decrease with frequency at any location. These predictions are verified by the measurements. Predicted phase lags are generally less than about 30°, with observations agreeing with theory to within about 20°C. In general, the measurements provide reasonable evidence to support the theory of wind-forced continental shelf waves from a geographical origin.     

FURTHER DEVELOPMENT OF A HIGH-FREQUENCY SEISMIC SOURCE FOR USE IN BOREHOLES1

A borehole sparker seismic source enclosed in a semi-flexible tube has been developed to produce a short compressional seismic pulse with a frequency content in the range 250 Hz to 3.5 kHz with a peak power at 570 Hz. The pulse shape and frequency content are shown to be a function of the input power, the diameter of the spark chamber, the salinity of the electrolyte, the material of the spark chamber and the electrode configuration. When in a borehole, the source produces a vertically polarized shear wave but, being similar to a small explosive charge does not allow phase reversal as a means of identifying the shear wave in the received pulse train. The source is shown to be ideal for tomographic imaging surveys because of its repetitive nature, high frequency content and reliability. Very high resolution seismic reflection surveys are also shown to be possible under favourable circumstances.     

A stochastic integral equation analog of rainfall-runoff processes for evaluating modeling uncertainty

In this paper a very general rainfall-runoff model structure (described below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. The spatial and temporal rainfall distribution over the catchment is probabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall with respect to the rain gauge measured data. The resulting link node model structure is a series of stochastic integral equations, one equation for each subarea. A cumulative stochastic integral equation is developed as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The resulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realizations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, each outcome being the results of calibration to a known storm event.     

Babbling brook to thunderous torrent: Using sound to monitor river stage

The passive, ambient sound above the water from a river has previously untapped potential for determining flow characteristics such as stage. Measuring sub-aerial sound could provide a new, efficient way to continuously monitor river stage, without the need for in-stream infrastructure. Previous published work has suggested that there might be a relationship between sound and river stage, but the analysis has been restricted to a narrow range of flow conditions and river morphologies. We present a method to determine site suitability and the process of how to record and analyse sound. Data collected along a 500 m length of the River Washburn during July 2019 is used to determine what makes a site suitable for sound monitoring. We found that sound is controlled by roughness elements in the channel, such as a boulder or weir, which influences the sound produced. On the basis of these findings, we collect audio recordings from six sites around the northeast of England, covering a range of flow conditions and different roughness elements, since 2019. We use data from those sites collected during storms Ciara and Dennis to produce a relationship between this sound and river stage. Our analysis has shown a positive relationship between an R² of 0.73 and 0.99 in all rivers, but requires careful site selection and data processing to achieve the best results. We introduce a filter that is capable of isolating a river's sound from other environmental sound. Future work in examining the role of these roughness elements is required to understand the full extent of this technique. By demonstrating that sound can operate as a hydrometric tool, we suggest that sound monitoring could be used to provide cost-effective monitoring devices, either to detect relative change in a river or, after more research, a reliable stage measurement.     

Design and application of a direct-push vadose zone gravel permeameter

A borehole permeameter is well suited for testing saturated hydraulic conductivity (K(sat)) at specific depths in the vadose zone. Most applications of the method involve fine-grained soils that allow hand auguring of test holes and require a small water reservoir to maintain a constant head. In non-cohesive gravels, hand-dug test holes are difficult to excavate, holes are prone to collapse, and large volumes of water are necessary to maintain a constant head for the duration of the test. For coarse alluvial gravels, a direct-push steel permeameter was designed to place a slotted pipe at a specific sampling depth. Measurements can be made at successive depths at the same location. A 3790 L (1000 gallons) trailer-mounted water tank maintained a constant head in the permeameter. Head in the portable tank was measured with a pressure transducer and flow was calculated based on a volumetric rating curve. A U.S. Bureau of Reclamation analytical method was utilized to calculate K(sat). Measurements with the permeameter at a field site were similar to those reported from falling-head tests.     

A stochastic integral equation analog of rainfall-runoff processes for evaluating modeling uncertainty

In this paper a very general rainfall-runoff model structure (described below) is shown to reduce to a unit hydrograph model structure. For the general model, a multi-linear unit hydrograph approach is used to develop subarea runoff, and is coupled to a multi-linear channel flow routing method to develop a link-node rainfall-runoff model network. The spatial and temporal rainfall distribution over the catchment is probabilistically related to a known rainfall data source located in the catchment in order to account for the stochastic nature of rainfall with respect to the rain gauge measured data. The resulting link node model structure is a series of stochastic integral equations, one equation for each subarea. A cumulative stochastic integral equation is developed as a sum of the above series, and includes the complete spatial and temporal variabilities of the rainfall over the catchment. The resulting stochastic integral equation is seen to be an extension of the well-known single area unit hydrograph method, except that the model output of a runoff hydrograph is a distribution of outcomes (or realizations) when applied to problems involving prediction of storm runoff; that is, the model output is a set of probable runoff hydrographs, each outcome being the results of calibration to a known storm event.     

Computing simple models for scatterers in eddy current problems using a modal decomposition

A modal decomposition method for computing the solution to an eddy-current problem is presented. Modes are computed using the finite element method and the modes produced are simplified to a magnetic polarizability dyadic in the form of a singularity expansion. This reduced form is a very compact and easily-implemented model for the scatterer's reaction to an arbitrary magnetic field. Due to scaling properties, a single model can be applied to scatterers with different sizes and conductivities. The modal decomposition method could be used to compute a variety of parameterized simple models for canonical shapes to assist in algorithm design for clutter discrimination in buried object detection systems. The method is verified using analytically known formulas for the dyadic of a sphere and a loop. The code is then used to predict the behavior of cylinders with arbitrary conductivity and size, showing excellent agreement with a set of measured cylinders.     

A DEVICE FOR MEASURING GULLY HEADWALL MORPHOLOGY

This paper describes a low-cost device for measuring the three-dimensional morphology of a gully headwall. The device was designed to operate in a gully system with the following characteristics: overhanging banks caused by a thick, dense root mat; retreat of the underlying unconsolidated sediments through small slab failures, leading to a considerable variation in retreat rate at each point on the headwall; and changes in the orientation of the headwall owing to changes in sediment properties and the topographical and hydrological controls of gully growth. The device is used to measure a series of closely spaced vertical profiles of the headwall, and the collected data are combined to draw a contour map showing the distance from the plane of the instrument to the headwall. Comparing maps for sequential times enables retreat rates for the diffferent proportions of the headwall to be quantified.     

Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels

We present a new approach to reservoir simulation that gives accurate resolution of both large-scale and fine-scale flow patterns. The method uses a mixed multiscale finite-element method (MMsFEM) to solve the pressure equation on a coarse grid and a streamline-based technique to solve the fluid transport on a fine-scale subgrid. The MMsFEM is based on the construction of special approximation velocity spaces that are adaptive to the local properties of the differential operator. As such, MMsFEM produces a detailed subgrid velocity field that reflects the impact of the fine-scale heterogeneous structures. By combining MMsFEM with rapid streamline simulation of the fluid transport, we aim towards a numerical scheme that facilitates routine reservoir simulation of large heterogeneous geomodels without upscaling. The new method is applied to two different test cases. The first test case consists of two (strongly) heterogeneous quarter five-spot problems in 2D. The second test case is a 3D upscaling benchmark taken from the 10th SPE Comparative Solution Project, a project whose purpose is to compare and validate upscaling techniques. The test cases demonstrate that the combination of multiscale methods and streamlines is a robust and viable alternative to traditional upscaling-based reservoir simulation.     

Updating default depths in the ISC bulletin

The International Seismological Centre (ISC) publishes the definitive global bulletin of earthquake locations. In the ISC bulletin, we aim to obtain a free depth, but often this is not possible. Subsequently, the first option is to obtain a depth derived from depth phases. If depth phases are not available, we then use the reported depth from a reputable local agency. Finally, as a last resort, we set a default depth.In the past, common depths of 10, 33, or multiples of 50 km have been assigned. Assigning a more meaningful default depth, specific to a seismic region will increase the consistency of earthquake locations within the ISC bulletin and allow the ISC to publish better positions and magnitude estimates. It will also improve the association of reported secondary arrivals to corresponding seismic events.We aim to produce a global set of default depths, based on a typical depth for each area, from well-constrained events in the ISC bulletin or where depth could be constrained using a consistent set of depth phase arrivals provided by a number of different reporters.In certain areas, we must resort to using other assumptions. For these cases, we use a global crustal model (Crust2.0) to set default depths to half the thickness of the crust.     

A RESPONSE OF A RANDOMLY LAYERED EARTH TO AN ELECTRIC POINT OR DIPOLE SOURCE*

A point source or a dipole source of electric current, placed on a randomly layered semi-infinite medium, produces an inhomogeneous random potential field on the surface. The variance of the random potential, normalized with reference to the normal field (that is, a field due to a point source or a dipole source on a homogeneous medium), falls off inversely as the distance from the source. The conductivity of the layers is assumed to vary randomly about a mean value (unity) such that the variations can be represented by a zero mean homogeneous random function. Further the variations are assumed to be small compared to the mean so that the first order perturbation is adequate. The analysis shows that the dipole field is more sensitive than the single pole field to the conductivity variations.     

Analytical configurations of a force-free magnetic cylinder in the solar wind

The problem of a smooth field configuration, which should be an initial configuration in modeling (using the method of coarse particles) the problem of a stationary solar wind flow around a magnetic cloud in the case of a spatially two-dimensional statement (when a magnetic cloud is considered as a force-free magnetic cylinder with a finite radius) is considered. It has been indicated that such a statement is possible only when the magnetic field in the solar wind is parallel to the cylinder axis. The method for finding the magnetic field of a force-free cylinder with a finite radius, when some field component is specified and another component is determined based on this one (which makes it possible to construct fields with preassigned properties), has been proposed. The variant for constructing the initial field configuration in the transition region around a cylinder has been proposed. This variant makes it possible to gradually pass from homogeneous crossed fields in the solar wind to a force-free magnetic and zero electric fields within a cylinder, an electric field being potential and orthogonal to a magnetic field (in the reference system related to a magnetic cloud).     

Thermal signature of in situ soil damping under severe seismic actions

This paper gives a synthesis on a series of studies demonstrating the possibility to have a direct access to in situ soil damping, exploiting the thermal dissipation due to irreversible mechanical phenomena under severe seismic conditions. The introduction provides a background to the three steps of such a study: instrumentation, modelling and inverse identification problem. Section 2 recalls the principle of the Seismic Harmonic System, equipment able to generate powerful in situ soil accelerations in the vicinity of a well. Evidence of a significant in situ soil temperature elevation is given under such seismic conditions. Section 3 reviews the mechanical and related thermal simulations for the prediction by a direct problem procedure of the mean temperature elevation in the vicinity of the borehole, using a two- or three-parameter behaviour model depending on the intensity of the actions. Section 4 is a synthesis of the possibilities offered by thermal in situ measurements to contribute, in parallel with mechanical measurements, to the identification and/or the validation of the damping characteristics of an in situ soil.     

Constant velocity migration in the various guises of plane-wave theory

The various analytic schemes for performing a wavefield extrapolation or seismic migration from measurements upon a planar surface within a constant velocity medium are inherently related to each other. All schemes can be derived from a simple plane-wave representation of the recorded wavefield. One scheme that is very easy to conceive is based on the Radon transform. It enables one to perform a wavefield extrapolation or seismic migration by a filtered projection and a back projection of the recorded wavefield. This reveals that the theory of seismic migration as well as the theory of seismic tomography are very closely related to each other.