Widths of imbricate thrust blocks and the strength of the front of accretionary wedges and fold-and-thrust belts

Highlights

• Models reveal the controls on fault block width at accretionary wedges.

• Width increases with sediment thickness and area forward of wedge with excess stress.

• Width increases with increasing sediment friction, cohesion, and pore-fluid pressure.

• Width decreases with increasing basal friction and dip.

• Scaling laws can be used to infer relative brittle strengths at the toe of wedges.

Abstract

Besides the large-scale wedge shape itself, the most prominent structural feature of accretionary wedges and fold-and-thrust belts is the common pattern of imbricate thrust faults. This study illuminates the fundamental mechanical processes and material properties controlling the width of the crustal blocks bounded by major thrusts using analytical solutions of stress as well as two-dimensional finite-difference models. The numerical models predict that the initial width w₀ of a thrust block is set when that block first forms at the very front of the wedge. The width is found to subsequently decreases approximately in proportion to the mean horizontal strain needed for an ideally triangular-shaped Coulomb wedge with a critical taper. Block width is proportional to the thickness H of the incoming, accreting sediment. A key quantity that influences the normalized initial block width w₀/H is the distance L forward of the frontal thrust needed for the net horizontal force from shear on the base of the incoming sediment to balance the net force on the frontal thrust. It is within this distance where stress in the incoming sediment is substantially elevated and thus where the new frontal thrust forms. Results show that L/H and, correspondingly, w₀/H increase with increasing sediment friction angle ϕ, cohesive strength C₀ and pore-fluid pressure ratio λ, and decrease with increasing basal friction angle ϕ_b and basal dip β. Normalized width is sensitive to ϕ and relatively insensitive to ϕ_b and λ. Results for submarine and subaerial wedges follow the same scaling law. The scaling law relates the observables, w₀/H and β, to the material properties, ϕ, ϕ_b, λ, and therefore provides a theoretical relation that can be used independent of, or together with critical Coulomb wedge theory (CWT) to constrain these properties.

Introduction

The classical critical Coulomb wedge theory (CWT) (Davis and Suppe, 1983; Dahlen, 1984, Dahlen, 1990) has provided an extremely valuable and elegant paradigm for understanding the basic mechanics responsible for the large-scale, tapered form of accretionary wedges and fold-and-thrust belts. The theory has been widely used to interpret observations of wedge tapers (angle between their dipping base and surface) in terms of the frictional strength of the wedge material (e.g., the friction coefficient μ or angle ϕ) or the basal décollement (e.g., μ_f or ϕ_f). An important shortcoming, however, is that a pair of observations of surface dip (α) and basal dip (β), enables only nonunique solutions for ϕ and ϕ_f, and therefore one must make assumptions about the value of one property in order to infer the value of the other. Also, a direct inference of the material properties is possible only when the taper is at the critical state, whereas it is well recognized that time-dependent processes such as erosion, sedimentation, and faulting can cause the taper to deviate from the critical value. Finally, the overall wedge shape is typically formed by a series of imbricate thrust sheets or blocks (Fig. 1), which introduces uncertainty in defining the wedge taper angle.

Observations of the geometry of the imbricate thrust blocks should provide additional insight about the stresses and material properties of these accreting systems. The challenge, however, lies in the fact that these thrust blocks represent spatial and temporal heterogeneities, and therefore formal physical descriptions are less amenable to closed form, general solutions like those for the (steady-state) critical Coulomb wedge. Thus, much of our understanding of the mechanics of imbricate thrust initiation and evolution is informed by modeling studies, beginning over a century ago with laboratory analogue studies, and more recently (within the past two decades) using numerical models (e.g., see Graveleau et al., 2012; Buiter, 2012; and references therein). Identifying the factors that control the widths of the major thrust blocks has been a long-standing target of interest, and yet a general theoretical framework remains outstanding. Establishing such a framework would provide a context in which to understand and interpret observations of thrust block widths.

How accretionary wedges and fold-and-thrust belts can be expected to grow by the formation of imbricate thrust faults has been illuminated by studies using geometric models based on force or energy optimization principles (e.g., Platt, 1990; Suppe, 1983; Cubas et al., 2008; Mary et al., 2013), computational models that solve the conservation equations provided by continuum mechanics (e.g. Stockmal et al., 2007; Simpson, 2011; Ruh et al., 2012), and analog experimental models (e.g., Mulugeta, 1988; Mulugeta and Koyi, 1992; Koyi, 1995; Gutscher et al., 1998a; Lohrmann et al., 2003; Bose et al., 2009). The analogue and numerical models predict alternating episodes of wedge widening as new frontal thrust faults form, and wedge thickening and shortening with continued frontal thrust activity as well as “out-of-sequence” faulting behind the frontal thrust. In this way, the formation and time-integrated configuration of the imbricate thrusts control the evolution of the wedge and its large-scale tapered form.

Some of the early studies of imbricate thrusts related their formation or spacing to heterogeneities associated with stratigraphy (Bombolakis, 1986; Platt, 1986), fluid pressure (Cello and Nurr, 1988), and the basal fault (Wiltschko and Eastman, 1982; Knipe, 1985), as well as folding of a ductile décollement (Dahlstrom, 1970; Goff et al., 1996). While undoubtedly, heterogeneity influences faulting, such heterogeneity is not required for the imbricate pattern. Early finite element models predicted that the horizontal shortening of a layer having homogeneous material properties leads to a series of V-shaped pairs of conjugate thrusts, whose spacing is approximately proportional to the thickness of the accreting sediment layer (Panian and Wiltschko, 2004, Panian and Wiltschko, 2007). The thickness of the sediments as being a fundamental length scale for the spacing of faults is supported by laboratory experiments (Mulugeta, 1988; Marshak and Wilkerson, 1992; Mandal et al., 1997; Gutscher et al., 1998b), numerical models (e.g., Stockmal et al., 2007; Ruh et al., 2012) as well as observations of mountain belts (Mascle et al., 1990; Marshak and Wilkerson, 1992; Gutscher et al., 1998b) and submarine wedges (Morley et al., 2011).

Other factors that influence the spacing of thrust faults include the frictional strength of the basal décollement. Laboratory studies have found thrust spacing to generally decrease with increasing basal friction (μ_b) (Mandal et al., 1997; Koyi and Vendeville, 2003; Yamada et al., 2006; Bose et al., 2009) as predicted by the elastic stress analysis of Mandal et al. (1997). A related issue is how thrust spacing changes with distance across the wedge. In two sandbox modeling studies (Mandal et al., 1997; Bose et al., 2009), thrust block width tended to decrease from the front to the back of the wedge. Subsequent experiments (Saha et al., 2013) showed that whether thrust spacing increases, decreases, or does not change from front to back is a function of basal friction, wedge surface dip (α) as well as basal dip (β) (Fig. 2b). Regarding the brittle strength of the material above the décollement, recent studies have shown that strain weakening by the loss of cohesion (Morgan, 2015) or the reduction of the coefficient of friction (Mary et al., 2013) tends to increase the spacing of imbricate thrusts.

Sediment deposition and transport have been found in numerical modeling studies to appreciably impact the morphology and taper of wedges, as well as the spacing of thrust faults (Simpson, 2010; Fillon et al., 2013; Ruh et al., 2014; Mannu et al., 2016). Generally, the deposition and the erosional transport of sediments in the area of the deformation front tend to increase the spacing between major thrusts. It is also understood that the internal stress state, morphology and taper in areas of high sedimentation or erosion may move the taper out of the critical state (e.g., Mannu et al., 2016).

This study takes a basic physics approach in quantifying how several key factors influence the width of imbricate thrust blocks. Two-dimensional (2-D) numerical models simulate the formation and evolution of imbricate thrust faults under idealized conditions so that the individual effects of physical-property variables can be distinguished and quantified. Those variables include the initial thickness H of the sediment layer entering and eventually accreting to the wedge; the intrinsic brittle strength of those sediments, as controlled by friction coefficient μ or angle ϕ, as well as the initial cohesion, C₀; the frictional strength at the base of the sediment layer, μ_b or ϕ_b; pore fluid pressure ratio λ; and dip of the basal décollement β (Fig. 2). We do not examine the effects of sedimentation and erosion. Elastic stress solutions are used to illuminate the underpinning mechanical interactions and to formulate scaling laws that are used to relate thrust block width to the above variables, based on empirical fits to the numerical model results. The scaling laws can be used to interpret observations of thrust block width at natural systems independent of whether the wedge taper is critical, or when combined with CWT, to enable tighter constraints on wedge frictional properties.