Showing papers on "Slab published in 1988"

Controls of the structure of subducted slabs

Abstract: Numerical simulations of subducting slabs are formulated in which the shape and dip of the slab are determined by the dynamics of the flow, rather than imposed a priori. The dip of slabs is a function of the time since the initiation of subduction. Slabs fold, develop a kink in dip, and thicken on entry into a high-viscosity lower mantle. Comparison of the simulations with seismic observations suggest that the lower mantle is at least 10–30 times more viscous than the upper mantle.

Tectonic and magmatic transitions in the Western Great Basin, USA

Abstract: The isotope and trace-element geochemistry of late Cenozoic basalts from the Western Great Basin of California and Nevada demonstrates contributions from two distinct mantle source regions. High concentrations of large-ion lithophile relative to high-field strength elements (50 < Ba/Nb < 250) are often taken to reflect a contribution from contemporaneous subduction processes. But in this area they are associated with a marked change in 87Sr/86Sr and 143Nd/144Nd across a major lithospheric boundary, which is normal to the orientation of the palaeo-subduction zone and implies that these samples derived their isotope and trace element signatures from the mantle lithosphere. The second component is similar to that seen in ocean island basalts, and is attributed to asthenospheric source regions within the convecting upper mantle. Significantly, the onset of asthenosphere dominated magmatism migrated northwards during the Plio-Pleistocene about 2–3 Myr behind the trailing edge of the subducted slab. During this period it is proposed that asthenospheric diapirs rose from the level of the subducted slab into the zone of melt generation, implying ascent rates of between 5 and 8 cm per annum.

Plastic instabilities: Implications for the origin of intermediate and deep focus earthquakes

Abstract: Adiabatic or catastrophic plastic shear has been reported in metals, polymers, and metallic glasses. The phenomenon is associated with rapid stress drops and audible pings or clicks as the material deforms in a plastic manner. The driving force for the plastic instability is the stored elastic strain energy of the loading system, and in many respects the behavior is reminiscent of the shear stress response arising from stick slip events during unstable frictional sliding, although the precise mechanism is different. It is shown here that adiabatic plastic shear is capable of explaining the detailed distribution of intermediate and deep focus earthquakes within subduction zones, the earthquake events being the result of instabilities in material undergoing plastic flow. It is argued that for a particular strain rate there exists a critical temperature, TC, which is depth dependent; for temperatures below TC the material is strain rate softening and, for a soft enough loading system, may undergo catastrophic plastic shear. For temperatures above TC the material is strain rate hardening and is always stable during plastic shear. The cutoff depth for deep focus earthquakes then corresponds to the transition from strain rate softening to strain rate hardening material, and for commonly accepted geothermal gradients within the slab corresponds to approximately 800 km. The precise distribution of earthquakes within the slab is a function of the subtle interplay between the geothermal gradient and the TC gradient. In particular, a decrease in seismic activity is to be expected below about 300 km in the slab with total stress drops decreasing from a maximum of 700 MPa above 300 km to a maximum of ≈ 50 MPa below 300 km. The differences in foci distribution between subduction zones such as Tonga, New Hebrides, and Peru result from minor differences in the geothermal gradients within the slabs. The model predicts the development of triple seismic zones high in the slab, double seismic zones down to approximately 300 km, and single seismic zones down to ≈ 800 km. Such a distribution is to be expected of relatively young, cool slabs; as the slab heats up, the seismic activity retreats up the slab. The paper only proposes a deformation mechanism for earthquake generation, it does not address the stress field within the slab but only the distribution of strength. Thus the distribution of focal plane mechanisms is not considered, only the locations where earthquakes due to plastic instabilities are possible. The absence of earthquakes does not necessarily mean that the slab does not exist, it only means that the slab is too hot to undergo plastic instability. This means that aseismic subduction is a distinct possibility in many regions of high geothermal gradient within the slab (i.e. > circa 3°C km−1).

Stress Transfer and Seismic Phenomena in Coupled Subduction Zones During the Earthquake Cycle

Abstract: An elementary mechanical model of a coupled subduction zone is presented. It is used to study the transfer of extensional stresses along the underthrusting plate, and shear stress interactions between the plate itself and its thrust contact zone with the overriding plate, during the earthquake cycle. The model assumes an elastic plate which deforms one dimensionally, has shear drag interactions (treated approximately by the Elsasser procedure) with a Maxwellian viscoelastic mantle, and is subject to steady gravitational sinking forces. Great thrust earthquakes are simulated as sudden stress-relieving displacements at the contact zone between the slab and overriding plate. The model allows analysis of the space- and time-variable stresses in the main thrust zone, the adjacent oceanic plate, and the subducting slab over each earthquake cycle. Stress variations leading to outer-rise events are discussed, as well as stress changes responsible for intraplate seismicity downdip from the main thrust zone, based on simulations of periodic great earthquakes. The results of simulated slow progression of deformation (slip) from below into the thrust contact zone are also presented. Such preslip, occurring over a time scale that is small in comparison with the whole seismic cycle (e.g., of the order of a tenth or so), is shown to transiently slow the rate of buildup of, or even relieve, extensional stresses in the slab. In the absence of preslip those stresses build up steadily in time during the latter part of the cycle. The results have implications for induction of sesimic quiescence as well as for explaining patterns of seismicity in relation to spatial position along the underthrusting plate and to time throughout the cycle. Correlations are reported between the model simulations and seismicity observations from coupled subduction zones around the world. The observations include tensional outer-rise events after large subduction earthquakes and compressional ones in the latter parts of the cycle, normal (tensional) intraplate earthquakes preceding the main thrust events and positioned downdip from the thrust zones, and interlaced periods of seismic activity in the lower part of the main thrust zone and in the descending slab.

Reinforced Concrete Fundamentals

Abstract: Introduction. Materials. Flexural Analysis and Serviceability of Beams. Design for Flexure. Shear and Torsion. Axial Load Plus Bending--Short Columns. Slender Columns. Development and Slicing of Reinforcement. Continuous Beams and One-Way Slabs. Detailing of Joints. Limit Design. Two-Way Slabs on Stiff Beams. Yield Line Theory for Slabs. Strip Method for Slab Design. Flat Plates and Flat Slabs. Interaction of Two-Way Slab Systems with Beams and Columns. Distribution of Concentrated Loads and Other Special Problems. Cantilever Retaining Wall Design. Footings. Prestressed Concrete Analysis. Composite Beams. Shear Walls. Detailing for Seismic Resistance. Appendices. Index.

Insulated concrete building panels and method of making the same

Abstract: A three-layer insulated concrete panel includes as the middle layer an insulating slab having grooves which provide a form for casting of concrete supporting ribs integral with a layer of concrete cast over the grooved face. A layer of material, such as particle board, is bonded to the ungrooved face of the slab. In preparing the panel, the slab is placed on a flat surface with the particle board face down. Forms are then placed in spaced-apart relation to panel edges, and concrete is cast into the forms and grooves and over the grooved panel face. The insulating slab provides a form for casting of supporting ribs and is permanently retained in the panel, giving it a high insulating value.

Tomographic image of the Juan de Fuca Plate beneath Washington and western Oregon using teleseismic P‐wave travel times

Abstract: Backprojection tomography is applied to teleseismic P-wave travel-time residuals to produce a detailed image of the upper mantle beneath Washington and western Oregon. Beneath the Cascades volcanic arc from central Oregon to central Washington the subducted Juan de Fuca plate is imaged as a high-velocity quasi-planar feature dipping ∼65°E. Resolution analysis shows that beneath southern Washington, where resolution is best, the steeply dipping slab extends to a depth of only about 300 km. The slab may end near this depth, or low-velocity structure in the vicinity of the slab or a shallowing of the slab dip may produce this result. Beneath Oregon, where resolution is poor, the slab extends steeply into the mantle to at least 150 km depth. The uppermost mantle beneath northeastern Washington is high in velocity, preventing the resolution of the slab geometry there.

Subduction zone earthquakes and stress in slabs

Abstract: The pattern of seismicity as a function of depth in the world, and the orientation of stress axes of deep and intermediate earthquakes, are explained using viscous fluid models of subducting slabs, with a barrier in the mantle at 670 km. 670 km is the depth of a seismic discontinuity, and also the depth below which earthquakes do not occur. The barrier in the models can be a viscosity increase of an order of magnitude or more, or a chemical discontinuity where vertical velocity is zero. LongN versus depth, whereN is the number of earthquakes, shows (1) a linear decrease to about 250–300 km depth, (2) a minimum near that depth, and (3) an increase thereafter. Stress magnitude in a subducting slab versus depth, for a wide variety of models, shows the same pattern. Since there is some experimental evidence thatN is proportional toeκσ, where κ is a constant and σ is the stress magnitude, the agreement is encouraging. In addition, the models predict down-dip compression in the slab at depths below 400 km. This has been observed in earlier studies of earthquake stress axes, and we have confirmed it via a survey of events occurring since 1977 which have been analysed by moment tensor inversion. At intermediate depths, the models predict an approximate but not precise state of down-dip tension when the slab is dipping. The observations do not show an unambiguous state of down-dip tension at intermediate depths, but in the majority of regions the state of stress is decidedly closer to down-dip tension than it is to down-dip compression. Chemical discontinuities above 670 km, or phase transitions with an elevation of the boundary in the slab, predict, when incorporated into the models, stress peaks which are not mirrored in the profile of seismicity versus depth. Models with an asthenosphere and mesosphere of appropriate viscosity can not only explain the state of stress observed in double Benioff zones, but also yield stress magnitude profiles consistent with observed seismicity. Models where a nonlinear rheology is used are qualitatively consistent with the linear models.

Seismic constraints on the morphology of deep slabs

Abstract: Residual sphere images from deep earthquakes not only detect the presence of slab-associated velocity anomalies but also lend insight into the flow and deformation of lithosphere subducted into the lower mantle. We have compared travel times from deep events in the Kuril and Mariana arcs with the seismic velocity anomalies implied by kinematical models that thicken the slab perpendicular to its plane by reducing the vertical velocity of the flow with depth. We assume that the details of the deformation (whether the slab buckles, imbricates, fragments, etc.) are averaged out along the ray paths, and hence our models constrain the scale, not the mode, of slab thickening. The deep event travel times are best fit by undeformed models, but the ability of the residual sphere method to resolve slab thickness is limited by ray bending effects. Although the Mariana times are consistent with advective thickening factors of 5 or more, factors larger than 3 are ruled out by the Kuril data. For all models examined, the data require that slab material extends to depths of 900–1000 km. Global tomographic models and regional studies which delineate high-velocity anomalies in the lower mantle beneath zones of Cenozoic subduction are consistent with our results, as is recent work on pulse distortion by slab gradients. Comparison of observed and predicted rates of seismic moment release suggests that if substantial advective thickening does occur, it is largely aseismic.

Experimental studies of magnetically scannable leaky-wave antennas having a corrugated ferrite slab/dielectric layer structure

Abstract: The radiation characteristics of a magnetically scannable leaky-wave antenna using a corrugated ferrite slab supported by a Teflon waveguide have been demonstrated experimentally. A corrugated polycrystalline yttrium iron garnet (YIG) slab having the dimensions 150.0 mm*15.0 mm*10 mm has been fabricated. The corrugation depth, corrugation spacing, and number of corrugations are 150.0 mu m, 2.0 mm, and 55.0, respectively. Experiments have been carried out in the millimeter-wave frequency range from 40.0 to 50.0 GHz. The main beam direction of the leaky wave shifts continuously about 41.0 degrees at the operating frequency 46.8 GHz by altering the DC magnetic field up to 1.4 T. It is found that the corresponding half-power beamwidth varies from 3.2 degrees to 3.6 degrees and a maximum scanning rate is 1.0 degrees /0.02 T. Experimental results are compared with theory based on the dispersion relation of the ferrite slab/dielectric layer structure. >

Uplift Load‐Displacement Behavior of Spread Foundations

Abstract: The design of spread foundations for uplift loads is based primarily on capacity considerations, largely because there has been only a limited effort to characterize the load‐displacement response of these foundations. This paper examines the results of 75 full‐scale field tests and synthesizes the results in a convenient design procedure that incorporates estimated displacements. The effects of soil type (granular versus cohesive) and foundation type (steel grillage versus concrete slab or steel plate) are investigated, and it is found that: (1) Granular soils lead to a slightly stiffer response than cohesive soils in the initial portion of the load‐displacement curve; and (2) slab or plate foundations lead to slightly stiffer response than grillages for granular soils only. The type of foundation has little influence for cohesive soils, and for practical purposes, a single generalized load‐displacement relationship can be used to represent the available data for all four cases at the 95% confidence level.

Finite-element formalism for nonlinear slab-guided waves

Abstract: A unified computer-aided numerical approach, based on the finite-element method, is developed for analyzing optical waves guided by dielectric slab waveguiding structures with arbitrary nonlinear media. In the formulations, both TE and TM polarizations are considered. For the TM case, the biaxial nature of nonlinear refractive index is considered without any approximation. Numerical results are presented for nonlinear TE and TM waves propagating in symmetric slab waveguides. The dependence of dispersion relations on the refractive-index profile of the film is examined. >

The 3-D shear wave structure in the mantle by overtone waveform inversion-II. Inversion of X-waves, R-waves and G-waves

Abstract: SUMMARY The 3-D upper-mantle structure from the surface of the Earth to a depth of about 1000 km is obtained by inverting waveforms of fundamental and higher-mode surface waves. Minor- and major-arc waves of R-waves, G-waves and X-waves (higher-mode wave packets) are used as basic data. Two features of the solution seem fairly robust; one is the shallow structure in the upper few hundred kilometres which is strongly correlated with the age of the crust. The second feature is the deep fast-velocity anomaly near the western Pacific (Indonesia, Philippines and Mariana) region and its antipodal region of South America, both of which are subduction zones, which forms a strong l= 2 pattern. Simple slab models with 100 km thicknesses of 10 per cent faster-velocity material do not explain such large-scale fast-velocity anomalies. This may indicate large-scale deformation of the 670 km discontinuity, piling up of slabs in the upper mantle or thickening lithosphere in the lower mantle or large horizontal motions of subducted material. These results are stable whether an earth model 1066A or PREM is used as a starting model.

Subduction Zone Seismicity and the Thermo-Mechanical Evolution of Downgoing Lithosphere

Abstract: In this paper we discuss characteristic features of subduction zone seismicity at depths between about 100 km and 700 km, with emphasis on the role of temperature and rheology in controlling the deformation of, and the seismic energy release in downgoing lithosphere. This is done in two steps. After a brief review of earlier developments, we first show that the depth distribution of hypocentres at depths between 100 km and 700 km in subducted lithosphere can be explained by a model in which seismic activity is confined to those parts of the slab which have temperatures below a depth-dependent critical valueTcr.

Characterization of high average power Nd:GGG slab lasers

Abstract: Performance characteristics of zig-zag optical path Nd:GGG slab lasers are reported. The sizes of the crystals are 6/sup t/ mm*10/sup w/ mm*100/sup l/ mm and 10/sup t/ mm*18/sup w/*167/sup l/ mm. These crystal slabs were polished with surface flatness of lambda /5 ( lambda =6328 AA), surface roughness of 8 AA rms, and surface parallelism of 10 s. In normal model oscillation, average output powers of 45 W were obtained with the smaller slab and 145 W with the larger slab. In Q-switched operation, an average output power of 11 W has been obtained, with a pulse width of 10 ns and repetition rate of 20 Hz. Long operating life has been also achieved by suppressing solarization of the Nd:GGG crystal with UV-cutoff filters placed in the pumping cavity. >

Transportation of beryllium with H2O at high pressures: Implication for magma genesis in subduction zones

Abstract: The degree of transportation of beryllium with H2O is measured under the upper mantle P/T conditions in order to examine the incorporation of 10Be in subduction zone magmas. 5.4±0.3% of original beryllium in the starting serpentinite is extracted with H2O from the system through the dehydration reaction of serpentine at 850°C and 1.5 GPa. It follows that the partial melting of oceanic lithosphere including 10Be-rich sediment layer is not necessarily required for inclusion of the isotope in island-arc lavas. We suggest that the dehydration processes in the subducted slab and mantle wedge materials dragged downward by the slab subduction govern the concentration of 10Be in arc lavas.

The horizontally lying slab

Abstract: An unusual earthquake (mb=6.2) occurred in the Izu-Bonin Island region in July 1982. The event, occurring at a depth of 545 km, was clearly separated from the main inclined seismic zone by a distance of about 200 km. To diagnose the situation, we have considered two possibilities: 1) the event might be an unusual event in the sense that its location is unrelated to the position of the subducted slab and that there is probably no slab around it, or 2) the slab, at this depth, might be lying horizontally on top of the 650 km discontinuity, and the unusual event occurred in this horizontal part. Both possibilities have been modeled structurally. We have computed the P-wave travel times for the present event, as well as for two other events located unambiguously in the inclined part of the seismic zone by employing a 3-D ray tracing program. The computed travel time residuals have been compared with the observations at stations in western Japan. The observations are found to be consistent with the model of the horizontally lying slab. Our result, thus, suggests that the slab might be horizontal at this depth in this part of the Izu-Bonin Islands.

A nonlinear analysis of convection in a porous vertical slab

Abstract: In 1969 A. E. Gill showed that convection in a porous vertical slab is not possible when the temperature difference is maintained across the layer. He attributed this to the lack of fluid inertia in Darcy's law and based his arguments on two-dimensional linear stability theory. We readdress the Gill problem but by using integral inequality estimates on the full three-dimensional nonlinear theory. We again find there is always stability, but now provided the initial data are less than a threshold which is proportional to the inverse of the Rayleigh number. Of course, this is in complete agreement with the result of Gill, although we believe it adds insight into the physical situation.

Shallow and Intermediate-Depth Seismicity in the New Hebrides Arc: Constraints on the Subduction Process

Abstract: Teleseismically located earthquakes in the New Hebrides Arc are unevenly distributed along the length of the subduction zone. Shallow seismicity near the plate boundary fits a static model of plate interaction along an interface with varying degrees of coupling between overriding and subducting plates. This interpretation is sup- ported by striking differences in source radiation from earthquakes occurring in different parts of the plate boun- dary, and by systematic along-strike variations in forearc morphology. The irregular distribution of intermediate-depth seismicity can be considered from two opposing points of view: one assuming a continuous or relatively uniform subducted slab; the other invoking an irregular, possibly discontinuous slab. At the northern and southern ends of the Neiv Hebrides Arc, abrupt changes in the length of the inclined seismic zone coincide with structural and geophysical discontinuities in the subduction zone; a recent elongation of a previously shorter island arc northward and southward could explain many of these obser- vations. In cross section, the intermediate-depth events define a spoon-shaped profile, with a nearly vertical plunge from 100 to 200 km depth and a gentler GO The disrupted morphology and seismicity of the central Neiv Hebrides Arc is also considered using both the uniform and non-uniform lithosphere models. Although the tectonic complexity at depth may imply disruption of the subducted lithosphere, the present subduction of the D'Entrecasteaux fracture zone plays a dominant role in the shallow deformation of this portion of the island arc. dip below that.

Temperature control of a solid state face pumped laser slab by an active siderail

Abstract: Optical and thermal distortion in a solid state slab geometry laser are controlled by active siderails disposed at the lateral surfaces of the slab. Each siderail may have a fluid passage therethrough and be connected in a separate fluid circuit which enables the volumetric flow rate and temperature of the fluid through the passageway to be controlled in order to control the temperature of the siderail and, accordingly, the temperature of the slab in regions proximate to the siderail. The invention enables compensation of asymmetric transverse gradients to afford a uniform transverse temperature distribution.

Electromagnetic interactions with an anisotropic slab

Abstract: An exact theory is developed for fields due to currents in the presence of an anisotropic slab. The anisotropy is of a type expected of a composite reinforced with unidirectional fiber and is described by a diagonal matrix in Maxwell's equations. A Green's matrix is defined with exact and explicitly computed solutions to Maxwell's equations for point currents. The Green's matrix reduces to quadrature the problems, in frequency and time domains, of computing the field produced inside and outside a slab by arbitrary current sources. Steady-state AC current sheets and loops are considered, and numerical results are presented. >

Laser with improved cooling system

Abstract: A laser has a slab in which the beam F is propagated in zig-zag manner between two opposing faces which have the property of ensuring total reflection. For this purpose each of these faces is covered with a solid layer of a good heat conducting material and having a refractive index below that of the slab. Its thickness is preferably greater than three times the operating wavelength of the laser. Thus, a cooling fluid can be in contact with the solid layer to effectively cool the slab. Pumped energy sources are preferably provided opposite the layers.

Web Openings in Composite Beams with Ribbed Slabs

Abstract: Fifteen tests to failure are performed on full-scale composite beams with web openings. The beams have ribbed slabs that use formed deck steel. The ribs are perpendicular or parallel to the steel section. The effects of moment-shear ratio, quantity, and placement of shear connectors, deck orientation, and deck thickness are studied. The concrete slab contributes significantly to both the flexural and shear strength of beams at web openings. Peak loads are governed by failure of the slab. Rib failure around shear connectors occurs in slabs with transverse ribs, while longitudinal shear failure occurs in slabs with longitudinal ribs. Strength at an opening increases as the shear-connector capacity above the opening and between the opening and the support increases. The implications for design are discussed.

Thermal response of a laser‐irradiated metal slab

Abstract: The analytical solution of temperature profiles in complex laser‐heated structures is only possible for a few simple cases This is partly due to the nature of heat‐source terms that preclude the use of conventional series‐type solutions In this study we utilize a Laplace‐transform method in conjunction with Fourier integrals to obtain solutions for the temperature profiles in a laser‐irradiated rare‐earth–transition‐metal slab The results provide a convenient qualitative tool to study the thermal response of laser‐irradiated solids

Seismic observation of a high‐velocity slab 1200–1600 km in depth

Abstract: A slablike high-velocity region 1200–1600 km beneath the east coast of North America apparently has a half-width of 450 km and a lateral extent of 3000 km and a depth extent of more than 800 km. This slab lies beneath the boundary where the Farallon Plate had been subducting for up to 120 MA. The high-velocity anomaly has been inferred previously from travel-time studies; this study uses body-waveforms to verify and refine its structure. The anomalous region has a peak shear wave velocity 1.5% greater than the surrounding region and compressional velocity 0.6% greater. The width and smoothness of this anomaly is constrained by the complexity observed in SH waveforms from deep earthquakes beneath South America observed at GDSN stations in North America. This slab is about 5 times broader and 5 times weaker in its velocity anomaly than most slabs observed in the upper mantle. This observation implies that if this slab has passed through the 650 km discontinuity, which is the most likely explanation for the observation, it has been spread by more than simply thermal conductivity. The possibility that there is two-layer convection with thermal coupling is not ruled out, however, as thermal coupling could lead to a similar pattern.

Is subducted lithosphere trapped at the 670-km discontinuity?

Abstract: Recent work1,2 on phase equilibria has shown that subducted oceanic lithosphere, which is differentiated into a basaltic crust and a harzburgitic residue layer, could be significantly denser than undifferentiated peridotite at depths between 650 and 700 km, but would be less dense in the range 700-740 km. It might thus be trapped in a gravitational!) stable layer between upper and lower mantle3. Here, using numerical experiments of isoviscous convec-tion, I explore the stability of such a layer, assuming that it had previously been formed. The results suggest that the survival of the intermediate layer is at best marginally feasible, provided that new subducted lithosphere is efficiently trapped.

Heat loss to the ground from a building : slab on the ground and cellar

Abstract: Heated buildings induce a heat flow from the building foundation into the ground. The topic of this thesis is the thermal process in the ground and, in particular, the heat losses from the building to the ground. Foundations of the three types slab on the ground, cellar, and crawl-space are dealt with. The crawl-space is treated in separate report. A reasonably complete theory for the thermal processes, and in particular the heat loss, is expounded. Dimensionless formulation, superposition technique, and analytical solutions for basic periodic and step-response components are used. The three-dimensional, steady-state heat loss component is obtained from numerical solutions. An accurate and manageable calculation method for heat losses to the ground has been developed. The method, which is based on both numerical calculations and analytical solutions, accounts for three-dimensional effects and the time-varying outdoor temperature in a proper way. The results from eight reports are used in the thesis: 1. Heat loss at the edge of a thermally insulated slab on the ground. Wiener- Hopf solution for periodic and step-change air temperature. Hagentoft C-E, Claesson J, Wallin N-0, 1985. 2. Temperature under a totally insulated slab on the ground due to variable ground surface temperature. Hagentoft, 1985. 3. Heat loss and temperature for a cellar of infinite depth. Periodic and step change air temperature. Hagentoft C-E, 1987. 4. Steady- state ground temperature and heat loss for a thermally insulated slab on the ground. Equal insulation thickness outside and inside the house. Hagentoft C-E, 1987. 5. Semi-analytical method for the temperature in the ground under a house with variable insulation thickness. Hagentoft C- E 1987. (Accepted for publication in International Journal of Building Science and its Applications.) 6. Analytical solution for the steady-state temperature in the ground at the edge of an insulaled cellar. Hagentoft C-E, 1987. 7. PC-program: Design rules for the slab on the ground and the cellar. Hagentoft C-E, 1988. 8. An analytical model for crawl-analytical model for crawl-space temperatures and heat flows. Steady-state, periodic and step-response components, Hagentoft C-E, 1986