How does Hardy's Tess of the d'Urbervilles explore the use of pathetic fallacy?
It may not be correct to say that Hardy "explores" pathetic fallacy in Tess of the d'Urbervilles because "explore" implies a novice experimenting with or developing usage or usage skill. Since pathetic fallacy--coined by John Ruskin--is a specialized branch of ancient personification, it is doubtful that Hardy, a seasoned and excellent writer, "explores" pathetic fallacy in this way.
Having said this, we can discuss some ways Hardy utilizes the literary technique of pathetic fallacy. To define it, pathetic fallacy is a form of personification that attributes human characteristics to inanimate objects, nature, and to animals. It differs from personification in that personification can be applied to abstract ideas as well, such as Love, Truth, and Duty, whereas pathetic fallacy, by Ruskin's definition, is restricted to inanimate objects, nature, and animals.
Hardy introduces pathetic fallacy (also simply called "fallacy") in the early parts of Chapter I. If legs may be said to be "inanimate objects," animated only by the higher consciousness possessing them, then the first instance of pathetic fallacy occurs in Hardy's description of Tess's father, John (Jack) Derbeyfield, whose legs have a contrary nature to what they ought to have:
The pair of legs that carried him were rickety, and there was a bias in his gait which inclined him somewhat to the left of a straight line.
The fallacy is shown in the phrases "that carried him" and "there was a bias." Often, a fallacy will rest in just one word, like "carried" and "bias." Both of these imply human characteristics as "carry" may be an action and "bias" may be a "preference or an inclination" (American Heritage Dictionary). These may decidedly be seen as human characteristics. Perhaps if Hardy may be seen as "exploring" pathetic fallacy, it may be in its application to individualized and localized body parts, like legs.
Another early example of fallacy that introduces Hardy's usage throughout the novel is in the narrator's description of Blackmoor Valley where the air is "languorous" and the large hills and dales mantle the smaller ones;
The atmosphere beneath is languorous, and is so tinged with azure ... mantling minor hills and dales within the major. Such is the Vale of Blackmoor.
To be "languorous" is to have no mental energy or to have a dreamy, lazy mood (American Heritage). To mantle is to cover up, to shield as with a "mantle" or cape. These too are decidedly human characteristics especially since only humans are said to have mental energy and to act to protect or cover another. This example is very standard pathetic fallacy and not what might be called exploring the form.