The physics of rupture: From the laboratory scale to the scale of our planet

Things fall apart, the center cannot hold
- William Butler Yeats, "The Second Coming"

Rupture processes abound in nature and are central to many natural systems, from a gecko detaching its sticky feet from a wall, to earthquakes on geological faults that shape the surface of our planet. Rupture processes are also of prime technological importance as they limit the strength, stability and durability of many man-made devices, from Micro-Electro-Mechanical Systems (MEMS) to bridges and airplanes.

Understanding, controlling and predicting the phenomenon of rupture has been a challenge to mankind from the early stages of cultural evolution. In modern times, scientists from diverse disciplines such as engineering, earth science, physics and materials science are continuously striving to develop a coherent and unified picture of rupture. A major stumbling block in achieving this goal is the fact that rupture is an inherently complex phenomenon; the evolution of even a single rupture couples dynamic behavior at length and time scales that are separated by many orders of magnitude, giving rise to a wealth of emergent behaviors.

Earthquakes are a striking example of the complexity of rupture phenomena, which involve highly separated interacting scales; immense tectonic forces work for hundreds to thousands of years to slowly load a geological fault separating two tectonic plates, gradually increasing the mechanical energy stored in the fault system. The release of this stored mechanical energy, however, is rapid and occurs at velocities approaching the theoretical speed of information (material sound speed). Most of the released energy is converted into heat that is generated by the frictional forces acting on the fault and opposing the sliding motion, or is used for fragmenting the rock at the fault. Part of it, however, is radiated out by mechanical waves and eventually is converted into the violent ground motion that we generally equate with earthquakes.

Earthquakes are thus initiated at geological faults, within a narrow interfacial region that couples two tectonic plates. This narrow interface may be a few millimeters wide, yet hundreds of kilometers long. The fault interface is highly nonuniform at small scales and is composed of a network of discrete load-bearing micro-scale contacts. As only a small fraction of the apparent contact area between the two plates is in real contact, the actual forces acting on this sparse contact network are enormous, reaching the maximal stresses that the material can bear. An earthquake is, essentially, the frictional slip that results from the abrupt release of the mechanical energy stored at the large (tectonic) scales. This huge amount of energy is only released when the ensemble of contacts that had been restraining the motion yields. The subsequent frictional motion of the earth's surface, results from continual contact renewal and fracture that takes place at the fault. This gives rise to extreme and rapidly fluctuating local conditions.

The micro-scale physics of the frictional interface, therefore, play a key role in determining the initiation, development and arrest of the rupture fronts that we know as earthquakes; these may be many kilometers long and release, within a few seconds, energy accumulated over centuries. Part of the released energy feeds back into the large scales and may have dramatic consequences such as violent ground motion or Tsunami waves hundreds of kilometers away.

Despite decades of intense research, many key aspects of rupture processes are far from understood and a general coherent picture of rupture phenomena is still missing. At the heart of this problem are two basic issues in 'complexity science'. The first concerns the multi-scale nature of rupture phenomena. How can one integrate the striking multi-scale nature of the physics of rupture into a single coherent theoretical framework? The second is the question of predictability; although rupture is inherently a coherent phenomenon it is unclear if its size or timing may be predicted.

The coupling between vastly separated time and length scales that drives an earthquake is characteristic of the seemingly diverse rupture phenomena observed in numerous geological, physical and biological systems. To illustrate these basic similarities, consider a gecko climbing a wall. Although this biological phenomenon may appear completely different from earthquake dynamics, some striking similarities exist. The contact between the gecko's foot and the wall is highly nonuniform and spans a wide range of scales. The foot is macroscopic in size and exhibits an incredible hierarchal structure; it is composed of 5 toes, each toe is composed of about 20 rows of sticky setal arrays, with each setal array consisting of thousands of micrometer-scale setal stalks amounting to approximately 200,000 setae per toe with each seta terminating with 100-1000 sub-micrometer-scale spatulae. Therefore, the frictional forces that adhere the gecko's feet to the wall are generated by the frictional strength of a huge ensemble of discrete sub-micro-scale contacts, as in the network of micro-scale contacts that hold a geological fault together prior to an earthquake. To climb, the gecko must initiate rapid rupture of the interface between its foot and the wall, a process in which the sub-micron scale contacts collectively detach at time scales significantly shorter than those of the global motion. Thus both gecko motion and earthquake dynamics exhibit a similar hierarchy of complex, multi-scale rupture processes.

Surprisingly, our current knowledge of earthquake dynamics is much less detailed than our understanding of a gecko's walk. The major stumbling block is that earthquakes are nucleated far below the earth's surface, at seismogenic depths that often exceed 10km. Our major source of information of how these complex processes unfold is due to seismology, where approximate reconstructions of the rupture dynamics are obtained from the sound waves emitted by the rupture and recorded at seismic stations located far from the rupture source. As direct observations of interfacial fault processes are nearly impossible, our understanding of the basic physics involved remains limited.

Developing a predictive theoretical framework for rupture phenomena entails the development of novel experimental, mathematical and conceptual tools to bridge over the numerous distinct scales. Here we propose a two-pronged investigation of rupture dynamics along a rough quasi-one-dimensional interface that models fault dynamics. We intend to gain new insights into the physics of rupture by embarking on this interdisciplinary research program, which couples multi-scale mathematical modeling with innovative laboratory experiments.

A major obstacle to fundamental understanding of rupture processes is a lack of detailed information about the space-time evolution of the contact area and stresses along the interface. We will overcome this by coupling direct real-time visualization of the real area of contact to precise local measurements of stresses, slip displacement and slip velocities at points adjacent to the interface. Such a comprehensive approach to rupture evolution, in which all of the relevant local quantities that characterize a frictional interface are simultaneously measured, has never been previously attempted. The experiments will provide a detailed record of the rupture process at an unprecedented range (from microseconds to minutes) of temporal and spatial scales. Preliminary results already indicate a crucial coupling between scales, where coherent elastic energy at very large wavelengths couples to dissipative processes which take place at the microscopic scale within the frictional interface.

These interfacial processes will be modeled by a novel multi-scale approach that is capable of investigating the interactions between the large elastic scales that characterize the energy stored within the system with the small-scale and rapid dissipative processes that occur within the interface and release this stored energy. This approach will be flexible enough to incorporate a wide range of small-scale physical processes, allowing us to investigate the intricate interactions between different time and length scales involved in the rupture process.

Once the nature of the small-scale and rapid frictional processes is unraveled, our next step will develop a continuum level description of the interfacial small-scale physics. Integrating this continuum description with analytical and numerical calculations will enable us to both systematically explore rupture phenomena at a macroscopic level, and to test the predictions of the emerging picture against experimental observations. Finally, we plan to explore the links between our results and available geological and geophysical insights and observations. Together, we hope to develop a physics-based picture of rupture along an interface in general and earthquake nucleation and evolution in particular. The time is right for this multidisciplinary study as both laboratory and modeling capabilities have recently advanced to a stage that makes the aims of the proposed research both feasible and timely.