1 Abstract The grain-to-grain stress vertically in sediments is given by the overburden less the pore fluid pressure, σ, divided by the fraction of the horizontal area which is the supporting matrix , (1 − φ), φ being the porosity. It is proposed that the fractional reduction of this ratio, Λ, with time is given by the product of φ 4m/3) , (1 − φ) 4n/3 , and one or more Arrhenius functions A exp(−E/RT ) with m and n close to 1. This proposal is tested for shale sections in six wells from around the world for which porosity-depth data are available. Good agreement is obtained above 30-40 C. A single activation energy of 23+-5 kJ/mole, indicating pressure solution of quartz, 24 kJ/mol, was obtained. The average value of m is 1, indicating fractal pore-matrix spaces and water-wet interfaces. Grain-to -grain interfaces may be fractal with m close to 1, but can have lower values suggesting smooth surfaces and even grain-to-grain welding. Results are independent of over- or under-pressure of pore water. This model explains shale compaction quantitatively.