## 1 Introduction  
Valley narrowing deformation is a phenomenon that riverbanks deform to their free faces and narrow the valley width. High arch dams, which are mainly located in narrow valleys, are sensitive to this kind of deformation because of their particular shape. Several arch dams were squeezed to crack by the valley narrowing deformation, such as the Beauregard arch dam in northwestern Italy [1] and Zeuzier arch dam in Switzerland [2]. In China, the same kind of deformation has also been reported at the Lijiaxia project [3], Jinping-I project [4], Xiluodu project [5], and several other high arch dams since their initial impoundments. It is a key step to figure out the valley narrowing mechanism to assess the structural safety of a certain dam [6]. Currently, the corresponding mechanisms for valley narrowing deformation of different arch dams are diverse. Classic theory on valley deformation mainly focuses on the slope stability directly affected by stress field changes and seepage field variations [7; 8; 9]. In the case of the Beauregard arch dam, a deep-seated gravitational slope deformation after impounding was confirmed using long-termmonitoring data by integrated techniques [10]. Because of the impoundment, the pore-pressure increased. The increased pore-pressure reduced the effective stresses along the basal shear zone. And the shear strength reduction of the rupture surface induced the plastic deformation of the slope [11]. Research works on the Zeuzier case by [PERSON] [2,12] show that the Zeuzier valley was narrowed due to the consolidation settlement of the bedrock, which was induced by tunnel excavation. It was the same case in the Swiss Alps valley. The deformation of several arch dams was observed after the excavation of the Gotthard base tunnel [13,14]. Further studies on horizontal deformation of the Alps valley reveal that cyclic water-table fluctuations in the mountain slopes could induce a cyclic deformation process [15,16,17]. The aforementioned studies examine the mechanism of valley deformation from the perspective of the hydro-mechanical coupling process in the bedrock of arch dams. Both elastic and plastic deformations in the reservoir banks can be induced by the pore-pressure variation because of impoundment, tunnel excavation, or seasonal precipitation changes. In the scope of dam engineering, the valley narrowing deformation is always explained to be a consequence of seepage variation while the effect of thermal field change is often neglected. In fact, the effect of subsurface temperature change on rock deformation has gradually been recognized by studies on tunnels [18], alpine geosystems [19], radioactive waste repositories [20], and many other kinds of fractured rock systems. [PERSON] [21] marks the daily fluctuation of surface temperature as the main cause of the rockfall at Rochers de Valabres slope in France. In the research on a rock slope at Randa (Switzerland), [PERSON] [22] demonstrates that the thermal effects driven by near-surface temperature cycles can lead to the deformation of deep rock slope. [PERSON] [23] suggests that a 0.5 \({}^{\circ}\)C temperature rise has the potential to induce slope instability. In Xiluodu, the traditional hydro-mechanical (HM) coupling theory has insufficient explanation because of the project's unique geological context and deformation pattern. On the one hand, pre-project exploration data spotted the existence of hot spring and abnormal high ground temperature beneath the dam site. On the other hand, the valley narrowing process does not coincide with the reservoir water level or seepage pressure fluctuation. Moreover, the valley narrowing deformation at Xiluodu high arch dam has reached 78 mm in seven years since the initial impoundment, which is near twice as much as the deformation of similar hydropower projects. Thus, new factors shall be taken into account to appropriately explain the deformation mechanisms and evaluate the dam's long-term safety.