The problem during the First World War was that initially, that's not what artillery was meant to do and because it's not what it was meant to do, people didn't really know how to do it.

When the war broke out, just about all the major belligerants thought that it would be a war similar to the Franco-Prussian War forty years earlier. During that conflict, Prussia had outmaneuvered the French and won a few decisive battles that led to its victory. As a result of that expereince armies had adopted artillery weapons such as the quick firing French 75mm field gun that could be moved quite quickly to respond to maneuver warfare. The problem with these weapons was that they fired on a fairly flat trajectory as they were designed to fire shells that would explode over the heads of enemy infantry and shower them in shrapnel. To destroy a trench, you need to be able to fire the shell on a higher trajectory so that it falls almost vertically into the trench and explodes IN the trench.

Diagram of artillery trajectories by type

So the war breaks out and armies are largely equipped with guns that fire shrapnel shells along a flat trajectory, great for shooting at columns of advancing infantry but then thanks to the threat of those shells and the range of rifles and machine guns, soldiers start digging holes to shelter in. Eventually these connect up and from the trench systems that we are familiar with. Added to this, armies start installing fields of barbed wire in front of the trenches that infantry can't get through. Shrapnel shells can't cut the barbed wire and they do nothing against trenches. It didn't take long for the belligerents to start producing high explosive shells to their armies that could destroy trench works but the guns required took longer. The British had a bit of an upper hand in this regard as before the war they had already approved designed for a 4.5-inch howitzer. All sides also needed bigger guns to fire bigger shells at greater range. The French had almost completely ignored the procurement of heavy artillery before the war and paid for it in the opening months when they found German artillery out ranged their 75mm field guns.

By 1916, all sides had massively increased the amount of guns they had of all types and also the number of shells. Did that mean that the trenches could finally be broken? No. The Battle of the Somme is a good case study to show why. The main British offensive of 1916 was intended to break through the German lines through sheer weight of firepower. For five days prior to the attack on 1 July, the German front line was pounded by almost 1,500 artillery pieces from trench mortars up to the 60-pounder field gun. This sounds like a lot but in reality, the German front line to be attacked was about 24,000 yards or 21 km and behind the front line was a further 150,000 yards or 137km of trenches that needed to be shelled. Broken down, the British had only 233 heavy guns to destroy the German dug outs and strong points and 1000 field guns, the faithful 18-pounder, to cut the wire entanglements. The remaining guns were supposed to destroy the German artillery. That the British artillery failed to achieve any of its objectives goes without saying. Faulty shells and guns, poor visibility and the lack of a proximity fuse meant most of the wire went uncut and the Germans, though shaken, remained safe underground. When the infantry went over the top, the Germans emerged from their shelters and manned the parapets. Only in the most southern of the British sectors was some measure of victory achieved. The sectors around Montauban were held by the British XIII Corps and ran up against the start of the French portion of the front. The artillery plan for the XIII Corps sector called for a prioritisation of counter-battery fire to neutralise German artillery and the use of a creeping barrage. A creeping barrage is an artillery technique in which field guns firing shrapnel and HE shells over the heads of advancing friendly infantry create a wall of lead and fire that moves forward at set intervals. The infantry advance at a safe distance behind and as the barrage crosses the Gemran trenches, the defenders are forced to take cover. By the time the barrage has moved on and the defenders begin to emerge, the advancing infantry are already on them.

The use of these techniques in the XIII Corps sector were remarkably successful and allowed the Corps to achieve their objectives.

The lessons taken from the Somme was that the artillery needed to shift its focus from destruction to neutralisation. Trenches didn't need to be destroyed so long as the defenders were incapable of firing on the advancing infantry. This led to the widespread adoption of the creeping barrage and more priority placed on neutralising German artillery. By April the following year, these techniques had largely become standard and were remarkably successful during battles such as Vimy Ridge. The Germans, in response to Allied artillery advances, shifted their defence doctrine from the hold at all costs strategy that saw them take staggering losses to artillery to a defence in depth that placed most of their manpower out of range of enemy artillery and utilised local counterattacks and their own artillery to recapture capture ground. By the mid-1917, the shift in German doctrine largely nullified the Allied artillery advantage and prevented the opportunity for large scale breakthroughs like what had been attempted at the Somme. Instead, smaller operations, bite and hold were utilised to inch the front line forward bit by bit, allowing friendly artillery to remain in contact with advancing infantry to provide support.

By 1918, the arrival in larger numbers of tanks allowed the Allies to attempt bigger breakthroughs again as the tanks provided mobile firepower. The first major use was at Cambrai in late 1917 which was initially massively successful but was not reinforced and so any gains were largely lost to German counterattacks. In August the following year, a combined arms battle was planned at Amiens utilising infantry in concert with tanks, artillery and aircraft. This was also massively successful and came to be called the 'Black Day of the German Army' by German commander Erich von Ludendorff. This form of warfare was utilised for much of the remainder of the war, eventually forcing the Germans to the negotiating table.

As I hope I've shown, it was not necessary to destroy the trenches once the right techniques were employed, trecnhes could be successfully captured without the widespread destruction caused by artillery by suppressing the defenders until the attacking infantry were able to close and assault. Once tanks became more common place, the mobile firepower offered a mean to overcome deeper trench lines with infantry following up.

Sources:

Battle Tactics of the Western Front: The British Army's Art of Attack, 1916-1918 by Paddy Griffith

The Somme by Peter Hart

Fire-Power: The British Army Weapons & Theories of War 1904-1945 by Shelford Bidwell and Dominick Graham

Command on the Western Front: The Military Career of Sir Henry Rawlinson 1914-18 by Robin Prior and Trevor Wilson

The Killing Ground: The British Army, the Western Front & the Emergence of Modern War 1900-1918 by Tim Travers

The Somme by Robin Prior and Trevor Wilson