Abstract. We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderón-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.

We study a function space JNp based on a condition introduced by John and Nirenberg as a variant of BMO. It is known that L p ⊂ JNp L p,∞ , but otherwise the structure of JNp is largely a mystery. Our first main result is the construction of a function that belongs to JNp but not L p , showing that the two spaces are not the same. Nevertheless, we prove that for monotone functions, the classes JNp and L p do coincide. Our second main result describes JNp as the dual of a new Hardy kind of space HK p ′ .

Many of the world reserves of fossil fuels are located at various water depths in fine-grained sediment under the seabed. The fine-grained sediment contains relatively large biogas bubbles, which has been posing challenges to the stability of offshore foundations supporting oil and gas platforms. Although fine-grained gassy soil was found to exhibit different undrained shear strengths (cu) by altering the initial pore pressure, ui (relevant to water depth), systematic studies concerning the effect of ui on undrained shear behaviours of the soil are still lacking. This study reports a series of undrained triaxial tests aiming to compare and investigate the responses of reconstituted fine-grained gassy soil with the same consolidation pressure ([Formula: see text]), but at a wide range of varying ui (0–1000 kPa). The shearing-induced excess pore pressure (Δu) in the gassy specimens highly depends on ui. It can be either smaller than that of the saturated specimen with the same [Formula: see text] (due to partial dissipation of Δu into relatively large bubbles at low ui) or larger than that of the saturated specimen (related to collapse of relatively small bubbles at high ui). Consequently, the presence of bubbles had beneficially increased cu at relatively low ui (ui/[Formula: see text] < 0.6), and vice versa. The critical stress ratio of the reconstituted fine-grained gassy soil, however, did not appear to be altered by ui.

No abstract

Suffusion involves fine particles migration within the matrix of coarse fraction under seepage flow, which usually occurs in the gap-graded material of dams and levees. Key factors controlling the soil erodibility include confining pressure (p′) and fines content (F c), of which the coupling effect on suffusion still remains contradictory, as concluded from different studies considering narrow scope of these factors. For this reason, a systematical numerical simulation that considers a relative wide range of p′ and F c was performed with the coupled discrete element method and computational fluid dynamics approach. Two distinct macroresponses of soil suffusion to p′ were revealed, ie, for a given hydraulic gradient i = 2, an increase in p′ intensifies the suffusion of soil with fines overfilling the voids (eg, F c = 35%), but have negligible effects on the suffusion of gap-graded soil containing fines underfilling the voids (eg, F c = 20%). The micromechanical analyses, including force chain buckling and strain energy release, reveal that when the fines overfilled the voids between coarse particles (eg, F c = 35%) and participated heavily in load-bearing, the erosion of fines under high i could cause the collapse of the original force transmission structure. The release of higher strain energy within samples under higher p′ accelerated particle movement and intensified suffusion. Conversely, in the case where the fines underfilled the voids between coarse particles (eg, F c = 20%), the selective erosion of fines had little influence on the force network. High p′ in this case prevented suffusion.