The stakes of this ambiguity are enormous. In field operations, hard rock and bit degradation can produce an identical macroscopic signature: increasing torque on bit, decreasing rate of penetration, and stronger vibration. A driller crossing into a harder layer may misclassify the change as bit failure, while a worn bit that briefly unloads after entering a softer layer may appear to have recovered. These bidirectional misreadings affect weight-on-bit and rotary-speed selection, the timing of trips to replace bits, estimates of remaining bit life, and the triggering of downhole failure alarms. Until now, most laboratory and numerical studies held either lithology or wear fixed, making it impossible to determine whether the torque increment caused by wear was constant across different rock types.

The missing link, the authors argue, is mechanical rather than merely statistical. Wear changes the effective depth of cut, the frictional contact area, the duration of contact, and the set of cutters actively engaged with the rock. Lithology changes the cutting and indentation coefficients and the manner in which contacts are renewed by fracture. Because full-bit torque is the sum of each cutter’s tangential force multiplied by its radial moment arm, a small change in the shoulder or gauge region of the bit can be strongly amplified. The same nominal wear state can therefore generate different, or even oppositely signed, departures from a simple additive torque model depending on which rock is being drilled.

To isolate this effect, the team built a full-bit model in PFC3D, a discrete-element simulation environment in which rock is represented as an assembly of bonded particles. The model contained 230 rigid wall components and more than 221,000 triangular facets, with weight-on-bit and torque summed consistently from the contact forces and moments of every component. Four controlled lithology proxies were constructed, spanning fine clastic, conglomeratic, pyroclastic, and rhyolitic rocks with densities from 2,450 to 2,650 kilograms per cubic meter and particle-scale stiffnesses from 8 to 16 gigapascals. Wear was imposed as axial edge recession of the cutters at four levels: 0, 50, 100, and 150 micrometers, with cutter friction changed synchronously.

The experimental design was unusually disciplined. An early discovery matrix of 48 cases and a replication matrix of 80 cases were used to identify the interaction pattern and lock the analysis protocol before any response data from the confirmation stage were inspected. Then a third, completely independent matrix was generated: four lithologies, four wear levels, and 12 new random seeds per cell, totaling 192 cases. Every case passed preregistered quality gates covering contact fraction, force-ratio equilibrium, and load reasonableness, and no design point was deleted or replaced according to its response. The result was unambiguous. The full lithology-by-wear interaction on the dimensionless torsional response, defined as torque divided by the product of weight-on-bit and bit radius, yielded F(9, 176) = 5.562, a permutation p-value below 0.0001, and a partial eta-squared of 0.221.

Sensitivity analyses confirmed the finding was not an artifact. Repeating the interaction test with raw torque, torque adjusted for weight-on-bit, and after excluding the lowest 5 percent of weight-on-bit cases all produced consistent results. A separate particle-size sensitivity study across three radius ranges showed the interaction pattern was robust to numerical resolution, and a paired endpoint decomposition of 48 cases revealed that at severe wear the combined response followed mainly the geometric recession term, with the friction contribution averaging nearly zero and its direction varying unpredictably with lithology.

What makes the study remarkable is that it did not stop at detecting the interaction; it localized the mechanism. Using an exact component-wise load identity, the team decomposed the dimensionless torque into three factors: the moment-arm-weighted tangential-force demand, the signed coherence of force directions among components, and the closure between component loads and wall-reaction torque. The interaction was concentrated almost entirely in the first factor, with an effect size matching that of the overall response, while the closure factor showed no interaction at all. This means the nonadditivity arose because lithology-dependent fracture and wear-dependent engagement changed which cutters carried tangential force and at what radius, not from any numerical artifact or simple cancellation of forces.

The practical consequences were quantified through a mechanism-conditioned interaction compensator, a ridge-regression predictor trained on observable quantities such as tangential-force direction, force ratios, and moment-weighted radii. In complete-cell holdout tests, where entire lithology-wear combinations were excluded from fitting, adding force direction raised explanatory power from 3.0 percent to 67.2 percent, and adding active-contact topology pushed it to 84.0 percent. The compensator reduced the interaction sum of squares by 78.0 percent and cut the maximum cellwise bias from 32.7 percent to 13.4 percent. At the same moderate wear level, fine clastic rock showed a torque deviation of minus 24.8 percent from the additive expectation while rhyolitic rock showed plus 32.7 percent, a stark demonstration that a universal wear correction or fixed threshold will fail in one direction or the other.

Field data from 29 complete drilling runs in a heterogeneous volcanic-sedimentary sequence reinforced the numerical conclusions. Meter-scale drilling-time trajectories captured both fast responses at lithologic boundaries and slow within-run drift, with each additional 100 meters of drilling multiplying drilling time by 1.205. Severe bit damage occurred far more often in the harder lithologies, with a pooled odds ratio of 37.5, yet the agreement between severe physical damage and performance-related pull decisions was only 60.7 percent, showing that operational labels are an unreliable proxy for actual bit condition. The authors propose deploying their compensator as a bypass correction layer alongside existing top-drive torque monitoring: the raw torque limit continues to protect equipment, while the corrected value identifies abnormal torsional demand relative to the current lithology and contact state. By subtracting the state-dependent nonadditive offset before applying any alarm threshold, the approach promises to reduce false hard-rock and wear alarms, improve detection of genuine degradation, and supply an interpretable correction term for drilling digital twins.

Subject of Research: Nonadditive coupling between PDC drill bit wear and rock lithology in full-bit torsional response

Article Title: Modulation mechanism of full-bit torsional response under nonadditive coupling between PDC-bit wear and lithology

Article References: Mei, D., Yan, L., Zhou, Z., Wu, X., & Jian, Y. (2026). Modulation mechanism of full-bit torsional response under nonadditive coupling between PDC-bit wear and lithology. Results in Engineering, 32, Article 113176. https://doi.org/10.1016/j.rineng.2026.113176

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113176

Keywords: PDC bit, drilling torque, bit wear, lithology, nonadditive interaction, PFC3D simulation, torsional response, rock cutting, drilling automation, moment arm, contact topology, drilling digital twin

The problem begins with the behaviour factor, the famous q-factor of Eurocode 8, which scales down the elastic seismic demand to account for a structure’s capacity to deform inelastically and dissipate energy. In the newest generation of the code, q is decomposed into three contributions: one for generalized ductility, one for overstrength arising from the redistribution of forces in redundant structures, and one for other sources of reserve strength. It is the second term, often called the system overstrength ratio or OSR, that has proved so troublesome for masonry. When a masonry building is pushed laterally, the first wall to reach its strength does not usually signal the end of the road. If that wall retains deformation capacity, the surplus load flows to its stiffer or stronger companions, and the building keeps picking up lateral resistance until several walls have exhausted both their strength and their displacement capacity. The ratio between this ultimate base shear and the shear at first yield can range widely, from a theoretical minimum of 1.0 in structures with no redundancy to values between roughly 1.4 and 2.5 for most unreinforced masonry configurations, and occasionally beyond 3.0.

That variability is the crux of the difficulty. The overstrength ratio depends on the wall layout, the pattern of openings, the number of storeys, the presence of reinforced concrete ring beams or masonry spandrels, the stiffness of the floor diaphragms, and the connection details, all of which vary enormously with regional building traditions. It also depends on modelling choices: whether walls are discretised as continuum finite elements, equivalent frames or macro-elements, what constitutive laws are adopted, and how coupling between intersecting walls is treated. Previous studies have shown that calculated overstrength ratios do not even depend strongly on the assumed deformation capacity of individual walls, which makes the task of tabulating representative values for design codes nearly hopeless. A single conservative default value, derived from statistics across many configurations, could impose seismic demands far higher than any specific building actually needs, forcing designs to fail strength checks that nonlinear analysis would comfortably pass.

The Pavia team’s answer is elegant in its simplicity: set the overstrength contribution to unity, and instead of encoding redundancy in a code-specified factor, let the designer exploit it explicitly through force redistribution, bounded by the physics of wall deformation. The logic rests on a simple observation about walls acting in parallel within a storey. All walls connected to a rigid floor diaphragm share the same top displacement, so the system’s ultimate state is reached when the wall with the lowest displacement capacity gives out, regardless of how much reserve the others still hold. Wall displacement is expressed through the chord rotation at the wall base, multiplied by the wall’s effective height and a kinematic conversion factor close to unity for typical single-storey boundary conditions. The ultimate displacement of each wall follows from its ultimate chord rotation capacity, which is governed by its failure mechanism, whether shear, flexural or a hybrid of the two.

This kinematic picture immediately reveals why redistribution cannot be unlimited. Consider a storey containing a very short, stiff squat wall alongside taller, more flexible companions, a scenario common in practice wherever foundations step or openings vary in height. The squat wall attracts a disproportionate share of the elastic shear and is also the first to hit its displacement limit. Once it reaches its ultimate chord rotation, the whole system has exhausted its capacity, and the taller walls may never have developed their full strength. The maximum shear that can be transferred to any of those taller walls is therefore capped by a simple similarity-of-triangles argument: the increment is proportional to the difference between the limiting system displacement, set by the weakest wall’s ultimate capacity, and the displacement computed in the linear elastic analysis. A deliberately conservative simplification assumes the governing wall is the shortest one in the storey, failing in pure shear in double bending at the minimum possible ultimate chord rotation, a value for which reference figures are provided by the new Eurocode 8 Part 1-2.

Extending the criterion to buildings that twist under seismic loading required a careful treatment of torsion. When the centres of mass, stiffness and strength do not coincide, different walls experience different displacement demands, and the neat assumption of equal top displacements breaks down. The researchers distinguish torsionally restrained systems, which possess at least one adequately stiff, strong and well-spaced wall couple in the perpendicular direction capable of developing restraining torque, from torsionally unrestrained systems, where in-plan rotation runs free. For restrained systems, they propose dividing the floor plan into two zones around the critical wall. In the soft-edge zone, ultimate displacements are conservatively taken equal to the critical wall’s capacity; in the stiff-edge zone, they are assumed proportional to the elastic displacement field, which is safe because nonlinear analyses consistently show that in-plan twist diminishes as walls yield. For unrestrained systems, no general rule is offered, and the authors argue such layouts should simply be avoided in new construction.

The validation campaign is one of the most thorough aspects of the work. Two single-storey case-study buildings were deliberately configured at the borderline of plan regularity and torsional restraint, with wall heights ranging from 1.00 to 3.40 metres to generate marked eccentricities. Walls were modelled in the Ruaumoko3D program as nonlinear beam-column elements with lumped plasticity, assigned flag-shaped hysteretic rules for flexural response and modified Takeda or Schoettler-Restrepo rules for shear response, calibrated against full-scale cyclic tests of clay-unit masonry walls conducted at the EUCENTRE and University of Pavia laboratories. Incremental dynamic analyses were then run under seven bi-directional ground-motion pairs selected for two Eurocode soil classes, applied with all four sign combinations, across three period variants and three hysteretic assumptions, yielding 1,008 simulations in total. The results were strikingly consistent: once nonlinear behaviour was mobilised, the in-plan twist dropped markedly relative to the elastic case, the shortest wall always governed the attainment of ultimate conditions, and soft-edge displacements never exceeded 0.70 centimetres against the 1.02-centimetre limit, confirming a substantial margin of conservatism in the proposed redistribution bounds.

The practical payoff is demonstrated through worked examples, including a three-storey terraced house whose weak direction exhibits an overstrength ratio of 3.2. Analysed linearly with the overstrength factor set to unity and the new deformation-based redistribution applied storey by storey, with wall capacities recomputed at each step as force eccentricities changed, all walls and ring beams passed their checks up to a design base shear of 1,200 kilonewtons, roughly 2.3 times the demand at which verification would have failed without redistribution, and far beyond the maximum overstrength factor of 1.4 the new code would otherwise admit. By contrast, the older heuristic limits tied to a code-specified overstrength factor proved so restrictive in one example that a building verifiable by other means could not be checked at all, a consequence of fixed percentage thresholds being disconnected from the actual redistribution capacity of the system. The authors also discuss a cautious extension to low-rise multi-storey buildings, adding an upper bound on redistributable shear increments and capping the ultimate chord rotation at the severe-damage rather than near-collapse state to cover the additional uncertainties of multi-storey response.

The criterion now underpins the provisions of the forthcoming Eurocode 8 Part 1-2 for new masonry buildings, giving practitioners a rational alternative to both conservative default factors and full nonlinear analysis. The authors are careful to note that nonlinear static procedures, where applicable, remain more convenient, since no automated software yet exists for post-linear redistribution, and that further dynamic validation of multi-storey applications is a future task. But the significance of the work lies in closing a forty-year-old gap: since the late 1970s, when the inadequacy of linear methods for masonry was first recognised in Europe, the profession has redistributed forces on the basis of analogy and judgement. It can now do so on the basis of displacement compatibility and measured deformation capacity, bridging the persistent gap between the elastic models of everyday design and the stubbornly nonlinear reality of masonry under earthquake attack.

Subject of Research: A deformation-based criterion for limiting seismic force redistribution in masonry buildings after linear elastic analysis

Article Title: A deformation-based criterion for redistribution of seismic forces in masonry buildings after linear analysis

Article References: Damiani, N., Manzini, C. F., & Magenes, G. (2026). A deformation-based criterion for redistribution of seismic forces in masonry buildings after linear analysis. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02685-5

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02685-5

Keywords: masonry buildings, seismic design, force redistribution, linear analysis, Eurocode 8, overstrength ratio, chord rotation, torsional response, nonlinear dynamic analysis, unreinforced masonry, behaviour factor, earthquake engineering