Legacy · Mechanical validation · §8.4

Hiramatsu–Oka (3D borehole)

Hole of radius $a$ in an infinite medium under remote stresses — Hiramatsu and Oka (1962); matrix form of Ruggeri and Gomes (2013). §8.4. Constant mechanical loading ( $\Delta T=0$ ): stresses do not creep; strains grow with $E(z_0)J(t,z_0)$ (Zhu’s Theorem I).

Article: Part I · DOI 10.70271/rirc.v1n2a007

Material (strains in time): Itumbiara

Source report (subscribers)

Matrix $[M]$ was rewritten from:

Ruggeri, N.; Gomes, F. M. P. Tensões “In Situ” em Maciços Rochosos — Relatório Final R0-1, 2013.

Erratum: $m_{56}$ — the report states $m_{56}=+0.5\,(1+2\eta^{2}-3\eta^{4})\cos(2\theta)$ ; the correct form is $m_{56}=(1+2\eta^{2}-3\eta^{4})\cos(2\theta)$ .

Schematic

Data sheet (article)

Item	Value
Hole radius	$a=1.5\,\mathrm{m}$
$\nu$	$0.20$
Remote tensor (MPa)	$\sigma_x^{\infty}=-2.0$ , $\sigma_y^{\infty}=-1.2$ , $\sigma_z^{\infty}=-3.0$ ; $\tau_{yz}^{\infty}=0.4$ , $\tau_{zx}^{\infty}=-0.5$ , $\tau_{xy}^{\infty}=0.8$
Opening age	$z_0=28\,\mathrm{d}$
Material (strain)	Rheological Itumbiara

Input files

ref_hiramatsu_params.csv — $a$ , $\nu$ , remote tensor, $z_0$
Material: Itumbiara — $J(t,28\,\mathrm{d})$

Output figures

Output files

File	Content
ref_hiramatsu_parede.csv	On the wall ( $\eta=1$ ): $\sigma_\theta$ , $\sigma_\zeta$ , $\tau_{\theta\zeta}$ vs $\theta$
ref_hiramatsu_campo_sigma_theta.csv	$\sigma_\theta(r,\theta)$ in the cross-section plane
ref_hiramatsu_eps_parede.csv	$\varepsilon_\theta(t)$ , $\varepsilon_r(t)$ at the point of max. $\lvert\sigma_\theta\rvert$ on the wall ( $z_0=28\,\mathrm{d}$ )
ref_hiramatsu_pontos_controle.csv	Checks (boundary, peak, equilibrium)

Code: hiramatsu_oka.py — M_matrix, field, creep_response, rosette_* (package).