## 1. Introduction

[2] Time-dependent healing of frictional strength [e.g., *Dieterich*, 1972] is one of the key mechanisms that govern earthquake cycles. It is also a cornerstone of rate and state friction laws, which have been successfully applied to explain a wide spectrum of earthquake phenomena [e.g., *Scholz*, 1998]. In the laboratory, many classes of materials [e.g., *Rabinowicz*, 1965] including rocks [e.g., *Dieterich*, 1972; *Beeler et al.*, 1994; *Nakatani and Mochizuki*, 1996] show that frictional strength μ increases linearly with the logarithm of quasi-stationary contact time *t*:

Here, μ_{0} is the frictional strength at the beginning of stationary contact and in slide-hold-slide tests may be evaluated as the sliding friction in the slide period prior to the hold. In addition to the healing phenomena due to solid-state deformation of contact asperities usually observed in nominally dry tests at room temperature, equation (1) can also fit some of the healing phenomena that relies on solution transfer processes [e.g., *Fredrich and Evans*, 1992; *Karner et al.*, 1997; *Nakatani and Scholz*, 2004].

[3] Although qualitative understanding of frictional healing as an increase of real contact area has been there all along [e.g., *Dieterich*, 1972; *Scholz and Engelder*, 1976], there had been no explanation for the particular functional form (logarithmic) of equation (1) until *Brechet and Estrin* [1994] proposed a general physical model that can produce it. Importantly, the Brechet and Estrin (BE) model provides expressions for the observational healing parameters (*b* and *t*_{c} in equation (1)) in terms of the properties of the underlying mechanism: assumed to be asperity creep driven by the contact normal stress. The effects of temperature and contact stress are included by assuming that the underlying creep mechanism is a stress-aided thermally activated process.

[4] In this paper, the values of *b* and *t*_{c} of the solution transfer healing phenomenon reported by *Nakatani and Scholz* [2004, hereinafter referred to as paper 1] will be examined in terms of the BE model. The suite of experiments in paper 1 established that the healing results from local solution transfer; its specific mechanism being yet to be determined. Although the BE model is applicable to any stress-driven healing process, we will primarily examine the quantitative agreements of the data with that model in which pressure solution is assumed as the particular underlying mechanism. We do this because the properties of pressure solution are relatively well known and because the mechanism is known to be active under the moderate hydrothermal conditions studied in paper 1 [e.g., *Rutter*, 1983; *Tada and Siever*, 1989; *Dewers and Hajash*, 1995]. The same analysis, for comparison, will be applied to other well-documented time-dependent growth phenomena that appear to also result from solution transfer processes.

[5] We note that the BE model, which assumes stress-driven creep as the underlying mechanism, is not a unique model for time-dependent healing phenomena. Mechanisms of local solution transfer driven by something other than stress may also cause healing phenomena [e.g., *Smith and Evans*, 1984; *Hickman and Evans*, 1992; *Bos and Spiers*, 2002], to which BE theory is not applicable. Such possibilities will be separately discussed.