Vol. 1, No. 2 · Manuscript (English)

An incremental creep-compliance formulation for aging concrete and thermally induced stresses in mass concrete — Part I: analytical–numerical validation

Flávio Mamede Pereira Gomes; Flávio Vasconcelos Souza

This paper presents Part I — analytical–numerical — of the validation of a viscoelastic constitutive model: an incremental formulation convenient when starting from the creep compliance J ( t , z ), with exact treatment of the initial stress step, the decomposition η n + q n [ V ]Δ σ n , and a verification battery (benchmark ladder) as a contribution in its own right, applied to thermally induced stresses in mass-concrete structures. The approach stands in the lineage of Bažant and Wu (1973); Liang et al. (2022) apply the same rate-type core in a TCM–learning setting, without a constitutive reformulation. It is distinguished by the anchor in J with Zocher et al.’s strategy, by the exact treatment of the initial step, and by the hierarchy of analytical–numerical checks. The starting point is the creep compliance obtained directly from tests (or from a rheological model fitted to it). Unlike the classical viscoelastic formulation of Zocher, Groves and Allen (1997), based on the relaxation moduli and without explicit aging, the present derivation operates on the creep compliance with aging, written as a Dirichlet–Prony series with coefficients that depend on the loading age. The strategy leads to a recursive algorithm in which the creep-strain increment at each time step separates into a known hereditary part and a part proportional to the current stress increment. The aging viscoelastic problem thus reduces, at each step, to an equivalent elastic problem suitable for finite-element implementation. The formulation is validated on analytical–numerical problems (in the manner of Zhu Bofang (2014) and Zocher et al. (1997), plane problems and a restrained slab). The numerical–experimental validation on site (VET / Santo Antônio HPP) is the subject of Part II.

Keywords: mass concrete, creep with aging, thermal stresses, viscoelasticity, finite elements, analytical–numerical validation

How to cite

English manuscript — not published. Please cite the Portuguese article: GOMES, Flávio Mamede Pereira; SOUZA, Flávio Vasconcelos. Formulação incremental a partir da função de fluência para concreto com envelhecimento e tensões de origem térmica no concreto massa — Parte I: validação analítico-numérica. Revista do Instituto Roy Carlson, v. 1, n. 2, 2026. https://institutoroycarlson.org/revista/edicoes/v1n2/artigos/calculo-tensoes-origem-termica-fm.html.