Characteristic roots of the truncated inhomogeneous shear beam

Roots \(a_n\) of the characteristic equation of Dakoulas and Gazetas (1985), a shear beam whose modulus grows with depth as a power law of exponent \(m\) and whose crest truncates the full wedge at the ratio \(\lambda\). Every root is solved in R at its node of the grid by the exact method of buildRootModel() (data-raw/CylinderRoots.R, recorded in data-raw/README.md). The grid, modes 1 to 8 with \(m\) from 0 to 0.95 in steps of 0.005 and \(\lambda\) from 0 to 0.5 in steps of 0.0025, is that of the tables of newmark 1.7.1, computed with Mathematica. The surrogates of buildRootModel() are fitted to this table.

Usage

CylinderRoots

Format

A data.table with 307128 rows and 4 variables, ordered by n, m and l:

n

Integer: mode number, 1 to 8.

m

Double: inhomogeneity exponent, 0 to 0.95.

l

Double: truncation ratio, 0 to 0.5.

an

Double: characteristic root of mode n.

Source

Dakoulas, P. and Gazetas, G. (1985). A class of inhomogeneous shear models for seismic response of dams and embankments. Soil Dynamics and Earthquake Engineering 4(4), 166-182.