# Metamorphic record of catastrophic pressure drops in subduction zones

Philippe Yamato, Jean-Pierre Brun

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Philippe Yamato, Jean-Pierre Brun. Metamorphic record of catastrophic pressure drops in subduction zones. Nature Geoscience, 2017, 10 (1), pp.46-50. 10.1038/ngeo2852 . insu-01409600

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# Metamorphic record of catastrophic pressure drops in subduction zones

P. Yamato* and J. P. Brun

When deeply buried in subduction zones, rocks undergo mineral transformations that record the increase of pressure and temperature. The fact that high-pressure metamorphic parageneses are found at the Earth's surface proves that rock burial is followed by exhumation. Here we use analysis of available data sets from high-pressure metamorphic rocks worldwide to show that the peak pressure is proportional to the subsequent decompression occurring during the initial stage of retrogression. We propose, using a simple mechanical analysis, that this linear relationship can be explained by the transition from burial-related compression to extension at the onset of exhumation. This major switch in orientation and magnitude of principal tectonic stresses leads to a catastrophic pressure drop prior to actual rock ascent. Therefore, peak pressures are not necessarily, as commonly believed, directly dependent on the maximum burial depth, but can also reflect a change of tectonic regime. Our results, which are in agreement with natural data, have significant implications for rock rheology, subduction zone seismicity, and the magnitudes of tectonic pressures sustained by rocks. Current views of subduction dynamics could be reconsidered in that perspective.

Metamorphic rocks are products of geodynamic processes acting at depths inaccessible to direct observation. The pressure-temperature-time-deformation (P-T-t-ε) paths followed by metamorphic rocks can be reconstructed from petrographic and chemical analyses of their mineral assemblages, and by dating their growth and the deformation recorded in these minerals¹,² (Fig. 1a). In this way, (ultra)high-pressure-low-temperature ((U)HP-LT) rocks have enormously contributed to our understanding of the processes operating during burial and exhumation in subduction zones¹,³⁻⁵. The discovery of UHP minerals⁶,⁷, considered as a proof of rock burial to depths > 100 km, constituted a revolution in the plate tectonics framework. In detail, P-T-t paths for the (U)HP-LT metamorphic rocks differ for each natural case, but they generally share a common pattern (Fig. 1a) composed of a prograde burial stage, a peak pressure, an initial retrograde stage of fast and almost isothermal decompression and a subsequent retrograde stage during which P and T decrease almost linearly with a P-T slope lower than in the prograde stage. Here we analyse available P-T data worldwide and show that the peak pressure and the first stage of decompression ΔP recorded by the rocks, what we refer to as pressure drop, appear linearly related (Fig. 1b, details and references in Supplementary Table 1).

## Metamorphic record of burial and exhumation

In classical interpretations, the pressures recorded in rocks are interpreted as lithostatic ($P_{litho}$). Consequently, prograde P-T-t paths are considered to represent the burial of rocks along a cold thermal gradient and the peak pressure directly relates to the maximum 'depth' reached by the buried rocks. In the same way, the pressure drop is considered to represent the vertical component of rock displacement towards the surface during the first stage of exhumation. However, the linear dependence between the burial depth and the vertical component of exhumation implied by this classical interpretation (Fig. 1b) is extremely difficult to reconcile with variations in slab dips, subduction velocities and nature of

overriding plates represented in the wide variety of tectonic settings where (U)HP rocks are found⁸.

In terms of tectonic processes, the peak pressure occurs at the time and conditions when there is a switch from burial to exhumation (Fig. 2). This distinction between burial and exhumation is of primary importance because, whereas subduction is a continuous process, the switch from burial to exhumation implies two completely different states of stress. During burial, the metamorphic rocks, which are part of the subducting plate, undergo a shear deformation with a compressive component against the overriding plate (Fig. 2a). Consequently, $P_{litho}$ increases with burial with a horizontal maximum principal stress $\sigma_1$ and a vertical minimum principal stress $\sigma_3$ (equal to $P_{litho}$). Following a rock mechanics formulation, the total pressure (that is, mean stress) recorded in rocks in compression $P_c$ is therefore higher than the lithostatic pressure⁹⁻¹³ (Fig. 2c). Conversely, exhumation occurs in response to extension¹⁴⁻¹⁶ (Fig. 2d) and to a lesser extent by erosion¹⁷. Consequently, $P_{litho}$ decreases during exhumation and the maximum principal stress $\sigma_1$ (equal to $P_{litho}$) is vertical. The pressure $P_c$ recorded in rocks is then lower than $P_{litho}$ (ref. 10) (Fig. 2c). Peak pressure could therefore correspond to a switch (Fig. 2b) from compression to extension (that is, between $\sigma_1$ and $\sigma_3$), which is in agreement with field evidence showing opposite shear senses associated with prograde and retrograde parts of the P-T-t paths¹⁸,¹⁹.

## A physical model for the linear relation between $P_c$ and $\Delta P$

Our analysis focuses on the total pressure and the pressure drop associated with a switch between $\sigma_1$ and $\sigma_3$. We first consider a dominant frictional behaviour of the subducted units as a limiting case. Considering an internal frictional angle $\Phi$ and a cohesion C (see Methods for the complete calculations and references) the yield equation is:

$$ \sigma_1 (1 - \sin \phi) - \sigma_3 (1 + \sin \phi) = 2C \cos \phi \quad (1) $$
<figure><img src="image_3.png" /><figcaption>**Figure 1 | P-T-t path, peak pressure and pressure drop.** a, P-T-t paths related to rocks within subduction zones (white star) generally show a prograde part (blue line), a pressure peak (red star) and a retrograde part (green line). Geochronological data provide time constraints along the P-T path (t₁, t₂, t₃) and usually show that the retrograde path occurs in two stages: stage 1 (between t₁ and t₂) being much faster than stage 2 (between t₂ and t₃). b, Pressure drop as a function of pressure peak from natural data. Error bars are a function of the error in P estimates. A circle is used instead of a square when a precise pressure estimate at t=t₂ exists to compute ΔP (see Supplementary Table 1).</figcaption></figure>

from which, taking $\sigma_2 = (\sigma_1 + \sigma_3)/2 = P$, $\phi = 30^\circ$ and $C = 0$ (see Methods), without pore fluid pressure, the total pressure in compression is:

$$P_c = 2P_{\text{litho}} \qquad (2)$$

and the total pressure in extension:

$$P_c = \frac{2}{3} P_{\text{litho}} \qquad (3)$$

Consequently, a switch from compression to extension leads to a pressure drop $\Delta P$, such that:

$$\Delta P = P_c - P_e = \frac{4}{3} P_{\text{litho}} \qquad (4)$$

Equations (2) and (3) show that, during subduction, rocks can successively undergo an overpressure $P_c$ two times higher than $P_{\text{litho}}$ (refs 9,10) and an underpressure $P_c < P_{\text{litho}}$ (ref. 10). The switch between $\sigma_1$ and $\sigma_3$ leads to a catastrophic pressure drop $\Delta P$ (Fig. 2c) whose value is higher than $P_{\text{litho}}$ and that, geologically, can be almost instantaneous (that is, as fast as the state of stress switch).

## Mechanical and tectonic implications

The relation between peak pressure $P_c$ and the pressure drop $\Delta P$ recorded by the rocks (Fig. 1b) fits with our analysis (Fig. 3a, equation (2)-(4) and Methods) and the fit quality increases when the frictional parameters used correspond to the Byerlee law. This result puts in question the classical interpretation of P-T-t paths and has important implications for understanding the processes acting in subduction zones:

(1) A stress switch between burial related compression (Fig. 2a) and extension at the onset of exhumation (Fig. 2b) can provide a simple physical explanation for the sudden, large and nearly isothermal pressure drop observed in P-T-t paths of (U)HP metamorphic rocks. This first stage of the retrograde path (Fig. 1a), commonly interpreted as a very fast exhumation stage²⁰, does not correspond to any significant rock ascent and occurs, for a large part, close to the metamorphic peak (Fig. 4). Moreover, such a sudden pressure drop could also explain why the peak parageneses are preserved after retrogression.

(2) The conversion of a P-T path into a $P_{\text{litho}}$-T path (Fig. 4) shows that burial stops at depths much shallower than expected from the classical interpretation and that exhumation starts at deeper levels than the recorded pressure $P_c$ (if assumed lithostatic, Fig. 4). Kinematic reconstructions of the structure prior to exhumation from the geometry and size of metamorphic units²¹⁻²⁴ can provide crucial independent tests for this. Further work is thus required to refine the role of extension as an explanation for the linear trend between $P_c$ and $\Delta P$.

(3) In mountain belts, such as the Alps or Himalayas, the structures and kinematic markers related to an extensional exhumation of (U)HP rocks can be obscured or even erased by later tectonic events. However, other field examples clearly show that exhumation occurred in extension (regardless of P-T estimates), driven either by slab rollback (for example, Mediterranean¹⁵) or by extension of the overriding plate (for example, Norwegian Caledonides¹⁴,¹⁸ or Papua New Guinea²⁵). It is remarkable that, whatever the tectonic setting, P-T data respect the same linear relation between peak pressure and pressure drop (Figs 1b and 3a), indicating that even where extensional exhumation is not obvious a transition from compression to extension probably occurred.

(4) The condition of steady-state frictional behaviour is not essential and our analysis remains valid for ductile rocks (see Methods) but with a state of stress very close to the frictional yield stress, as shown by the location of natural cases in the $P_c-\Delta P$ diagram (Fig. 3a).

Moreover, growing field evidence demonstrates frictional behaviour (for example, pseudotachylytes in the eclogites facies²⁶,²⁷ or eclogites breccias²⁸,²⁹) with potential links to subduction zone seismicity (that is, both intermediate and deep earthquakes). At the rock sample scale, it is also common that (U)HP eclogites do not show evidence of ductile shear³⁰. This means that (U)HP mineralogical transformations could occur almost statically³¹ and that exhumation-related deformation is localized at the
a

<figure><img src="image_4.png" /></figure>

b

<figure><img src="image_5.png" /></figure>

c

<figure><img src="image_6.png" /></figure>

**Figure 2** | State of stress during subduction-exhumation process driven by slab rollback (left) or upper plate extension (right). Black stars: examples of rock submitted to (U)HP conditions and exhumed on the surface. Red stripes: rocks passed through (U)HP conditions. Blue lines represent thrusts and dark green lines represent normal faults. a, During subduction, the minimum principal stress σ₃ is vertical and corresponds to P_litho. The maximum principal stress σ₁ is horizontal. b, Full shear delamination of crust or slab breakoff and divergence of the upper plate control the onset of extension and stress switch. c, Mohr circle representation (shear stress τ versus normal stress σₙ) of the state of stress at the Mohr-Coulomb yield (C is cohesion, and φ is the internal friction angle). The vertical stress σ_v that is σ₃ in compression (blue circle) becomes σ₁ in extension (green circle). The stress switch leads to a pressure drop ΔP (red arrow). d, Extensional exhumation.

edges of the metamorphic units. This does not necessarily
imply that the long-term behaviour of (U)HP rocks is frictional
but that the initial localizing process is frictional. This would
correspond to brittle fractures where strain weakening enhanced
by incoming fluids accommodates their evolution into ductile
shear zones³².

In addition, at a larger scale, the thrust-related delamination of
large and thick (U)HP crustal units (up to 100 km and 15 km³,
respectively) from the subducting slab and their stacking in
the subduction zone also requires high strength and therefore
probably frictional behaviour. Subducting continental crust must be

mechanically coupled to the downgoing mantle slab to be pulled
down to (U)HP conditions. This would be the case for thinned
continental crust with Moho temperatures lower than 550 °C (for
example, passive margins).

(5) The sudden pressure drop associated with the stress switch described in this paper could be linked to subduction earthquakes. This should therefore be considered in combination with other mechanisms for failure and co-seismic faulting, such as dehydration embrittlement³³,³⁴ or self-localizing thermal runaway³⁵,³⁶.

In conclusion, the tectonic switch, from compression to extension
at the maximum burial depth, has a dramatic effect on the P-T-t
<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

**Figure 3** | Pressure drop occurring at peak pressure. **a**, The black line corresponds to our analytical solution when a switch from compression to extension occurs for frictional behaviour with Byerlee law parameters (see Methods). The dashed lines correspond to the minimum and maximum values for the pressure drop at a given peak pressure. The pink field corresponds to the ductile regime, in which four examples of maximum shear stress (pink lines) are presented (see Methods). Natural data (Fig. 1b) are recalled for comparison. **b**, Mohr circle representation (as in Fig. 2c) when the shear stress ($\tau_{lim}$, pink dashed line) is limited by ductile flow (see Methods). $\Delta P_{FRIC}$ and $\Delta P_{DUC}$ correspond to pressure drops in the frictional and ductile regimes, respectively.

conditions recorded in metamorphic rocks and on deformation within the subduction zones. The magnitude of the resulting pressure drop, which occurred prior to exhumation, is too large to be ignored. This mechanism provides a new and consistent alternative to interpret P-T-t paths and appears large enough to generate seismicity. Our results do not question the subduction processes of the oceanic and/or continental lithosphere, which explains the asymmetric structure of mountain belts and the coherent stacking of (U)HP metamorphic units. Nevertheless, they point out the necessity to rethink our understanding of rock rheology, particularly at the subduction interface. They also require another method for estimating the effective volume of material subducted at convergent plate boundaries that is likely to be much less than currently accepted.

## Methods

Methods, including statements of data availability and any associated accession codes and references, are available in the online version of this paper.

<figure><img src="image_9.png" /></figure>

**Figure 4** | New interpretation of P-T paths. Left panel: P-T path as recorded by rocks where pressure corresponds to the total pressure. Right panel: corresponding $P_{litho}-T$ path. The blue and green lines correspond to the total pressure gradients recorded under compression and under extension, respectively. The dashed lines are the corresponding lithostatic pressure gradients. At the peak pressure, the major part of the decompression ($\Delta P$) corresponds to the switch between compression and extension and only a minor part ($\delta P$) could correspond to a true vertical displacement during the switch.

Received 13 July 2016; accepted 4 November 2016; published online 5 December 2016

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Acknowledgements

We thank T. Duretz for scientific advice and K. Gallagher for style checking.

Author contributions

P.Y. conceived the study and realized the compilation of the natural data. Both authors discussed the results and interpretations, and wrote the manuscript.

Additional information

Supplementary information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints.
Correspondence and requests for materials should be addressed to P.Y.

Competing financial interests

The authors declare no competing financial interests.
Methods

**Definition of pressure and failure criterion.** Pressure is defined as the isotropic part of the stress tensor such that:

$$P = \frac{\sigma_{xx} + \sigma_{yy} + \sigma_{zz}}{3} \qquad (5)$$

In principal stress coordinates, this equation becomes:

$$P = \frac{\sigma_1 + \sigma_2 + \sigma_3}{3} \qquad (6)$$

with $\sigma_3 \le \sigma_2 \le \sigma_1$.

For simplicity, we first follow the analytic development from ref. 9, assuming that the deformation is plane strain and the material is incompressible³⁷ (that is, $\sigma_2 = P$).

In this condition, the total pressure corresponds to:

$$P = \frac{\sigma_1 + \sigma_3}{2} \qquad (7)$$

The failure criterion equation (friction law) is then defined in terms of a Mohr circle diagram such that:

$$\tau = \tan(\phi) \cdot \sigma_n + C \qquad (8)$$

where $\tau$ corresponds to the shear stress, $\sigma_n$ is the normal stress, and $\phi$ and $C$ are the internal friction angle and the cohesion of the material, respectively. Experimental data³⁸ shows that this equation constitutes the best way to represent the brittle behaviour of rocks according to the two following relations:

$$\tan(\phi) = 0.85 \text{ (that is, } \phi \sim 40^{\circ}\text{) and } C = 0 \text{ for } \sigma_n < 200 \text{ MPa, and} \qquad (9)$$

$$\tan(\phi) = 0.60 \text{ (that is, } \phi \sim 31^{\circ} \text{) and } C = 50 \text{ MPa for } \sigma_n \ge 200 \text{ MPa} \qquad (10)$$

From the Mohr circle diagram, $\sigma_1$ and $\sigma_3$ can be expressed as a function of $\phi$ and $C$ as follows³⁹:

$$\sigma_1 (1 - \sin \phi) - \sigma_3 (1 + \sin \phi) = 2C \cos \phi \qquad (11)$$

**Effective pressure under compression.** As in ref. 9, the stress state in compression is such that:

$$\sigma_3 = \sigma_v = P_{\text{litho}} = \rho g z, \text{ and} \qquad (12)$$

$$\sigma_1 = \frac{\sigma_3 (1 + \sin \phi) + 2C \cos \phi}{1 - \sin \phi} \qquad (13)$$

where $\sigma_v$ is the vertical stress, $\rho$ is the rock density, $g$ is the acceleration of gravity and $z$ is the depth.

Introducing equations (12) and (13) into equation (7), the general equation for the effective pressure in compression $P_e$ is then:

$$P_e = \frac{1}{2} \left( P_{\text{litho}} + \frac{P_{\text{litho}} (1 + \sin \phi) + 2C \cos \phi}{1 - \sin \phi} \right) \qquad (14)$$

which, taking $\phi = 30^{\circ}$ and $C = 0$ (first-order approximation of the coefficients for rocks on Earth³⁸), simplifies to:

$$P_e = 2P_{\text{litho}} \qquad (15)$$

**Effective pressure under extension.** In extension, stress states acting on the rocks are different and given by:

$$\sigma_1 = \sigma_v = P_{\text{litho}} \qquad (16)$$

$$\sigma_3 = \frac{\sigma_1 (1 - \sin \phi) - 2C \cos \phi}{1 + \sin \phi} \qquad (17)$$

and the general equation for the effective pressure in extension $P_e$ is then:

$$P_e = \frac{1}{2} \left( P_{\text{litho}} + \frac{P_{\text{litho}} (1 - \sin \phi) - 2C \cos \phi}{1 + \sin \phi} \right) \qquad (18)$$

which, taking $\phi = 30^{\circ}$ and $C = 0$, simplifies to:

$$P_e = \frac{2}{3} P_{\text{litho}} \qquad (19)$$

**Pressure drop at the pressure peak.** At the peak of pressure, the switch between compression and extension, corresponding to a switch between $\sigma_1$ and $\sigma_3$, leads to a pressure drop $\Delta P$, as a function of $P_{\text{litho}}$:

$$\Delta P = \left( \frac{P_{\text{litho}} (1 + \sin \phi) + 2C \cos \phi}{2 (1 - \sin \phi)} - \frac{P_{\text{litho}} (1 - \sin \phi) - 2C \cos \phi}{2 (1 + \sin \phi)} \right) \qquad (20)$$

or when expressed as a function of the pressure peak $P_c$:

$$\Delta P = P_c \left( 1 - \frac{1 - \sin \phi}{1 + \sin \phi} \right) + \frac{2C \cos \phi}{1 + \sin \phi} \qquad (21)$$

which, taking $\phi = 30^{\circ}$ and $C = 0$, simplifies to:

$$\Delta P = \frac{4}{3} P_{\text{litho}} = \frac{2}{3} P_c \qquad (22)$$

**General solutions for the pressure drop computation and upper-lower bounds calculation.** The same development can be done considering all the possible values for $\sigma_2$ (ranging between $\sigma_1$ and $\sigma_3$) inserted into equation (6). This provides a solution valid for any $\phi$ and $C$ but, above all, also provides maximum and minimum possible values for the pressure drop, essential for comparing the results with natural data (Fig. 3a).

The effective pressure in compression $P_c$ lies between a minimum value of:

$$P_{c(\sigma_2=\sigma_3)} = \frac{1}{3} \left( 2P_{\text{litho}} + \frac{P_{\text{litho}} (1 + \sin \phi) + 2C \cos \phi}{1 - \sin \phi} \right) \qquad (23)$$

and a maximum value of:

$$P_{c(\sigma_2=\sigma_3)} = \frac{1}{3} \left( P_{\text{litho}} + 2 \frac{P_{\text{litho}} (1 + \sin \phi) + 2C \cos \phi}{1 - \sin \phi} \right) \qquad (24)$$

The effective pressure in extension $P_e$ lies between a minimum value of:

$$P_{e(\sigma_2=\sigma_3)} = \frac{1}{3} \left( P_{\text{litho}} + 2 \frac{P_{\text{litho}} (1 - \sin \phi) - 2C \cos \phi}{1 + \sin \phi} \right) \qquad (25)$$

and a maximum value of:

$$P_{e(\sigma_2=\sigma_3)} = \frac{1}{3} \left( 2P_{\text{litho}} + \frac{P_{\text{litho}} (1 - \sin \phi) - 2C \cos \phi}{1 + \sin \phi} \right) \qquad (26)$$

Taking $\phi = 30^{\circ}$ and $C = 0$, the four above equations (23–26) summarize as follows:

$$\frac{5}{3} P_{\text{litho}} \le P_e \le \frac{7}{3} P_{\text{litho}} \qquad (27)$$

$$\frac{5}{9} P_{\text{litho}} \le P_e \le \frac{7}{9} P_{\text{litho}} \qquad (28)$$

The specific case $\sigma_2 = P$ corresponds to the average of each endmember.

Therefore, a range of value for $\Delta P$ can be expressed as a function of lithostatic pressure that can be written as:

$$P_{c(\sigma_2=\sigma_3)} - P_{c(\sigma_2=\sigma_3)} \le \Delta P \le P_{c(\sigma_2=\sigma_3)} - P_{c(\sigma_2=\sigma_3)} \qquad (29)$$

corresponding to:

$$\frac{8}{9} P_{\text{litho}} \le \Delta P \le \frac{16}{9} P_{\text{litho}} \qquad (30)$$

for $\phi = 30^{\circ}$ and $C = 0$.
For a better comparison with natural data, it is convenient to express ΔP as a function of the compressive effective pressure (which corresponds to the peak pressure) such that:

$$ \begin{aligned} & \left[ 1 - \left( \frac{1-s}{1+s} \right) \left( \frac{3+s}{3-s} \right) \right] P_c + \frac{1}{3} \left( \frac{A}{1+s} \right) \left( 1 + \frac{3+s}{3-s} \right) \le \Delta P \\ & \le \left[ 1 - \left( \frac{1-s}{1+s} \right) \left( \frac{3-s}{3+s} \right) \right] P_c + \frac{2}{3} \left( \frac{A}{1+s} \right) \left( 1 + \frac{3-s}{3+s} \right) \end{aligned} \quad (31) $$

where s stands for sin φ and A = 2C cos φ, giving:

$$ \left(1 - \frac{7}{15}\right) P_c \le \Delta P \le \left(1 - \frac{5}{21}\right) P_c \quad (32) $$

for φ = 30° and C = 0.

A graphical representation of equation (31) is given in Fig. 3a (dashed lines), according to the following parameters (from ref. 38): tan φ = 0.6 and C = 50 MPa, see equation (10).

**Mechanical behaviour of rocks in (U)HP conditions and applicability of our analysis in ductile regime.** It is commonly stated that deformation of metamorphic rocks within subduction zones is ductile. Therefore, the above analysis of peak pressure and pressure drop, which postulates a frictional behaviour, could possibly be considered as irrelevant. However, in contrast to the term 'frictional', the term 'ductile' is vague, as corresponding differential stresses can range over several orders of magnitude. As shown above, when a rock fails in friction, the strength is precisely defined, as it occurs at a very specific state of stress (σ₁-σ₃) in the Mohr-Coulomb diagram (Fig. 2c). However, when a rock flows in a ductile manner, shear stress values are highly dependent on temperature (which controls the effective viscosity of the rocks) and on strain rate. Consequently, shear stress

values can be very high, up to several gigapascals, even considering them as ductile in P-T conditions of the eclogite facies. As the strain rate depends both on shear zone width (from millimetre to kilometre scale) and on the displacement velocity accommodated by the shear zone (up to several centimetres per year), the shear stress value can be extremely variable, ranging over several orders of magnitude.

Deformation of frictional rocks occurs at the yield stress value. At the same depth, rocks deforming below this stress value are ductile (Fig. 3b). Such a configuration is illustrated in Fig. 3b by a cutoff (τᵢₘ) in shear stress (that is, a flow stress). The pressure drop resulting from the switch between compression and extension in a ductile regime (ΔP<sub>DUC</sub>) is then always lower than the pressure drop expected for frictional behaviour (ΔP<sub>FRIC</sub>). If this occurs in nature, the pressure drops extracted from natural data should fall on the left side of the frictional domain (in grey in Fig. 3a). Moreover, there is no reason to consider a unique flow stress (τᵢₘ) for all rocks because, at a given depth, they can have different rheological properties and different strain rates. In this case, the pressure drops extracted from natural data would be randomly distributed within the 'ductile domain' (in pink in Fig. 3a) to the left side of the 'frictional domain'. Consequently, ductile deformation of U(HP) rocks clearly occurs but our compilation (Fig. 1b) and new interpretation suggest that such ductile flow occurs with rather high differential stresses, close to those of the frictional yield (Fig. 3a).

**Data availability.** The data that support the findings of this study are available from the corresponding author on request.

References

37. Mancktelow, N. S. Tectonic overpressure in competent mafic layers and the development of isolated eclogites. *J. Metamorph. Geol.* **11**, 801–812 (1993).

38. Byerlee, J. Friction of rocks. *Pure Appl. Geophys.* **116**, 615–626 (1978).

39. Jaeger, J. C. & Cook, N. G. W. *Fundamentals of Rock Mechanics* (Chapman Hall, 1979).