- 1 PNEUMATIC TIRE TECHNICAL FIELD [0001] The present invention relates to a pneumatic tire and, in particular, 5 to a pneumatic tire with improved mud-expelling performance. BACKGROUND ART [0002] Tires for vehicles adapted for running on muddy ground are gener ally required to have traction performance for gripping the ground with 10 grooves in the tread surfaces thereby allowing the tires to kick the ground, as well as mud-expelling performance for discharging mud clogging the grooves thereby preventing the grooves from being clogged with mud. [0003] In view of the above, tires for light trucks adapted for running on muddy ground are conventionally provided with lug grooves that extend in the 15 tire width direction and open at one end to the tread edge on the tread surface. The grooves serve to catch the mud and thereby allow the trucks to kick the ground. Furthermore, there have been proposed pneumatic tires wherein the lug grooves have a groove wall with a wall angle (i.e., the angle formed with the tread surface and the groove wall), which gradually increases from the tire 20 equator side toward the edge of the tread in order to prevent the lug grooves from being clogged with mud (refer, for example, to PTL 1: JP 2001-55014 A). More specifically, the pneumatic tire according to PTL 1 has lug grooves whose walls are gradually inclined toward land portions, which are disposed between the lug grooves, largely toward the tread edge. Such grooves of the 25 pneumatic tire widen their widths gradually toward the tread edge and gradu ally toward the outside of the tire in the tire radial direction. This allows the mud clogging the lug grooves to be readily expelled to the outside of the tire in the tire width direction and in the tire radial direction as the tire rotates. 30 CITATION LIST Patent Literature(s) [0004] PTL 1: JP 2001-55014 A P0124384-PCT (1/15) 5436639_1 (GHMatters) P97203.AU -2 SUMMARY OF INVENTION (Technical Problem) [0005] Unfortunately, the aforementioned conventional pneumatic tire having the lug wall angle that increases gradually toward the tread edge has 5 not achieved sufficiently improved mud-expelling performance. It is there fore an object of the present invention to provide a pneumatic tire with en hanced mud-expelling performance. (Solution to Problem) [0006] The present invention is intended to advantageously solve the 10 aforementioned problem. The pneumatic tire according to the present in vention includes a tread surface with a lug groove extending in a tire width direction and terminating at one end that opens to a tread edge. The lug groove includes groove walls lying on both sides in a tire circumferential di rection. At least one of the groove walls has a surface portion with a curved 15 surface of a predetermined shape. The curved surface of the predetermined shape is defined by a cross-sectional curve as seen in the direction perpen dicular to an opening edge of the lug groove leading to the tread surface, or perpendicular to an extended line of the opening edge. The cross-sectional curve is convex toward the side away from the lug groove and has a curvature 20 that gradually decreases from a tire equator side toward the tread edge. As used herein with reference to the lug groove, the phrase "extending in the tire width direction" is intended to describe not only an arrangement where the lug groove extends simply along the width of the tire, but also an arrangement where the lug groove extends obliquely to the direction par 25 allel to the width of the tire. Also, the phrase "the curvature of the cross-sectional curve gradually decreases" is intended to describe that, when the cross-sectional curve is divided equally into two, three, four or more sec tions, either in the width direction (i.e., the direction perpendicular to the opening edge of the lug groove to the tread surface or to the extended line of 30 the opening edge) or in the height direction (i.e., tire radial direction), the curvatures of the curved surface portion at such sections exhibit a gradual decrease. P0124384-PCT (2/15) 5436639_1 (GHMatters) P97203.AU -3 (Advantageous Effect of Invention) [0007] The pneumatic tire according to the present invention provides highly-improved mud-expelling performance for vehicles adapted for running on muddy ground or the like. 5 BRIEF DESCRIPTION OF DRAWINGS [0008] The present invention will be further described below with refer ence to the accompanying drawings, wherein: FIG. 1 is a partial plan view of a representative tread of a pneumatic tire 10 according to the present invention; FIG. 2 is an enlarged plan view of a shoulder block land of the pneumatic tire shown in FIG. 1; FIG. 3A illustrates the shoulder block land of FIG. 2 viewed from the direction of arrow A shown in FIG. 2, and FIG. 3B illustrates the shoulder 15 block land of FIG. 2 viewed from the direction of arrow B shown in FIG. 2; FIGS. 4A, 4B, and 4C are cross-sectional views of the shoulder block land shown in FIG. 2, taken along lines I-I, II-II and III-III, respectively; and FIGS. 5A and 5B are cross-sectional views of the shoulder block land shown in FIG. 2, taken along lines IV-IV and V-V, respectively. 20 DESCRIPTION OF PREFERRED EMBODIMENT [0009] An embodiment of the present invention will be described in fur ther detail hereinafter, with reference to the accompanying drawings. The present invention provides a pneumatic tire that achieves improved 25 mud-expelling performance and can be advantageously used particularly for vehicles adapted for running on muddy ground. [0010] FIG. 1 is a partial plan view of a tread of the exemplary pneumatic tire of the present invention. The pneumatic tire shown in FIG. 1 may be preferably, but not necessarily, used as tires for light trucks. 30 [0011] The pneumatic tire shown in FIG. 1 includes a tread surface 100 formed with a center main groove 1 extending in the tire circumferential di rection on the equatorial line CL of the tire, and two main grooves 2 extending in the tire circumferential direction, which are disposed on opposite outer sides of the center main groove 1 in the tire width direction (i.e., the sides P0124384-PCT (3/15) 5436639_1 (GHMatters) P97203.AU -4 near the tread edges TEs). The tread surface 100 also includes multiple lug grooves 3 each extending in the tire width direction between one of the main grooves 2 and one of the tread edges TEs, and multiple lateral grooves 4 each extending in the tire width direction between the center main groove 1 and one 5 of the main grooves 2, which are adjacent to the center main groove 1. Each main groove 2 may be referred to as "adjacent main groove". As used herein with reference to the lug groove, the phrase "extending in the tire circumferential direction" is intended to describe not only an ar rangement where the lug groove extends simply along the circumference of 10 the tire, but also an arrangement where the lug groove extends obliquely to the direction parallel to the tire circumferential direction. [0012] The tread surface 100 further includes shoulder block lands 10 and center block lands 20. The shoulder block lands 10 are defined by the main grooves 2, lug grooves 3, and tread edges TEs. The center block lands 20 are 15 defined by the center main groove 1, main grooves 2, and lateral grooves 4. [0013] In the illustrated embodiment, the center main groove 1 has a sub stantially linear shape in a plan view of the pneumatic tire according to the present invention, and extends continuously in the tire circumferential direc tion. However, the center main groove 1 is not limited to any particular 20 shape, and may have a zigzag shape in the plan view of the pneumatic tire. Moreover, the center main groove may not necessarily be formed along the tire equatorial line CL in the pneumatic tire according to the present invention. However, the center main groove is preferably formed, for example, at the center of the tread surface in order to achieve high drainage performance. 25 Such a center main groove formed at the center of the tread surface should achieve high drainage performance even when the load on the tire is so light that the tire can contact only a small area of the ground, or specifically, even when the vehicle fitted with the tires is not loaded with any cargos (i.e., in the unloaded state of the vehicle). The center main groove is preferably formed 30 as a straight line in a plan view to achieve the high drainage performance. [0014] In the illustrated embodiment, the pair of main grooves 2 on the opposite sides of the center main groove 1 have substantially zigzag shape in the plan view of the pneumatic tire according to the present invention, and continuously extend in the tire circumferential direction. However, these P0124384-PCT (4/15) 5436639_1 (GHMatters) P97203.AU -5 main grooves 2 are not limited to any particularly shape, and may have a straight shape in the plan view of the pneumatic tire. [0015] Each lug groove 3 opens at one end to one of the tread edges TEs and opens at the other end to one of the main grooves 2. In the illustrated 5 embodiment, the lug groove 3 has a curved shape that is convex toward one direction along the tire circumference in the plan view of the tire, and extends obliquely to the direction parallel to the width of the tire. However, the lug groove 3 is not limited to any particular shape. [0016] Each lateral groove 4 opens to the center main groove 1 at one end 10 and opens to one of the main grooves 2 at the other end, which is disposed adjacent to the center main groove 1 and which extends in the tire circumfer ential direction. Each main groove 2 may be referred to as an "adjacent main groove". The lateral groove 4 has a curved shape in the plan view of the pneumatic tire according to the present invention, and extends obliquely to the 15 direction parallel to the width of the tire. However, the lateral groove 4 is not limited to any particular shape. Furthermore, the width of the opening of the lateral groove 4 to the tread surface 100 is narrowed on the side of the center main groove 1. However, the location where the opening is narrowed is not limited to such arrangement. The term "width of the opening of the 20 lateral groove 4" refers to the distance between the opposite groove walls at the opening end of the lateral groove 4, as measured in the tire circumferential direction. [0017] Each shoulder block land 10 formed on the tread surface 100 of the tire has substantially a trapezoidal shape on the tread surface. Each center 25 block land 20 formed on the tread surface 100, in turn, has substantially a staysail shape on the tread surface. [0018] In the illustrated embodiment, the groove walls on opposite sides of the lug groove 3 in the tire circumferential direction, or the side walls of the shoulder block land 10 in the tire circumferential direction, have prede 30 termined shapes. Specifically, one of the groove walls that lies on one side of the groove wall 3 in the tire circumferential direction has a curved surface portion 35 having a curved surface of a predetermined shape. The other groove wall that lies on the other side of the lug groove 3 in the tire circum P0124384-PCT (5/15) 5436639_1 (GHMatters) P97203.AU -6 ferential direction has a tapered portion 36 having a tapered surface of a pre determined shape. In the present invention, as long as at least one of the groove walls of the lug groove has a curved surface, the other groove wall may be of any shape. 5 Further, the curved surface portion or the tapered portion on the groove wall may be provided over the full width of the groove wall, or may be provided over a portion of the groove wall. To maximize the potential advantage of the curved surface portion or the tapered portion, however, the curved surface portion or the tapered portion is preferably provided over the full width of the 10 groove wall. [0019] With reference to FIG. 2, which illustrates an enlarged plan view of the shoulder block land 10, the curved surface portion 35 is provided over substantially the full width of the one of the groove walls lying on the one side of the lug groove 3 in the tire circumferential direction. This can be 15 also seen in FIG. 3A that illustrates the shoulder block land 10 viewed from the direction of arrow A of FIG. 2. As shown in FIGS. 1, 2 and 3A, the groove wall with the curved surface portion 35 has a slope 37 at the opening of the lug groove 3 to the main groove 2. The height of the slope 37 from the bottom of the lug groove 3 gradually 20 lowers toward the main groove 2. More specifically, in the plan view of the shoulder block land 10, the groove wall with the curved surface portion 35 has the slope 37 in the area surrounded by (i) the extended line of the outer edge of the side wall of the shoulder block land 10 in the tire radial direction near the main groove 2, (ii) an imaginary line (not shown) passing the end of the 25 opening edge 3 1 of the lug groove 3 near the main groove perpendicularly to the opening edge 31, and (iii) the inner edge of the groove wall in the tire ra dial direction. The curved surface portion 35 extends over substantially the full width of the groove wall including the slope 37. [0020] As shown in FIGS. 4A, 4B and 4C, which show the cross sections 30 taken along lines I-I, II-II, III-III of FIG. 2, respectively, the curved surface of the predetermined shape forming the curved surface portion 35 satisfies the following conditions (1) and (2). (1) The cross-sectional curve 35A as seen in the direction perpendicular to the opening edge 31 of the lug groove 3 leading to the tread surface 100, or P0124384-PCT (6/15) 5436639_1 (GHMatters) P97203.AU -7 perpendicular to the extended line EL of the opening edge 31, that is convex toward the side away from the lug groove 3 (i.e., toward the inside of the shoulder block land 10). (2) The cross-sectional curve 35A having a curvature that gradually de 5 creases from the tire equatorial line CL side toward the tread edge TE. [0021] As shown in FIGS. 2 and 4A to 4C, the curved surface of the pre determined shape forming the curved surface portion 35 of the exemplary pneumatic tire also satisfies the following conditions (3) and (4). (3) The distance between the line of the tire radial direction passing the 10 outer edge 35B of the cross-sectional curve 35A in the tire radial direction and the cross-sectional curve 35A, in the direction perpendicular to the line of the tire radial direction, in which the distance gradually increases radially in wardly of the tire. In other words, the wall of the lug groove 3 inclines to ward the direction in which the shoulder block land 10 protrudes toward the 15 inside of the lug groove 3. (4) As seen in the plan view of the tread surface 100, the distance be tween the opening edge 31 of the lug groove 3 to the tread surface 100 or the extended line EL of the opening edge 3 land the inner edge 33 of the curved surface portion 35 in the tire radial direction, in the direction perpendicular to 20 the opening edge 31 or to the extended line EL of the opening edge 31, in which the distance gradually decreases from the tire equatorial line CL side toward the tread edge TE. [0022] In the present invention, the aforementioned curved surface is not limited to any particular shape, though it may be defined by a cross-sectional 25 curve 35A, as seen in the direction perpendicular to the opening edge 31 of the lug groove 3 or to the extended line EL of the opening edge 31, which satisfies the following conditions (5) to (7). (5) The cross-sectional curve 35A passes the intersection point P of the line that bisects the cross-sectional curve 35A in the width direction in the 30 cross section (i.e., in the direction parallel to the direction that is perpendic ular to the opening edge 31 or to the extended line EL of the opening edge 31) and the innermost line in the tire radial direction out of three lines that divide the cross-sectional curve 35A into four sections in the height direction (i.e., in the tire radial direction) in the cross section. P0124384-PCT (7/15) 5436639_1 (GHMatters) P97203.AU -8 (6) The cross-sectional curve 35A contacts the line extending in the height direction in the cross section (i.e., the line of the tire radial direction) at the outer edge 35B in the tire radial direction. (7) The cross-sectional curve 35A contacts the line extending in the 5 width direction in the cross section (i.e., the line parallel to the line that is perpendicular to the opening edge 31 of the lug groove 3 or to the extended line EL of the opening edge 31) at the inner edge 35C in the tire radial direc ti on. [0023] As shown in FIG. 2, which illustrates the plan view of the shoulder 10 block land 10 in enlarged scale, the tapered portion 36 is provided over the full width of the other one of the groove walls that lies on the other side of the lug groove 3 in the tire circumferential direction. This can be also seen in FIG. 3B that illustrates the shoulder block land 10 viewed from the direction of arrow B shown in FIG. 2. 15 [0024] In the plan view of the tread surface 100 as shown in FIG. 2, the length of the tapered portion 36 in the direction perpendicular to the opening edge 32 of the lug groove 3 to the tread surface 100 (i.e., the opening edge opposite the opening edge 31 in the tire circumferential direction) gradually increases from the tire equatorial line CL side toward the tread edge TE. As 20 shown in FIG. 3B, the height of the lug groove 3 of the tapered portion 36 measured from the bottom of the groove (or specifically, the height of the groove wall measured from the inner edge 34 in the tire radial direction) gradually decreases from the tire equatorial line CL side toward the tread edge TE. 25 As shown in FIGS. 5A and 5B, which illustrate cross sections taken along lines IV-IV and V-V of FIG. 2, respectively, the other one of the groove walls that lies on the other side of the lug groove 3 in the tire circumferential direction extends along the tire radial direction except for the tapered portion 36. 30 [0025] Further, as shown in FIG. 1, each center block land 20 of the ex emplary pneumatic tire includes a protrusion 21 that protrudes toward the lateral groove 4 provided on one side of the center block land 20 in the tire circumferential direction. More specifically, the center block land 20 in cludes substantially a triangle protrusion 21, in a plan view, that protrudes P0124384-PCT (8/15) 5436639_1 (GHMatters) P97203.AU -9 inside the lateral groove 4. The protrusion 21 is formed on the one side of the center block land 20 in the tire circumferential direction near the center main groove 1. The protrusion 21 narrows the opening width of the lateral groove 4 at the center main groove 1. 5 According to the present invention, the protrusion may be provided on both sides of the center block land in the tire circumferential direction. [0026] In the illustrated embodiment, as shown in FIG. 1, the side wall of the center block land 20 on which the protrusion 21 is provided, i.e., the groove wall of the lateral groove 4 on which the protrusion 21 is formed, has a 10 curved surface 41 whose length in the direction perpendicular to the extending direction of the lateral groove 4 gradually increases toward the protrusion 21. The shape of the groove wall is, however, not particularly limited thereto. [0027] In the illustrated embodiment, one of the walls of the lug groove 3 including the curved surface portion 35 having the curved surface of the pre 15 determined shape ensures the intended running performance on muddy ground (particularly traction performance) while achieving enhanced mud-expelling performance. Specifically, according to the illustrated embodiment, rather than including a curved surface having a constant curvature or a plane surface having a constant angle of inclination with respect to the tread surface, the 20 groove wall of the lug groove 3 includes a curved surface portion 35 that is convex toward the side away from the lug groove 3 and having a curvature that gradually decreases toward the tread edge TE. Such a change in curva ture along the curved surface portion 35 achieves enhanced mud-expelling performance while ensuring traction performance. More specifically, the 25 curved surface portion 35 has a greater curvature in its cross-sectional curve 35A (i.e., having a smaller curvature radius) on the tire equatorial line CL side to have the lug groove be laid down lengthwise on the equatorial line CL side of the tire. This shape enables the lug groove 3 to easily catch mud into the groove near the tire equatorial line CL for vehicles that run on muddy ground, 30 while ensuring traction performance. On the other hand, the curved surface portion 35 has a smaller curvature in its cross-sectional curve 35A (i.e., hav ing a greater curvature radius) on the tread edge TE side to have the lug groove be set upright near the tread edge TE. This shape enables the lug groove 3 to increase its groove volume and allows the easy release of mud P0124384-PCT (9/15) 5436639_1 (GHMatters) P97203.AU -10 from the lug groove 3. Furthermore, the curved surface portion 35 has a smaller curvature in its cross-sectional curve 35A toward the tread edge and three-dimensionally changes the shape of the groove wall on which the curved surface portion 35 is formed. This change in shape promotes the release of 5 the mud (mud-column) caught in the lug groove 3 through the tread as the tire rotates. [0028] In the illustrated embodiment, the curved surface of the predeter mined shape forming the curved surface portion 35 is defined by the distances as defined by the aforementioned conditions (3) and (4). Specifically, the 10 groove wall of the lug groove 3 inclines to the direction in which the shoulder block land 10 protrudes within the lug groove 3. Thus, according to the exemplary pneumatic tire, the curved surface of the predetermined shape forming the curved surface portion 35 can be made as a smooth surface to achieve enhanced mud-expelling performance compared with the case where 15 the lug groove 3 is formed by hollowing the shoulder block land 10 in the tire circumferential direction. [0029] Further, in the illustrated embodiment, the groove wall of the lug groove 3 includes a slope 37 and the curved surface portion 35 extending over the slope 37. This slope 37, which is formed by extending the wall of the lug 20 groove 3 toward the main groove 2, allows the lug groove 3 to catch mud more positively, thereby improving the traction performance of the tire. In addi tion, the curved surface of the predetermined shape extending widely toward the main groove 2 achieves highly-improved mud-expelling performance. [0030] Still further, in the illustrated embodiment, one of the walls of the 25 lug groove 3 is formed as the curved surface portion 35 while the other one of walls of the lug groove 3 is formed as the tapered portion 36. The walls having such shapes allow prevention of substantial decrease in the groove volume of the lug groove 3, thereby achieving highly-improved mud-expelling performance. Specifically, while a lug groove 3 having the curved surface 30 portion 35 on both sides of its groove walls would decrease in its groove volume near the tire equatorial line CL where the curvature is greater, the lug groove 3 having the curved surface portion 35 only on one side of the walls can avoid such a decrease in the lug volume of the lug groove 3. In addition, the tapered portion 36 with the sloped surface formed on the other side of the P0124384-PCT (10/15) 5436639_1 (GHMatters) P97203.AU - 11 groove walls facilitates the discharge of the mud caught in the lug groove 3, compared with the lug groove without the tapered portion 36. [0031] Furthermore, in the illustrated embodiment, the center main groove 1 formed on the tread surface 100 achieves high drainage performance. 5 The center block land 20 includes the protrusion 21 that narrows the opening width of the lateral groove 4 to the center main groove 1. This narrowed opening prevents mud coming from the tread edge TE side from entering into the center main groove 1 for vehicles adapted for running on muddy ground. This also prevents the center main groove 1 from being 10 clogged with mud and from failing to provide the required drainage perfor mance. In addition, according to the exemplary pneumatic tire, the groove wall of the lateral groove 4 with the protrusion 21 is formed as the curved surface 41. This enables the center block land 20 to maintain its rigidity while including the protrusion 21. 15 [0032] While the present invention has been described with reference to a preferred embodiment illustrated in the drawings, the pneumatic tire accord ing to the present invention is not limited to such specific example. Need less to say, various modifications may be made to the pneumatic tire accord ing to the present invention as appropriate. 20 INDUSTRIAL APPLICABILITY [0033] The present invention provides a pneumatic tire with highly im proved mud-expelling performance for vehicles adapted for running on muddy ground and the like. 25 PO124384-PCT (11/15) 5436639_1 (GHMatters) P97203.AU - 12 REFERENCE SIGNS LIST [0034] 1 Center main groove 2 Main groove (adjacent groove) 3 Lug groove 5 4 Lateral groove 10 Shoulder block land 20 Center block land 21 Protrusion 31 Opening edge 10 32 Opening edge 33 Inner edge in tire radial direction 34 Inner edge in tire radial direction 35 Curved surface portion 35A Cross-sectional curve 15 35B Outer edge in tire radial direction 35C Inner edge in tire radial direction 36 Tapered portion 37 Slope 41 Curved surface 20 100 Tread surface P0124384-PCT (12/15) 5436639_1 (GHMatters) P97203.AU