skip to main content


Title: Back-calculation of soil parameters from displacement-controlled cavity expansion under geostatic stress by FEM and machine learning
Abstract

Estimating soil properties from the mechanical reaction to a displacement is a common strategy, used not only in in situ soil characterization (e.g., pressuremeter and dilatometer tests) but also by biological organisms (e.g., roots, earthworms, razor clams), which sense stresses to explore the subsurface. Still, the absence of analytical solutions to predict the stress and deformation fields around cavities subject to geostatic stress, has prevented the development of characterization methods that resemble the strategies adopted by nature. We use the finite element method (FEM) to model the displacement-controlled expansion of cavities under a wide range of stress conditions and soil properties. The radial stress distribution at the cavity wall during expansion is extracted. Then, methods are proposed to prepare, transform and use such stress distributions to back-calculate the far field stresses and the mechanical parameters of the material around the cavity (Mohr-Coulomb friction angle$$\phi $$ϕ, Young’s modulusE). Results show that: (i) The initial stress distribution around the cavity can be fitted to a sum of cosines to estimate the far field stresses; (ii) By encoding the stress distribution as intensity images, in addition to certain scalar parameters, convolutional neural networks can consistently and accurately back-calculate the friction angle and Young’s modulus of the soil.

 
more » « less
NSF-PAR ID:
10372030
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Springer Science + Business Media
Date Published:
Journal Name:
Acta Geotechnica
Volume:
18
Issue:
4
ISSN:
1861-1125
Format(s):
Medium: X Size: p. 1755-1768
Size(s):
p. 1755-1768
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Analog quantum simulators rely on programmable and scalable quantum devices to emulate Hamiltonians describing various physical phenomenon. Photonic coupled cavity arrays are a promising alternative platform for realizing such simulators, due to their potential for scalability, small size, and high-temperature operability. However, programmability and nonlinearity in photonic cavities remain outstanding challenges. Here, using a silicon photonic coupled cavity array made up of$$8$$8high quality factor ($$Q$$Qup to$$\, \sim 7.1\times {10}^{4}$$~7.1×104) resonators and equipped with specially designed thermo-optic island heaters for independent control of cavities, we demonstrate a programmable photonic cavity array in the telecom regime, implementing tight-binding Hamiltonians with access to the full eigenenergy spectrum. We report a$$\sim 50\%$$~50%reduction in the thermal crosstalk between neighboring sites of the cavity array compared to traditional heaters, and then present a control scheme to program the cavity array to a given tight-binding Hamiltonian. The ability to independently program high-Q photonic cavities, along with the compatibility of silicon photonics to high volume manufacturing opens new opportunities for scalable quantum simulation using telecom regime infrared photons.

     
    more » « less
  2. Abstract

    We propose a new observable for the measurement of the forward–backward asymmetry$$(A_{FB})$$(AFB)in Drell–Yan lepton production. At hadron colliders, the$$A_{FB}$$AFBdistribution is sensitive to both the electroweak (EW) fundamental parameter$$\sin ^{2} \theta _{W}$$sin2θW, the weak mixing angle, and the parton distribution functions (PDFs). Hence, the determination of$$\sin ^{2} \theta _{W}$$sin2θWand the updating of PDFs by directly using the same$$A_{FB}$$AFBspectrum are strongly correlated. This correlation would introduce large bias or uncertainty into both precise measurements of EW and PDF sectors. In this article, we show that the sensitivity of$$A_{FB}$$AFBon$$\sin ^{2} \theta _{W}$$sin2θWis dominated by its average value around theZpole region, while the shape (or gradient) of the$$A_{FB}$$AFBspectrum is insensitive to$$\sin ^{2} \theta _{W}$$sin2θWand contains important information on the PDF modeling. Accordingly, a new observable related to the gradient of the spectrum is introduced, and demonstrated to be able to significantly reduce the potential bias on the determination of$$\sin ^{2} \theta _{W}$$sin2θWwhen updating the PDFs using the same$$A_{FB}$$AFBdata.

     
    more » « less
  3. Abstract

    The crystal structure and bonding environment of K2Ca(CO3)2bütschliite were probed under isothermal compression via Raman spectroscopy to 95 GPa and single crystal and powder X-ray diffraction to 12 and 68 GPa, respectively. A second order Birch-Murnaghan equation of state fit to the X-ray data yields a bulk modulus,$${K}_{0}=46.9$$K0=46.9GPa with an imposed value of$${K}_{0}^{\prime}= 4$$K0=4for the ambient pressure phase. Compression of bütschliite is highly anisotropic, with contraction along thec-axis accounting for most of the volume change. Bütschliite undergoes a phase transition to a monoclinicC2/mstructure at around 6 GPa, mirroring polymorphism within isostructural borates. A fit to the compression data of the monoclinic phase yields$${V}_{0}=322.2$$V0=322.2 Å3$$,$$,$${K}_{0}=24.8$$K0=24.8GPa and$${K}_{0}^{\prime}=4.0$$K0=4.0using a third order fit; the ability to access different compression mechanisms gives rise to a more compressible material than the low-pressure phase. In particular, compression of theC2/mphase involves interlayer displacement and twisting of the [CO3] units, and an increase in coordination number of the K+ion. Three more phase transitions, at ~ 28, 34, and 37 GPa occur based on the Raman spectra and powder diffraction data: these give rise to new [CO3] bonding environments within the structure.

     
    more » « less
  4. Abstract

    $$B^\pm \rightarrow DK^\pm $$B±DK±transitions are known to provide theoretically clean information about the CKM angle$$\gamma $$γ, with the most precise available methods exploiting the cascade decay of the neutralDintoCPself-conjugate states. Such analyses currently require binning in theDdecay Dalitz plot, while a recently proposed method replaces this binning with the truncation of a Fourier series expansion. In this paper, we present a proof of principle of a novel alternative to these two methods, in which no approximations at the level of the data representation are required. In particular, our new strategy makes no assumptions about the amplitude and strong phase variation over the Dalitz plot. This comes at the cost of a degree of ambiguity in the choice of test statistic quantifying the compatibility of the data with a given value of$$\gamma $$γ, with improved choices of test statistic yielding higher sensitivity. While our current proof-of-principle implementation does not demonstrate optimal sensitivity to$$\gamma $$γ, its conceptually novel approach opens the door to new strategies for$$\gamma $$γextraction. More studies are required to see if these can be competitive with the existing methods.

     
    more » « less
  5. Abstract

    We consider the spectrum of random Laplacian matrices of the form$$L_n=A_n-D_n$$Ln=An-Dnwhere$$A_n$$Anis a real symmetric random matrix and$$D_n$$Dnis a diagonal matrix whose entries are equal to the corresponding row sums of$$A_n$$An. If$$A_n$$Anis a Wigner matrix with entries in the domain of attraction of a Gaussian distribution, the empirical spectral measure of$$L_n$$Lnis known to converge to the free convolution of a semicircle distribution and a standard real Gaussian distribution. We consider real symmetric random matrices$$A_n$$Anwith independent entries (up to symmetry) whose row sums converge to a purely non-Gaussian infinitely divisible distribution, which fall into the class of Lévy–Khintchine random matrices first introduced by Jung [Trans Am Math Soc,370, (2018)]. Our main result shows that the empirical spectral measure of$$L_n$$Lnconverges almost surely to a deterministic limit. A key step in the proof is to use the purely non-Gaussian nature of the row sums to build a random operator to which$$L_n$$Lnconverges in an appropriate sense. This operator leads to a recursive distributional equation uniquely describing the Stieltjes transform of the limiting empirical spectral measure.

     
    more » « less