Rheometry for large particle fluids and debris flows

Mitteilungen der Versuchsanstalt fur Wasserbau, Hydrologie und Glaziologie an der Eidgenossischen Technischen Hochschule Zurich

Volumn , Issue 187, 2005, Pages

  Schatzmann, Markus ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

DEBRIS FLOW; MUDFLOW; RHEOLOGY;

EID: 23144438576     PISSN: 03740056     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (120)

1. Ancey C. & Evesque P. (2000). Frictional-collisional regime for granular suspension flows down an inclined channel. Physical Review E, 62: 8349-8360.
2. Ancey C. & Jorrot H. (2001). Yield stress for particle suspension within a clay dispersion. Journal of Rheology, 45: 297-319.
3. Ansley R.W. & Smith T.N. (1967). Motion of spherical particles in a Bingham plastic. AIChE Journal, 13: 1193-1196.
4. Arattano M. & Franzi L. (2003). Resistance laws for debris-flow numerical simulation. Proc. of the 3rd Int. Conf. on debris flow hazards mitigation, Davos, Sept. 10-12. Rickenmann&Chen (editors). Millpress, Rotterdam: 565-576.
5. Armanini A., Dalri C., Fraccarollo L., Larcher M. & Zorzin E. (2003). Experimental analysis of the general features of uniform mud-flow. Proc. of the 3rd Int. Conf. on debris flow hazards mitigation, Davos, Sept. 10-12. Rickenmann&Chen (editors). Millpress, Rotterdam: 423-434.
6. Armanini A. (2004). Mechanics of wet layered granular flow. Lecture at the "Workshop on wet granular material in movement", Wet Granular Material Rheology Group, Federal Institute of Technology (EPFL), Lausanne, Switzerland, February 5.
7. Atapattu D.D., Chhabra R.P. & Uhlherr P.H.T. (1995). Creeping sphere motion in Herschel-Bulkley fluids: flow field and drag. Journal of Non-Newtonian Fluid Mechanics, 59: 245-265.
8. Bagnold R.A. (1954). Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. of the Royal Society London, Series A, 225: 49-63.
9. Banfill P.F.G. (1994). Rheological methods for assessing the flow properties of mortar and related materials. Construction and Building Materials, 8: 43-50.
10. Banfill P.F.G, Beaupré D., Chapdelaine F., Larrard F., Domone P., Nachbaur L., Sedran T., Wallevik O.H., Wallevik J.E. (2000). Comparison of concrete rheometers: International tests at LCPC (Nantes, France) in October 2000. NISTIR-Report 6819 of the NIST (National Institute of Standards and Technology). U.S Department of Commerce. 147 p.
11. Bardou E., Ancey C., Bonnard C. & Vuillet L. (2003). Classification of debris-flow deposits for hazard assessment in alpine areas. Proc. of the 3rd Int. Conf. on debris flow hazards mitigation, Davos, Sept. 10-12. Rickenmann&Chen (editors). Millpress, Rotterdam: 799-808.
12. Baudez J-C., Chabot F. & Coussot P. (2002). Rheological interpretation of the Slump Test. Applied Rheology, 12: 133-141.
13. Beaulne M. & Mitsoulis E. (1997). Creeping motion of a sphere in tubes filled with Herschel-Bulkley fluids. Journal of Non-Newtonian Fluid Mechanics, 72: 55-71.
14. Beris A.N., Tsamopoulos J.A., Armstrong R.C. & Brown R.A. (1985). Creeping motion of a sphere through a Bingham plastic. Journal of Fluid Mechanics, 158: 219-244.
15. Bergomi T. (2001). Numerische Untersuchung von Murgängen - Das Programm Flo-2D. Diplomarbeit an der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie. ETH Zürich.
16. Bezzola G.R. (2003). Flussbau. Vorlesungsskriptum. Professur für Wasserbau. ETH Zürich.
17. Bezzola G.R. & Minor H.-E. (2002). Hochwasser und Murgänge in Alpentälern. ETH-Bulletin, Magazin der Eidg. Technischen Hochschule (ETH) Zürich, 284: 32-35.
18. Blackery J. & Mitsoulis E. (1997). Creeping motion of a sphere in tubes filled with a Bingham plastic material. Journal of Non-Newtonian Fluid Mechanics, 70: 59-77.
19. Borgia A. & Spera F.J. (1990). Error analysis for reducing noisy wide-gap concentric cylinder rheometric data for nonlinear fluids: Theory and applications. Journal of Rheology, 34: 117-136.
20. Bozhinskiy A.Y., Nazarov A.N. (2000). Two-phase model of debris-flow. Proc. of the 2nd international conference on debris-flow hazards mitigation, Taipei, Taiwan, 16-18 august 2000. A.A. Balkema, Rotterdam, Brookfield: 263-269.
21. BWG, Bundesamt für Wasser und Geologie (2002). Hochwasser 2000. Ereignis-analyse/Fallbeispiele. Berichte des BWG, Serie Wasser, Nr. 2. Bern 2002.
22. Chhabra R.P. & Richardson J.F. (1999). Non-Newtonian Flow in the Process Industries. Butterworth-Heinemann. Oxford, Auckland, Boston, Johannesburg, Melbourne, New Delhi. 436 p.
23. Chhabra R.P. & Uhlherr P.H.T. (1988). Static equilibrium and motion of spheres in viscoplastic liquids. Encyclopedia of Fluid Mechanics, Volume 7: Rheology and Non-Newtonian Fluids. Chereminisinoff N. (editor): 611-633.
24. Clift R., Grace J.R. & Weber M.E. 1978. Bubbles, drops and particles. New York, San Francisco, London: Academic Press. 380 p.
25. Contreras S. M. & Davies T. R. H. (2000). Coarse-Grained Debris-Flows, Hysteresis and Time-Dependent Rheology. Journal of Hydraulic Engineering, ASCE, 126: 938-941.
26. Coussot P. (1992). Rhéologie des boues et laves torrentielles. Etude de dispersions et suspensions concentrées. Thèse. Laboratoire de Rhéologie. CEMAGREF. Grenoble. 415 p.
27. Coussot P. (1994a). Rhéologie des laves torrentielles. La Houille Blanche, 49: 32-37.
28. Coussot P. (1994b). Lois d'écoulement des laves torrentielles boueuses. La Houille Blanche, 49: 38-43.
29. Coussot P. & Laigle D. (1994). Etude des laves torrentielles sur modèle réduit en similitude des phénomènes naturels. La Houille Blanche, 49: 44-49.
30. Coussot P. & Piau J-M. (1995). A large-scale field concentric cylinder rheometer for the study of the rheology of natural coarse suspensions. Journal of Rheology, 39: 105-124.
31. Coussot P. & Boyer S. (1995). Determination of yield stress fluid behaviour from inclined plane test. Rheologica acta, 34: 534-543.
32. Coussot P. (1996). Les laves torrentielles - Connaissances à l'usage du practicien. Collection Etudes du Cemagref, serie 'Equipments pour l'eau et l'environnement', no23. CEMAGREF. Grenoble. 177 p.
33. Coussot P. & Meunier M. (1996). Recognition, classification and mechanical description of debris flows. Earth Science Reviews, 40: 209-227.
34. Coussot P., Proust S. & Ancey C. (1996). Rheological interpretation of deposits of yield stress fluids. Journal of Non-Newtonian Fluid Mechanics, 66: 55-70.
35. Coussot P. (1997). Mudflow Rheology and Dynamics. IAHR Monograph Series. A.A. Balkema, Rotterdam, Brookfield. 255 p.
36. Coussot P., Laigle D., Arattano M., Deganutti A. & Marchi L. (1998). Direct Determination of Rheological Characteristics of Debris Flow. Journal of Hydraulic Engineering, 124: 865-868.
37. Coussot P. & Ancey C. (1999). Rhéophysique des pâtes et des suspensions. EDP Sciences.7, avenue du Hoggar. Parc d'Activité de Courtaboeuf, BP 112. 91944 Les Ulis Cedex A. France. 264 p.
38. Coussot P., Raynaud J.S. & Ancey C. (2003). Combined MRI-rheometry determination of the behavior of mud. Proc. of the 3rd Int. Conf. on debris flow hazards mitigation, Davos, Sept. 10-12. Rickenmann&Chen (editors). Millpress, Rotterdam: 291-301.
39. Davies T.R.H. (1988): Debris flow surges - a laboratory investigation. Mitteilungen der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, Nr. 96. ETH Zürich.
40. Denlinger R.P. & Iverson R.M., (2001). Flow of variably fluidized granular masses across 3-D terrain. 2. Numerical predictions and experimental tests. Journal of Geomorphological Research, B, 106: 553-566.
41. Flügge S. (1963): Fluid Dynamics II. Encyclopedia of Physics. Springer Verlag. Berlin-Göttingen-Heidelberg.
42. Genevois R., Tecca P.R., Berti M. & Simoni A. (2000). Debris-flows in the Dolomites: Experimental data from a monitoring system. Proc. of the 2nd international conference on debris-flow hazards mitigation, Taipei, Taiwan, 16-18 august 2000. A.A. Balkema, RotterdamBrookfield: 283-292.
43. Gostner W., Bezzola G.R., Schatzmann M. & Minor H.E. (2003). Integral analysis of debris flow in an alpine torrent - the case study of Tschengls. Proc. of the 3rd Int. Conf. on debris flow hazards mitigation, Davos, Sept. 10-12. Rickenmann&Chen (editors). Millpress, Rotterdam: 1129-1140.
44. Hemphill T., Campos W. & Pilevahri A. (1993). Yield-power law model more accurately predicts mud rheology. Oil and Gas Journal, 91: 45-50.
45. Hübl J., Steinwendtner H. (2000). Estimation of rheological properties of viscous debris flows using a belt conveyor. Phys. Chem. Earth (B), 25: 751-755.
46. Hunt M.L., Zenit R., Campbell C.S. & Brennen C.E. (2002). Revisiting the 1954 suspension experiments of R.A. Bagnold. Journal of Fluid Mechanics, 452: 1-24.
47. Hutter K., Svendsen B. & Rickenmann D. (1996). Debris flow modeling: A review. Continuum Mech. Thermodynamics, 8: 1-35.
48. Iverson R.M. & LaHusen R.G. (1993). Friction in debris flows: Inferences from large-scale flume experiments. Proc. of the 1993 Conf. 'Hydraulic Engineering 93', San Francisco, ASCE, (2): 1604-1609.
49. Iverson R.M. (1997). The physics of debris flows. Reviews of Geophysics, 35: 245-296.
50. Iverson R.M., Reid M.E. & LaHusen R.G. (1997). Debris-flow mobilization from landslides. Annu. Rev. Earth Planet, 25: 85-138.
51. Iverson R.M., Reid M.E., Iverson N.R., LaHusen R.G., Logan M., Mann J.E. & Brien D.L.(2000). Acute sensitivity of landslide rates to initial soil porosity. Science, 290: 513-516.
52. Iverson R.M. & Vallance J.W. (2001). New views of granular mass flows. Geology, 29: 115-118.
53. Iverson, R.M. & Denlinger R.P. (2001). Flow of variably fluidized granular masses across 3-D terrain. 1. Coulomb mixture theory. Journal of Geomorphological Research, B, 106: 537-552.
54. Jan, C.-D. & Shen, H.S. (1993). Review dynamic modeling of debris flows. Proc. of the International workshop on debris flow, September 6-8, 1993, Kagoshima, Japan: 33-42.
55. Jenkins J.T. & Savage S.B. (1983). A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. Journal of Fluid Mechanics, 130: 187-202.
56. Johnson A.M. (1970). A method for interpretation of natural phenomena - intrusions in igneous rocks, fractures and folds, flow of debris and ice. Physical processes in geology. Freeman, Cooper and Co., San Francisco, California.
57. Julien P.Y. & Lan Y. (1991). Rheology of hyperconcentrations. Journal of Hydraulic Engineering, 117: 346-353.
58. Kahr G. (2001). Interpretation of debris flow clay mineral composition based on XRD spectrum analysis and program "Autoquan". Oral explications. Laboratory of clay minerals, Institute of Geotechniques, ETH Zürich, Zürich.
59. Kern M. (2000). Inverse grading in granular flow. Thesis No. 2287, Federal Institute of Technology (EPFL), Lausanne, Switzerland.
60. Kolenko A., Teysseire P. & Zimmermann M. (2004). Safety concept for debris flow hazards - the Täsch case study. Proc. of the 10th Congress Interpraevent. Riva del Garda, May 24-27, 2004, Trento, Italy.
61. Krieger I.M. & Maron S.H. (1952): Direct determination of the flow curves of non-Newtonian fluids. Journal of applied physics, 23: 147-149.
62. Krieger I.M. (1972). Rheology of monodisperse latices. Adv. Colloid Interface Science, 3: 111-136.
63. Laigle D. & Coussot P. (1994). Modélisation numérique des écoulements de laves torrentielles. La Houille Blanche, 49: 50-56.
64. Laigle D. (1996a). Two-dimensional modeling of debris flow spreading on alluvial fans. Proc. of 'Hydroinformatics 96'. A.A.Balkema, Rotterdam: 651-657.
65. Laigle D. (1996b). Note de calcul concernant un essai sur modèle réduit d'écoulement de lave torrentielle boueuse sur le torrent du Pissot, commune de Villeneuve (VD). Interne paper. 4 p.
66. Laigle D. & Coussot P. (1997). Numerical modeling of mudflows. Journal of Hydraulic Engineering, ASCE, 123: 617-623.
67. Laigle D. & Marchi M. (2000). Example of mud/debris-flow hazard assessment, using numerical models. Proc. of the 2nd Int. Conf. on debris flow hazards mitigation, Taipei, Aug. 16-18. Wieczorek&Naeser (editors). A.A.Balkema, Rotterdam/Brook-field: 417-424.
68. Laigle D., Hector A.-F., Hübl J. & Rickenmann D. (2003). Comparison of numerical simulation of muddy debris-flow spreading to records of real events. Proc. of the 3rd Int. Conf. on debris flow hazards mitigation, Davos, Sept. 10-12. Rickenmann&Chen (editors). Millpress, Rotterdam: 635-646.
69. Liao W.M. & Chou H.T. (2003). Debris flows generated by seepage failure of landslide dams. Proc. of the 3rd Int. Conf. on debris flow hazards mitigation, Davos, Sept. 10-12. Rickenmann&Chen (editors). Millpress, Rotterdam: 315-325.
70. Lin M.L. & Chang B.S. (2003). Triggering of debris flow caused by groundwater upwelling and surface runoff. Proc. of the 3rd Int. Conf. on debris flow hazards mitigation, Davos, Sept. 10-12. Rickenmann&Chen (editors). Millpress, Rotterdam: 327-338.
71. Liu K.F. & Mei C.C. (1989). Slow spreading of a sheet of Bingham fluid on an inclined plane. Journal of Fluid Mechanics, 207: 505-529.
72. Major J.J. & Pierson T. (1992). Debris flow rheology: Experimental analysis of fine-grained slurries. Water Resources Research, 28: 841-857.
73. Malet J.-P., Remaître A., Maquaire O., Ancey C. & Locat J. (2003). Flow susceptibility of heterogeneous marly formations: implications for torrent hazard control in the Barcelonnette Basin (Alpes-de-Haute-Provence, France). Proc. of the 3rd Int. Conf. on debris flow hazards mitigation, Davos, Sept. 10-12. Rickenmann&Chen (editors). Millpress, Rotterdam: 351-362.
74. Mezger T. (2000). Das Rheologie-Handbuch. Für Anwender von Rotations- und Oszillations-Rheometern. Vincentz Verlag, Hannover. 271 p.
75. Metzner A.B. & Otto R.E. (1957). Agitation of Non-Newtonian Fluids. AIChE Journal, 3: 3-10.
76. Müller M., Tyrach J. & Brunn P.O. (1999). Rheological characterization of machine-applied plasters. ZKG International, 52: 252-258.
77. Nakagawa H. & Takahashi T. (1997). Estimation of a debris flow hydrograph and hazard area. Proc. of the 1st Int. Conf. on debris flow hazards mitigation, San Francisco, Aug. 7-9. Chen-lung Chen (editors). ASCE, New York: 64-73.
78. Nakagawa H., Takahashi T., Satofuka Y. & Kawaike K. (2003). Numerical simulation of sediment disasters caused by heavy rainfall in the Camuri Grande basin, Venezuela 1999. Proc. of the 3rd Int. Conf. on debris flow hazards mitigation, Davos, Sept. 10-12. Rickenmann&Chen (editors). Millpress, Rotterdam: 671-682.
79. Nguyen Q.D. & Boger D.V. (1987). Characterization of yield stress fluids with concentric cylinder viscometers. Rheologica acta, 26: 508-515.
80. Nguyen Q.D. & Boger D.V. (1992). Measuring the flow properties of yield stress fluids. Annual Review of Fluid Mechanics, 24: 47-88.
81. O'Brien J.S. & Julien P.Y. (1985). Physical properties and mechanics of hyperconcentrated sediment flows. Proc. of the specialty conference on delineation of landslide, flash flood and debris flow hazards in Utah, Utah State University, Logan, Utah, June 14-15, 1984. Utah Water Research Laboratory, General Series, UWRL/G-85/03: 260-279.
82. O'Brien J.S. & Julien P.Y. (1988). Laboratory analysis of mudflow properties. Journal of Hydraulic Engineering, 114: 877-887.
83. O'Brien J.S., Julien P.Y. & Fullerton W.T. (1993). Two-dimensional water flood and mudflow simulation. Journal of Hydraulic Engineering, 119: 244-261.
84. Parsons J.D., Whipple K.X. & Simoni A. (2001). Experimental study of the grainflow, fluid-mud transition in debris flows. Journal of Geology, 109: 427-447.
85. Pashias N., Boger D.V., Summers J. & Glenister D.J. (1996). A fifty cent rheometer for yield stress measurement. Journal of Rheology, 40: 1179-1189.
86. Phillips C. J. & Davies T.R.H. (1991). Determining rheological parameters of debris flow material. Geomorphology, 4: 101-110.
87. Physica Messtechnik GMBH (1999). A new ball measuring system for large particle suspensions. Applied Rheology, 9: 145-146.
88. Rickenmann D. (1999). Empirical relationships for debris flows. Natural Hazards, 19: 47-77.
89. Rickenmann D. & Weber D. (2000). Flow resistance of natural and experimental debris-flows in torrent channels. Proc. of the 2nd international conference on debris-flow hazards mitigation, Taipei, Taiwan, 16-18 august 2000. A.A. Balkema, RotterdamBrookfield: 245-254.
90. Roberts G.P., Barnes H.A. & Mackie C. (20001). Using the Microsoft Excel 'Solver' tool to perform non-linear curve fitting, using a range of non-Newtonian flow curves as examples. Applied Rheology, 11: 271-276.
91. Savage S.B. & McKeown S. (1983). Shear stresses developed during rapid shear of concentrated suspensions of large spherical particles between concentric cylinders. Journal of Fluid Mechanics, 127: 453-472.
92. Savage S.B. & Hutter K. (1989). The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics, 199: 177-215.
93. Schatzmann, M., Fischer, P., Bezzola, G.R. & Minor H.E. (2003a). The ball measuring system - a new method to determine debris flow rheology? Proc. of the 3rd Int. Conf. on debris flow hazards mitigation, Davos, Sept. 10-12. Rickenmann&Chen (editors). Millpress, Rotterdam: 387-398.
94. Schatzmann M., Fischer P. & Bezzola G.R. (2003b). Rheological behaviour of fine and large particle suspensions. Journal of Hydraulic Engineering, ASCE, 129: 796-803.
95. Schowalter W.R., Christensen G. (1998). Toward a rationalization of the slump test for fresh concrete: Comparison of calculations and experiments. Journal of Rheology, 42: 865-870.
96. Schulze B., Brauns J. & Schwalm I. (1991). Neuartiges Baustellen-Messgerät zur Bestimmung der Fliessgrenze von Suspensionen. Sonderdruck aus Geotechnik 3/1991. Heidelberger Zement, Berliner Strasse 6, D-6900 Heidelberg.
97. Shen H. & Ackermann N.L. (1983). Constitutive relationships for fluid-solid mixtures. Journal of Engineering Mechanics, ASCE, 108: 748-763.
98. Springman S.M., Jommi C., Teysseire P. (2003). Instabilities on moraine slopes induced by loss of suction: a case of history. Géotechnique 53: 3-10.
99. Steiger (1999). Maschänserrüffe. Untersuchungsbericht 20686. Büro F. Steiger, Beratender Ingenieur+Erdbaulabor, Chur.
100. Steiger (2001). Solid density of the Maschänserrüfe material. Oral explications. Büro F. Steiger, Beratender Ingenieur+Erdbaulabor, Chur.
101. Stiefel A. & Stockmeyer M. (1995). Geotechnische und chemische Analyse von Opalit. Büchi und Müller AG, Regensdorf.
102. Suwa H. (2003). Repetition of debris flows on sunny days at a torrent in Karakorum. Proc. of the 3rd Int. Conf. on debris flow hazards mitigation, Davos, Sept. 10-12. Rickenmann&Chen (editors). Millpress, Rotterdam: 1025-1035.
103. SwissRe (2004). Natural catastrophes and man-made disasters in 2003. Sigma report, 01/2004, SwissReinsurance company, Economic research&consulting, Zürich.
104. Takahashi, T. (1980). Debris flow on prismatic open channel. Journal of Hydraulic Engineering, ASCE, 106: 381-396.
105. Takahashi T. (1991). Debris Flow. IAHR Monograph Series. A.A.Balkema, Rotterdam. 165 p.
106. Takahashi T., Nakagawa H., Harada T. & Yamashiki Y. (1993). Routing debris flows with particle segregation. Journal of Hydraulic Engineering, ASCE, 118: 1490-1507.
107. Tattersall G.H. & Bloomer S.J. (1979). Further development of the Two-Point test for workability and extension of its range. Magazine of Concrete Research, 31: 202-210.
108. Tattersall G.H. & Banfill P.F.G. (1983). The rheology of fresh concrete. Pitman, London. 356 p.
109. Tognacca C. (1999). Beitrag zur Untersuchung der Entstehungsmechanismen von Murgängen. Mitteilungen der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, Nr. 164. ETH Zürich. 259 p.
110. Tyrach J. (2001). Rheologische Charakterisierung von zementären Baustoffsystemen. Dissertation. Technische Fakultät der Universität Erlangen-Nürnberg. 149 p.
111. Uhlherr P.H.T., Park K.H., Tiu C. & Andrews J.R.G. (1984). Yield stress fluid behaviour on an inclined plane. in Advances in Rheology, B. Mena, A. Garcia-Rejon, C. Rangel-Nagaile (editors), Mexico City, 2. 183-190.
112. Vanoni V.A. (Ed.) (1975). Sedimentation Engineering. ASCE, New York, 1975.
113. VAW (1992). Murgänge 1987 - Dokumentation und Analyse. Bericht Nr. 97.6 der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie. ETH Zürich.
114. Wacker (1993). Silikonöle AK. Produktbeschreibung. Wacker-Chemie GmbH, München.
115. Wallevik O.H. and Gjorv O.E. (1990). "Development of a coaxial cylinder viscometer for fresh Concrete." Proc. of the Rilem Colloquium, October 1990, Chapman and Hall, Hannover: 213-224.
116. Wallevik J.E. (brother from O.H.) (1998). Rheology of concrete and matrix systems, the single-phase approach & measuring technique. Proc. of the Borregaard symposium on workability and workability retention, Borregaard, September 1998.
117. Whipple K.X. (1997). Open-Channel flow of Bingham fluids: applications in debris flow research. Journal of Geology, 105: 243-262.
118. Whittaker J.G., Jäggi M.N.R. (1986). Blockschwellen. Mitteilungen der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, Nr. 91, ETH Zürich.
119. Wilson S.D.R., Burgess S.L. (1998). The steady, spreading flow of a rivulet of mud. Journal of Non-Newtonian Fluid Mechanics, 79: 77-85.
120. Windhab E.J. (2001). Verfahrenstechnik IV. Vorlesungsskriptum für Studierende der Departemente Chemie und Agrarwissenschaften. Institut für Lebensmittelwissenschaft der ETH Zürich. 124 p.