The so-called “brittle-ductile transition” is thought to be the strongest part of the lithosphere, and defines the lower limit of the seismogenic zone. It is characterized not only by a transition from localized to distributed (ductile) deformation, but also by a gradual change in microscale deformation mechanism, from microcracking to crystal plasticity. These two transitions can occur separately under different conditions. The threshold conditions bounding the transitions are expected to control how deformation is partitioned between localized fault slip and bulk ductile deformation. Here, we report results from triaxial deformation experiments on pre-faulted cores of Carrara marble over a range of confining pressures, and determine the relative partitioning of the total deformation between bulk strain and on-fault slip. We find that the transition initiates when fault strength (σf) exceeds the yield stress (σy) of the bulk rock, and terminates when it exceeds its ductile flow stress (σflow). In this domain, yield in the bulk rock occurs first, and fault slip is reactivated as a result of bulk strain hardening. The contribution of fault slip to the total deformation is proportional to the ratio (σf − σy)/(σflow − σy). We propose an updated crustal strength profile extending the localized-ductile transition toward shallower regions where the strength of the crust would be limited by fault friction, but significant proportions of tectonic deformation could be accommodated simultaneously by distributed ductile flow. INTRODUCTION AND METHODOLOGY Under the low pressure and temperature conditions of the upper crust, rocks generally deform by grain-scale microcracking, and crustal-scale deformation is accommodated by slip on discrete fault planes. In this regime, the overall strength of the crust is limited by fault friction (Scholz, 2002; Paterson and Wong, 2005). Deeper in the crust, at higher pressure and temperature, rock deformation becomes more diffuse, and may be driven by crystal plastic phenomena such as dislocation creep. Here, the overall strength of rocks can generally be described by a steady-state flow law sensitive primarily to temperature and strain rate (e.g., Goetze and Brace, 1972; Evans and Kohlstedt, 1995). The transition between these two rheological domains, the so-called “brittle-ductile transition”, occurs over a pressure and temperature range where rocks deform by an interplay of cracking and crystal plasticity. The brittle-ductile transition commonly loosely refers to the progressive change in crustal rheology with increasing depth; here we will use the term “ductile” in the sense described by Rutter (1986), whereby it refers to macroscale distributed flow, regardless of the nature of the deformation mechanism, and will use “brittle” to describe fracturing processes at all scales. In nature, the brittle-ductile transition zone has been identified in exhumed shear zones showing markers of crystal plasticity (e.g., mylonites) overprinted by slip planes and pseudotachylytes that are inherent to the brittle regime (e.g., Sibson, 1980; Passchier, 1982; Hobbs et al., 1986). Such field evidence suggests that the transition in deformation mechanism is associated with a change in the degree of strain localization, from narrow frictional slip zones to wider plastic shear zones. Laboratory experiments have shown that the transition from localized fracture to ductile flow generally occurs when the frictional strength of the fault, σf, equals the bulk flow stress of the rock, σflow (Byerlee, 1968; Kohlstedt et al., 1995). However, distributed deformation at the macroscopic scale may still be dominated by brittle microscale processes, and only further increases in pressure and temperature lead to fully crystal-plastic flow. This shows that the macroscale transition in strain localization ( localized-ductile transition) is not necessarily the same as the microscale transition in deformation mechanism (brittle-plastic transition) and that the two transitions can occur under different pressure and temperature conditions. The resulting complex interplay between brittle and plastic mechanisms makes the flow stress σflow sensitive to a large number of parameters in the ductile regime (see Evans and Kohlstedt, 1995, and references therein), notably the imposed strain rate and the accumulated strain. Furthermore, the criterion σflow > σf for the onset of ductile deformation was originally established from studies on initially intact materials undergoing a simple monotonic loading history, and describes deformation regimes in a binary manner (localized or distributed) without emphasizing the potential for coexistence of both fault slip and bulk ductile flow. The applicability of this criterion to the crust might therefore be limited, because crustal-scale deformation is controlled by preexisting structures (faults and shear zones; see, e.g., Goetze and Evans, 1979; Brace and Kohlstedt, 1980). Thus, it remains unclear if and how faults are reactivated across the brittle-ductile transition. Previous experimental studies have commonly used sample geometries that enforce sliding on narrow shear zones between essentially rigid blocks under increasing pressure and temperature conditions (e.g., Shimamoto, 1986; Pec et al., 2016), which do not allow for quantification of partitioning between fault slip and bulk strain. Here, we conducted rock deformation experiments on pre-faulted samples of Carrara marble and monitored strain partitioning and fault reactivation across the localized-ductile transition. Our experiments were performed at room temperature and confining pressures (Pc) from 5 to 80 MPa. We determined partitioning of the total shortening between fault slip and off-fault matrix strain by subtracting the matrix strain (measured with strain gauges) from the total shortening (measured with external displacement transducers). Downloaded from https://pubs.geoscienceworld.org/gsa/geology/article-pdf/doi/10.1130/G46516.1/4850305/g46516.pdf by University College of London user on 17 October 2019 2 www.gsapubs.org | Volume XX | Number XX | GEOLOGY | Geological Society of America Experiments were conducted in two stages. During the first stage, samples were pre-faulted by loading at Pc = 5 MPa until localized brittle failure occurred. Following failure, an additional increment of shortening ε̇ = ΔL/L (L—length) of either 0.1% or 1% was allowed to accumulate before proceeding to the second stage, in order to test any effect of accumulated fault slip on the transition. In the second stage, Pc was increased stepwise from 5 to 80 MPa in 5 or 10 MPa increments. At each pressure step, the samples were reloaded at an axial shortening rate of ε̇ = 10−5 s−1 until 0.1% of irrecoverable axial shortening was accumulated, and then unloaded before proceeding to the next pressure step (see Section DR1 and Fig. DR2 in the GSA Data Repository1 for an extended methodology, and Table DR3 for a summary of experimental conditions). RESULTS During the first stage (Fig. 1), the sample behaves in a manner typical of the brittle regime, and the stress drop (accompanied by partial relaxation of the off-fault elastic strain) marks the formation of the macroscopic shear fault. During the second stage, at each confining pressure step, the stress-shortening relationship is initially linear, but deviates from linearity at some threshold stress σy, and then tends to plateau (Fig. 1A). This “plateau” stress increases significantly with increasing Pc. At low Pc (10 and 20 MPa), the matrix strain (εmatrix) initially increases at the same rate as the total shortening (ΔL/L), then deviates toward a constant value. The deviation point occurs at a stress denoted σf, and marks the onset of fault slip (triangles in Fig. 1B). At intermediate Pc (30–60 MPa), the same deviation is observed to occur, but εmatrix continues to increase beyond this point, albeit at a lower rate, indicating contributions from both matrix strain and fault slip to the total shortening. This observation appears to be independent of shortening, as demonstrated in an additional experiment where a single, second-stage deformation cycle was performed at Pc = 35 MPa, which shows no further deviation in matrix strain for a total shortening of up to a further 2% (Fig. DR4). Finally, at the highest Pc (70 MPa and above), εmatrix remains equal to ΔL/L throughout the deformation cycle, which implies that the fault is fully locked. To assess the extent of microcracking in the matrix, we measured the horizontal P-wave speed across the fault during each deformation cycle (Fig. DR5). The wave speed at the start of each cycle increased with confining pressure. During deformation, the wave speed changed very little for cycles at Pc <30 MPa, but decreased progressively for all cycles at higher pressures. The magnitude of the decrease in P-wave speed increased with increasing Pc from 30 to 60 MPa but then decreased at higher confinement. At Pc = 10 and 20 MPa, the yield stress and the fault strength are equal, and the calculated slip contributes close to 100% of the total shortening (Figs. 2A and 2D). Between Pc = 30 MPa and Pc = 60 MPa, σf increases linearly with Pc, whereas σy remains approximately constant at ∼115 MPa. Over this pressure range, the slip contribution progressively decreases from ∼80% at Pc = 30 MPa down to ∼15% at Pc = 60 MPa. At Pc = 70 MPa and above, the fault is fully locked, σf becomes inaccessible, and the slip contribution drops to zero. During the experiment where more slip is accumulated on the fault (1% rather than 0.1%) prior to stage 2 (Figs. 2B and 2E), σf and σy behave in a comparable manner to that described above, but σf increases with increasing Pc at a slightly higher rate. As a result, the deviation between the two initiates at Pc = 20 MPa and the fault becomes fully locked around Pc = 55 MPa. Similarly, the slip contribution decreases from >60% at Pc = 20 MPa to 20%

中文翻译：

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脆-韧转变过程中的断层再激活和应变划分

所谓的“脆-韧转变”被认为是岩石圈最强的部分，它定义了地震带的下限。它的特点不仅是从局部变形到分布（延展）变形，而且还表现为微观变形机制的逐渐变化，从微裂纹到晶体塑性。这两种转变可以在不同条件下分别发生。预计边界过渡的阈值条件将控制变形如何在局部断层滑动和整体延性变形之间进行划分。在这里，我们报告了在一系列围压下对卡拉拉大理石的预断层岩心进行三轴变形实验的结果，并确定体应变和断层滑移之间总变形的相对分配。我们发现，当断层强度 (σf) 超过大块岩石的屈服应力 (σy) 时，转变开始，并在超过其延性流动应力 (σflow) 时终止。在该域中，首先发生块体岩石的屈服，并且由于块体应变硬化而重新激活断层滑动。断层滑动对总变形的贡献与比率 (σf − σy)/(σflow − σy) 成正比。我们提出了一个更新的地壳强度剖面，将局部韧性过渡延伸到较浅的区域，在那里地壳的强度将受到断层摩擦的限制，但分布的韧性流可以同时适应相当大比例的构造变形。引言和方法论 在上地壳的低压和低温条件下，岩石通常通过晶粒尺度的微裂纹变形，地壳尺度的变形是由离散断层面上的滑动所适应的。在这种情况下，地壳的整体强度受到断层摩擦的限制（Scholz，2002；Paterson 和 Wong，2005）。在地壳深处，在更高的压力和温度下，岩石变形变得更加分散，可能是由晶体塑性现象驱动的，例如位错蠕变。在这里，岩石的整体强度通常可以通过主要对温度和应变率敏感的稳态流动定律来描述（例如，Goetze 和 Brace，1972；Evans 和 Kohlstedt，1995）。这两个流变域之间的转变，即所谓的“脆-韧转变”，发生在压力和温度范围内，在该范围内，岩石因开裂和晶体塑性的相互作用而变形。脆-韧转变通常泛指地壳流变学随着深度的增加而逐渐变化；这里我们将使用 Rutter (1986) 所描述的意义上的“延展性”一词，它指的是宏观分布的流动，无论变形机制的性质如何，并将使用“脆性”来描述所有尺度的压裂过程。在自然界中，已经在挖掘出的剪切带中发现了脆性-韧性过渡区，显示出晶体可塑性的标记（例如糜棱岩）被脆性体系固有的滑移面和伪速溶物覆盖（例如，Sibson，1980 年；Passchier，1982 年；霍布斯等人，1986 年）。这样的现场证据表明，变形机制的转变与应变局部化程度的变化有关，从狭窄的摩擦滑移区到更宽的塑性剪切区。实验室实验表明，当断层的摩擦强度 σf 等于岩石的整体流动应力 σflow 时，通常会发生从局部断裂到韧性流的转变（Byerlee，1968；Kohlstedt 等，1995）。然而，宏观尺度上的分布变形可能仍以脆性微观过程为主，只有进一步增加压力和温度才能导致完全晶体塑性流动。这表明应变局部化的宏观转变（localized-ductile transition）与变形机制的微观转变（脆塑性转变）不一定相同，两种转变可以在不同的压力和温度条件下发生。由此产生的脆性和塑性机制之间复杂的相互作用使得流动应力 σflow 对延展状态中的大量参数敏感（参见 Evans 和 Kohlstedt，1995 年，以及其中的参考资料），特别是施加的应变率和累积应变。此外，用于延性变形开始的标准 σflow > σf 最初是根据对经历简单单调加载历史的初始完整材料的研究而建立的，并以二元方式（局部或分布）描述变形状态，而没有强调两者共存的可能性断层滑移和整体韧性流动。因此，该标准对地壳的适用性可能受到限制，因为地壳尺度变形受先前存在的结构（断层和剪切带；参见，例如 Goetze 和 Evans，1979；布雷斯和科尔斯泰特，1980 年）。因此，尚不清楚断层是否以及如何在脆韧转变过程中重新激活。以前的实验研究通常使用样本几何形状，这些几何形状在增加的压力和温度条件下强制在基本刚性块之间的狭窄剪切带上滑动（例如，Shimamoto，1986 年；Pec 等人，2016 年），这不允许量化断层之间的分区滑移和体应变。在这里，我们对卡拉拉大理岩的断层前样品进行了岩石变形实验，并监测了局部延性过渡过程中的应变划分和断层再激活。我们的实验是在室温和 5 至 80 MPa 的围压 (Pc) 下进行的。我们通过从总缩短量（用外部位移传感器测量）中减去基体应变（用应变仪测量）来确定断层滑动和断层外矩阵应变之间的总缩短量的划分。伦敦大学学院用户于 2019 年 10 月 17 日从 https://pubs.geoscienceworld.org/gsa/geology/article-pdf/doi/10.1130/G46516.1/4850305/g46516.pdf 下载 2 www.gsapubs.org | 卷XX | 编号 XX | 地质 | 美国地质学会的实验分两个阶段进行。在第一阶段，样品通过在 Pc = 5 MPa 下加载来预断，直到发生局部脆性破坏。失效后，允许在进入第二阶段之前累积额外的缩短 ε̇ = ΔL/L（L-长度）0.1% 或 1%，以测试累积断层滑动对过渡的任何影响。在第二阶段，Pc 以 5 或 10 MPa 的增量从 5 MPa 逐步增加到 80 MPa。在每个压力步骤中，样品以 ε̇ = 10-5 s-1 的轴向缩短率重新加载，直到累积了 0.1% 的不可恢复的轴向缩短，然后在进行下一个压力步骤之前卸载（参见第 DR1 部分和图 3）。 GSA Data Repository1 中的 DR2 用于扩展方法，表 DR3 用于总结实验条件）。结果在第一阶段（图1），样品表现出典型的脆性状态，应力下降（伴随着断层弹性应变的部分松弛）标志着宏观剪切断层的形成。在第二阶段，在每个围压步骤中，应力-缩短关系最初是线性的，但在某个阈值应力 σy 处偏离线性，然后趋于平稳（图 1A）。这种“平台”应力随着 Pc 的增加而显着增加。在低 Pc（10 和 20 MPa）下，基体应变 (εmatrix) 最初以与总缩短量 (ΔL/L) 相同的速率增加，然后偏离恒定值。偏差点出现在一个用 σf 表示的应力处，并标志着断层滑动的开始（图 1B 中的三角形）。在中间 Pc (30-60 MPa)，观察到相同的偏差发生，但 εmatrix 继续增加超过这一点，尽管速率较低，表明基质应变和断层滑动对总缩短的贡献。这种观察似乎与缩短无关，正如在另一个实验中所证明的那样，单个，第二阶段变形循环是在 Pc = 35 MPa 下进行的，这表明基体应变没有进一步偏差，总缩短量又增加了 2%（图 DR4）。最后，在最高 Pc（70 MPa 及以上），εmatrix 在整个变形循环中保持等于 ΔL/L，这意味着断层被完全锁定。为了评估基质中微裂纹的程度，我们测量了每个变形周期中穿过断层的水平 P 波速度（图 DR5）。每个循环开始时的波速随着围压而增加。在变形过程中，波速在 Pc <30 MPa 的循环中变化很小，但在较高压力下的所有循环中逐渐降低。P 波速度的下降幅度随着 Pc 从 30 MPa 增加到 60 MPa 而增加，但随后在更高的约束下下降。在 Pc = 10 和 20 MPa 时，屈服应力和断层强度相等，计算出的滑移对总缩短量的贡献接近 100%（图 2A 和 2D）。在 Pc = 30 MPa 和 Pc = 60 MPa 之间，σf 随 Pc 线性增加，而 σy 在 ~115 MPa 保持近似恒定。在这个压力范围内，滑移贡献逐渐从 Pc = 30 MPa 时的~80% 下降到 Pc = 60 MPa 时的~15%。在 Pc = 70 MPa 及以上时，断层被完全锁定，σf 变得不可接近，滑移贡献降至零。在第 2 阶段（图 2B 和 2E）之前，在断层上积累更多滑移（1% 而不是 0.1%）的实验期间，σf 和 σy 的表现与上述类似，但 σf 随 Pc 的增加而增加以略高的速度。因此，两者之间的偏差始于 Pc = 20 MPa，并且故障在 Pc = 55 MPa 附近完全锁定。类似地，滑移贡献从 Pc = 20 MPa 时的 >60% 降低到 20%