The basic concept of texture is that you will transform your image, which has a certain texture, to a different space, where the texture will be recognised (i.e. the classification, which can be SVM, or any other, even thresholding if there is clear separation of the textures) depending on what texture method (GLCM, spatial filtering, Fourier filtering) you apply.
GLCM is just one of many methods, simple and effective, but not the most powerful. Have a look at this document for a guide to co-occurrence:
You could also explore filtering in the Fourier domain, and the matlab code is available here:
This recent paper compares different texture segmentations with different algorithms:
Hope this gives you some ideas of how to proceed. Let me know if you need more information, or if solved, please accept the answer.